diff --git a/docs/en/_toc.yml b/docs/en/_toc.yml
index 516d0ccd..936b112a 100644
--- a/docs/en/_toc.yml
+++ b/docs/en/_toc.yml
@@ -35,6 +35,7 @@ parts:
         title: Typical Problems
   - caption: Release Note
     chapters:
+      - file: releases/jijmodeling-2.5.0
       - file: releases/jijmodeling-2.4.1
       - file: releases/jijmodeling-2.4.0
       - file: releases/jijmodeling-2.3.2
diff --git a/docs/en/advanced/generation.ipynb b/docs/en/advanced/generation.ipynb
index b5a13869..4010a6fc 100644
--- a/docs/en/advanced/generation.ipynb
+++ b/docs/en/advanced/generation.ipynb
@@ -43,17 +43,17 @@
    "id": "34020325-4747-42ce-ab64-4114e871dca0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:29.173976Z",
-     "iopub.status.busy": "2026-03-24T02:05:29.173922Z",
-     "iopub.status.idle": "2026-03-24T02:05:29.226519Z",
-     "shell.execute_reply": "2026-03-24T02:05:29.226149Z"
+     "iopub.execute_input": "2026-06-04T02:50:29.958298Z",
+     "iopub.status.busy": "2026-06-04T02:50:29.957998Z",
+     "iopub.status.idle": "2026-06-04T02:50:30.029414Z",
+     "shell.execute_reply": "2026-06-04T02:50:30.029023Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'B': 3, 'A': 4}"
+       "{'A': 5, 'B': 3}"
       ]
      },
      "execution_count": 1,
@@ -93,17 +93,17 @@
    "id": "9ea06ded-9bc5-4eb9-85c7-837538a5940b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:29.227611Z",
-     "iopub.status.busy": "2026-03-24T02:05:29.227545Z",
-     "iopub.status.idle": "2026-03-24T02:05:29.229816Z",
-     "shell.execute_reply": "2026-03-24T02:05:29.229508Z"
+     "iopub.execute_input": "2026-06-04T02:50:30.030492Z",
+     "iopub.status.busy": "2026-06-04T02:50:30.030442Z",
+     "iopub.status.idle": "2026-06-04T02:50:30.032725Z",
+     "shell.execute_reply": "2026-06-04T02:50:30.032370Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'B': 5, 'A': 89}"
+       "{'B': 5, 'A': 66}"
       ]
      },
      "execution_count": 2,
@@ -129,17 +129,17 @@
    "id": "8fedb42a-12d2-41f6-b3de-c989ea1aa4ab",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:29.230837Z",
-     "iopub.status.busy": "2026-03-24T02:05:29.230782Z",
-     "iopub.status.idle": "2026-03-24T02:05:29.233098Z",
-     "shell.execute_reply": "2026-03-24T02:05:29.232823Z"
+     "iopub.execute_input": "2026-06-04T02:50:30.033607Z",
+     "iopub.status.busy": "2026-06-04T02:50:30.033556Z",
+     "iopub.status.idle": "2026-06-04T02:50:30.035445Z",
+     "shell.execute_reply": "2026-06-04T02:50:30.035127Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'B': 4, 'A': 68}"
+       "{'A': 78, 'B': 3}"
       ]
      },
      "execution_count": 3,
@@ -167,17 +167,17 @@
    "id": "19a45cfe-40de-4e5e-9cad-62114b225b09",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:29.234144Z",
-     "iopub.status.busy": "2026-03-24T02:05:29.234093Z",
-     "iopub.status.idle": "2026-03-24T02:05:29.282052Z",
-     "shell.execute_reply": "2026-03-24T02:05:29.281678Z"
+     "iopub.execute_input": "2026-06-04T02:50:30.036186Z",
+     "iopub.status.busy": "2026-06-04T02:50:30.036144Z",
+     "iopub.status.idle": "2026-06-04T02:50:30.102466Z",
+     "shell.execute_reply": "2026-06-04T02:50:30.102067Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': array([3, 9, 9, 4, 6, 9, 9, 9, 6, 8], dtype=object)}"
+       "{'A': array([1, 7, 9, 9, 5, 9, 9, 7, 4, 6], dtype=object)}"
       ]
      },
      "execution_count": 4,
@@ -209,19 +209,18 @@
    "id": "ac97241e-47bd-4b5b-b8f6-49d5ddb43254",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:29.282996Z",
-     "iopub.status.busy": "2026-03-24T02:05:29.282922Z",
-     "iopub.status.idle": "2026-03-24T02:05:29.312705Z",
-     "shell.execute_reply": "2026-03-24T02:05:29.312400Z"
+     "iopub.execute_input": "2026-06-04T02:50:30.103512Z",
+     "iopub.status.busy": "2026-06-04T02:50:30.103449Z",
+     "iopub.status.idle": "2026-06-04T02:50:30.155520Z",
+     "shell.execute_reply": "2026-06-04T02:50:30.155220Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': array([-7.170054915922748, 4.5286379717568614, -0.7378605301076355,\n",
-       "        -9.881771095294587, -6.66134733378656, -9.639830308073524,\n",
-       "        7.636033231278233, -7.2784681900176595, 2.46134220723353],\n",
+       "{'A': array([-5.815946180687299, 9.389031074526667, -2.4827675577336272,\n",
+       "        -7.263302071169142, -5.2497517062747745, 1.9978528278141283],\n",
        "       dtype=object)}"
       ]
      },
@@ -314,7 +313,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/advanced/named_expr.ipynb b/docs/en/advanced/named_expr.ipynb
index ab1edde4..d1a85062 100644
--- a/docs/en/advanced/named_expr.ipynb
+++ b/docs/en/advanced/named_expr.ipynb
@@ -44,10 +44,10 @@
    "id": "2ac9c9d4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:30.709402Z",
-     "iopub.status.busy": "2026-03-24T02:05:30.709347Z",
-     "iopub.status.idle": "2026-03-24T02:05:30.900832Z",
-     "shell.execute_reply": "2026-03-24T02:05:30.900063Z"
+     "iopub.execute_input": "2026-06-04T02:50:31.212571Z",
+     "iopub.status.busy": "2026-06-04T02:50:31.212430Z",
+     "iopub.status.idle": "2026-06-04T02:50:31.451485Z",
+     "shell.execute_reply": "2026-06-04T02:50:31.451115Z"
     }
    },
    "outputs": [
@@ -61,7 +61,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack (Unnamed)\", sense=MAXIMIZE, objective=sum(w.len_at(0).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(w.len_at(0).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack (Unnamed)\", sense=MAXIMIZE, objective=sum(set(w.len_at(0)).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(set(w.len_at(0)).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 1,
@@ -106,10 +106,10 @@
    "id": "eef87a2e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:30.902082Z",
-     "iopub.status.busy": "2026-03-24T02:05:30.901973Z",
-     "iopub.status.idle": "2026-03-24T02:05:31.067538Z",
-     "shell.execute_reply": "2026-03-24T02:05:31.067176Z"
+     "iopub.execute_input": "2026-06-04T02:50:31.452647Z",
+     "iopub.status.busy": "2026-06-04T02:50:31.452582Z",
+     "iopub.status.idle": "2026-06-04T02:50:31.671476Z",
+     "shell.execute_reply": "2026-06-04T02:50:31.671182Z"
     }
    },
    "outputs": [
@@ -123,7 +123,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 2,
@@ -172,10 +172,10 @@
    "id": "a1980058",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:31.068706Z",
-     "iopub.status.busy": "2026-03-24T02:05:31.068645Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.352063Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.351689Z"
+     "iopub.execute_input": "2026-06-04T02:50:31.672753Z",
+     "iopub.status.busy": "2026-06-04T02:50:31.672694Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.106917Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.106485Z"
     }
    },
    "outputs": [],
@@ -227,10 +227,10 @@
    "id": "de325406",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.353639Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.353384Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.400433Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.400104Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.108307Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.108205Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.163790Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.163453Z"
     }
    },
    "outputs": [
@@ -238,7 +238,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Scalar}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[5;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}scalar&=\\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}&\\quad &\\in \\left\\{0, 1\\right\\}\\\\&&&\\text{\\texttt{save\\_{}in\\_{}ommx=True}}\\\\\\end{alignedat}\\end{array}\n",
+       "\\text{Problem}\\colon &\\text{Scalar}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[5;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}scalar&=\\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}&\\quad &\\in \\mathbb{N}\\\\&&&\\text{\\texttt{save\\_{}in\\_{}ommx=True}}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
@@ -265,10 +265,10 @@
    "id": "b86892f7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.401429Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.401375Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.536699Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.536396Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.164889Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.164839Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.316842Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.316496Z"
     }
    },
    "outputs": [
@@ -304,10 +304,10 @@
    "id": "f2859f29",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.537878Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.537817Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.623433Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.623068Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.317865Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.317811Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.417636Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.417256Z"
     }
    },
    "outputs": [
@@ -354,10 +354,10 @@
    "id": "6051c494",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.624428Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.624367Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.629533Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.629140Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.418594Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.418540Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.425628Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.425397Z"
     }
    },
    "outputs": [],
@@ -371,10 +371,10 @@
    "id": "276ffb44",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.630573Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.630508Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.649968Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.649557Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.426680Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.426632Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.460138Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.459869Z"
     }
    },
    "outputs": [
@@ -401,10 +401,10 @@
    "id": "69a09dfa",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.650995Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.650942Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.658867Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.658578Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.461213Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.461158Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.473307Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.473008Z"
     }
    },
    "outputs": [
@@ -431,10 +431,10 @@
    "id": "c3d56b52",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.659946Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.659887Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.675976Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.675660Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.474413Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.474358Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.501844Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.501553Z"
     }
    },
    "outputs": [
@@ -479,10 +479,10 @@
    "id": "d5d13841",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.677059Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.677004Z",
-     "iopub.status.idle": "2026-03-24T02:05:32.871249Z",
-     "shell.execute_reply": "2026-03-24T02:05:32.870949Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.502958Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.502909Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.772263Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.771953Z"
     }
    },
    "outputs": [
@@ -496,7 +496,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=total_weight, right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=total_weight, right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 11,
@@ -541,10 +541,10 @@
    "id": "dba7ad0a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:32.872464Z",
-     "iopub.status.busy": "2026-03-24T02:05:32.872404Z",
-     "iopub.status.idle": "2026-03-24T02:05:33.214174Z",
-     "shell.execute_reply": "2026-03-24T02:05:33.213701Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.773389Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.773330Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.861765Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.861356Z"
     }
    },
    "outputs": [],
@@ -566,10 +566,10 @@
    "id": "2e3710ba",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:33.215352Z",
-     "iopub.status.busy": "2026-03-24T02:05:33.215291Z",
-     "iopub.status.idle": "2026-03-24T02:05:33.225769Z",
-     "shell.execute_reply": "2026-03-24T02:05:33.225449Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.862919Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.862860Z",
+     "iopub.status.idle": "2026-06-04T02:50:32.870131Z",
+     "shell.execute_reply": "2026-06-04T02:50:32.869691Z"
     }
    },
    "outputs": [
@@ -675,10 +675,10 @@
    "id": "37c9e656",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:33.226786Z",
-     "iopub.status.busy": "2026-03-24T02:05:33.226736Z",
-     "iopub.status.idle": "2026-03-24T02:05:33.491441Z",
-     "shell.execute_reply": "2026-03-24T02:05:33.491017Z"
+     "iopub.execute_input": "2026-06-04T02:50:32.871349Z",
+     "iopub.status.busy": "2026-06-04T02:50:32.871294Z",
+     "iopub.status.idle": "2026-06-04T02:50:33.156660Z",
+     "shell.execute_reply": "2026-06-04T02:50:33.156339Z"
     }
    },
    "outputs": [
@@ -723,7 +723,7 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>46.0</td>\n",
+       "      <td>45.0</td>\n",
        "      <td>{0, 1, 2, 3, 4, 5}</td>\n",
        "      <td>total_weight</td>\n",
        "      <td>[]</td>\n",
@@ -737,7 +737,7 @@
       "text/plain": [
        "    value            used_ids          name subscripts  \\\n",
        "id                                                       \n",
-       "0    46.0  {0, 1, 2, 3, 4, 5}  total_weight         []   \n",
+       "0    45.0  {0, 1, 2, 3, 4, 5}  total_weight         []   \n",
        "\n",
        "                              description parameters.subscripts  \n",
        "id                                                               \n",
@@ -791,7 +791,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/advanced/serialize.ipynb b/docs/en/advanced/serialize.ipynb
index 30d626b0..4a5cd463 100644
--- a/docs/en/advanced/serialize.ipynb
+++ b/docs/en/advanced/serialize.ipynb
@@ -16,10 +16,10 @@
    "id": "545186b3-caf3-4c92-a0a9-c7515923bffd",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:34.913506Z",
-     "iopub.status.busy": "2026-03-24T02:05:34.913412Z",
-     "iopub.status.idle": "2026-03-24T02:05:34.958083Z",
-     "shell.execute_reply": "2026-03-24T02:05:34.957577Z"
+     "iopub.execute_input": "2026-06-04T02:50:34.335806Z",
+     "iopub.status.busy": "2026-06-04T02:50:34.335677Z",
+     "iopub.status.idle": "2026-06-04T02:50:34.397052Z",
+     "shell.execute_reply": "2026-06-04T02:50:34.396623Z"
     }
    },
    "outputs": [],
@@ -48,10 +48,10 @@
    "id": "271e3da1-63a5-448e-ab1a-ccff3476b945",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:34.959384Z",
-     "iopub.status.busy": "2026-03-24T02:05:34.959313Z",
-     "iopub.status.idle": "2026-03-24T02:05:34.964237Z",
-     "shell.execute_reply": "2026-03-24T02:05:34.963959Z"
+     "iopub.execute_input": "2026-06-04T02:50:34.398262Z",
+     "iopub.status.busy": "2026-06-04T02:50:34.398199Z",
+     "iopub.status.idle": "2026-06-04T02:50:34.399892Z",
+     "shell.execute_reply": "2026-06-04T02:50:34.399572Z"
     }
    },
    "outputs": [],
@@ -79,7 +79,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/basics/expressions.ipynb b/docs/en/basics/expressions.ipynb
index 9aa0da52..065fa335 100644
--- a/docs/en/basics/expressions.ipynb
+++ b/docs/en/basics/expressions.ipynb
@@ -25,10 +25,10 @@
    "id": "e511a2c6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:51.250049Z",
-     "iopub.status.busy": "2026-04-16T07:03:51.249843Z",
-     "iopub.status.idle": "2026-04-16T07:03:51.285753Z",
-     "shell.execute_reply": "2026-04-16T07:03:51.284748Z"
+     "iopub.execute_input": "2026-06-04T02:50:22.904659Z",
+     "iopub.status.busy": "2026-06-04T02:50:22.904395Z",
+     "iopub.status.idle": "2026-06-04T02:50:22.920392Z",
+     "shell.execute_reply": "2026-06-04T02:50:22.919816Z"
     }
    },
    "outputs": [],
@@ -58,10 +58,10 @@
    "id": "fdd9d4ad",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:51.288701Z",
-     "iopub.status.busy": "2026-04-16T07:03:51.288546Z",
-     "iopub.status.idle": "2026-04-16T07:03:51.623277Z",
-     "shell.execute_reply": "2026-04-16T07:03:51.622658Z"
+     "iopub.execute_input": "2026-06-04T02:50:22.921690Z",
+     "iopub.status.busy": "2026-06-04T02:50:22.921630Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.127114Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.117768Z"
     },
     "label": "test-problem"
    },
@@ -182,10 +182,10 @@
    "id": "e38e46d8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:51.625014Z",
-     "iopub.status.busy": "2026-04-16T07:03:51.624895Z",
-     "iopub.status.idle": "2026-04-16T07:03:51.673186Z",
-     "shell.execute_reply": "2026-04-16T07:03:51.672645Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.144619Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.144482Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.189023Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.188679Z"
     }
    },
    "outputs": [
@@ -225,10 +225,10 @@
    "id": "e7874eab",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:51.674685Z",
-     "iopub.status.busy": "2026-04-16T07:03:51.674553Z",
-     "iopub.status.idle": "2026-04-16T07:03:51.752515Z",
-     "shell.execute_reply": "2026-04-16T07:03:51.751337Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.190112Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.190056Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.203916Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.203603Z"
     }
    },
    "outputs": [
@@ -238,13 +238,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `x + Located { inner: \"hoge\", src_span: NoSrcSpan }',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/594888127.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/594888127.py\", line 3, col 19-29\n",
       "    while inferring the type of expression `x + Located { inner: \"hoge\", src_span: NoSrcSpan }',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/594888127.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/594888127.py\", line 3, col 19-29\n",
       "    while checking if types `binary!' and `Literal[\"hoge\"]' can be combined with numeric operator `Add',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/594888127.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/594888127.py\", line 3, col 19-29\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/594888127.py\", line 3, col 19-29:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/594888127.py\", line 3, col 19-29:\n",
       "\n",
       "    3  |      problem.infer(x + \"hoge\")\n",
       "                            ^^^^^^^^^^\n",
@@ -319,10 +319,10 @@
    "id": "dc85ae1d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:51.754458Z",
-     "iopub.status.busy": "2026-04-16T07:03:51.754333Z",
-     "iopub.status.idle": "2026-04-16T07:03:53.730095Z",
-     "shell.execute_reply": "2026-04-16T07:03:53.729682Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.205001Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.204949Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.497727Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.497384Z"
     }
    },
    "outputs": [
@@ -384,10 +384,10 @@
    "id": "4cdd5152",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:53.731292Z",
-     "iopub.status.busy": "2026-04-16T07:03:53.731198Z",
-     "iopub.status.idle": "2026-04-16T07:03:53.749974Z",
-     "shell.execute_reply": "2026-04-16T07:03:53.749636Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.499191Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.499100Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.515515Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.515202Z"
     }
    },
    "outputs": [
@@ -415,10 +415,10 @@
    "id": "28d877b6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:53.751054Z",
-     "iopub.status.busy": "2026-04-16T07:03:53.750995Z",
-     "iopub.status.idle": "2026-04-16T07:03:53.881347Z",
-     "shell.execute_reply": "2026-04-16T07:03:53.880994Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.516867Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.516806Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.552444Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.552110Z"
     }
    },
    "outputs": [
@@ -446,10 +446,10 @@
    "id": "f96d34c7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:53.882501Z",
-     "iopub.status.busy": "2026-04-16T07:03:53.882436Z",
-     "iopub.status.idle": "2026-04-16T07:03:53.936561Z",
-     "shell.execute_reply": "2026-04-16T07:03:53.936045Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.553594Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.553529Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.578468Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.576969Z"
     }
    },
    "outputs": [
@@ -477,10 +477,10 @@
    "id": "5adad4bc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:53.937974Z",
-     "iopub.status.busy": "2026-04-16T07:03:53.937884Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.072652Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.072134Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.581255Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.581165Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.611463Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.611142Z"
     }
    },
    "outputs": [
@@ -508,10 +508,10 @@
    "id": "6ab268e5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.073869Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.073777Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.155655Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.155126Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.612965Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.612869Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.638648Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.638243Z"
     }
    },
    "outputs": [
@@ -547,10 +547,10 @@
    "id": "75aa08e2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.157695Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.157496Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.180138Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.179701Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.639831Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.639774Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.655826Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.655457Z"
     }
    },
    "outputs": [
@@ -560,13 +560,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `S * y',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/2932800859.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/2932800859.py\", line 3, col 19-24\n",
       "    while inferring the type of expression `S * y',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/2932800859.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/2932800859.py\", line 3, col 19-24\n",
       "    while checking if types `TotalDict[N; float]' and `Array[N, M; int!]' can be combined with numeric operator `Mul',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/2932800859.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/2932800859.py\", line 3, col 19-24\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/2932800859.py\", line 3, col 19-24:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/2932800859.py\", line 3, col 19-24:\n",
       "\n",
       "    3  |      problem.infer(S * y)\n",
       "                            ^^^^^\n",
@@ -589,10 +589,10 @@
    "id": "17c3299c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.181246Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.181178Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.201250Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.200873Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.656985Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.656925Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.673397Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.672977Z"
     }
    },
    "outputs": [
@@ -602,13 +602,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `y + z',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/3762455632.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/3762455632.py\", line 3, col 19-24\n",
       "    while inferring the type of expression `y + z',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/3762455632.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/3762455632.py\", line 3, col 19-24\n",
       "    while checking if types `Array[N, M; int!]' and `Array[N, M, N; float!]' can be combined with numeric operator `Add',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/3762455632.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/3762455632.py\", line 3, col 19-24\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_62910/3762455632.py\", line 3, col 19-24:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4482/3762455632.py\", line 3, col 19-24:\n",
       "\n",
       "    3  |      problem.infer(y + z)\n",
       "                            ^^^^^\n",
@@ -642,10 +642,10 @@
    "id": "8654fb78",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.203129Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.202957Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.564392Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.563929Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.674937Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.674864Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.750103Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.749726Z"
     }
    },
    "outputs": [
@@ -695,10 +695,10 @@
    "id": "58b52480",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.565751Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.565661Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.844680Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.844197Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.751107Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.751052Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.827769Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.827403Z"
     }
    },
    "outputs": [
@@ -750,10 +750,10 @@
    "id": "ba29b19b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:54.845879Z",
-     "iopub.status.busy": "2026-04-16T07:03:54.845808Z",
-     "iopub.status.idle": "2026-04-16T07:03:54.860047Z",
-     "shell.execute_reply": "2026-04-16T07:03:54.859485Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.828830Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.828780Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.837565Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.837282Z"
     }
    },
    "outputs": [
@@ -819,14 +819,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "id": "6c81d662",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:55.024305Z",
-     "iopub.status.busy": "2026-04-16T07:03:55.024197Z",
-     "iopub.status.idle": "2026-04-16T07:03:55.241419Z",
-     "shell.execute_reply": "2026-04-16T07:03:55.240558Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.838440Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.838393Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.865758Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.865421Z"
     }
    },
    "outputs": [
@@ -839,7 +839,7 @@
        "Comparison[binary!, Array[N, M; int!]]"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -850,14 +850,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "id": "b43188e5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:55.243486Z",
-     "iopub.status.busy": "2026-04-16T07:03:55.243268Z",
-     "iopub.status.idle": "2026-04-16T07:03:55.270778Z",
-     "shell.execute_reply": "2026-04-16T07:03:55.269975Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.866686Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.866636Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.880945Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.880668Z"
     }
    },
    "outputs": [
@@ -870,7 +870,7 @@
        "bool"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -881,14 +881,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "id": "49d90ad4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:55.272857Z",
-     "iopub.status.busy": "2026-04-16T07:03:55.272767Z",
-     "iopub.status.idle": "2026-04-16T07:03:55.708341Z",
-     "shell.execute_reply": "2026-04-16T07:03:55.707270Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.881894Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.881848Z",
+     "iopub.status.idle": "2026-06-04T02:50:23.923914Z",
+     "shell.execute_reply": "2026-06-04T02:50:23.923540Z"
     }
    },
    "outputs": [
@@ -901,7 +901,7 @@
        "Comparison[Array[N, M; float!], Array[N, M; float!]]"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -948,14 +948,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "id": "c4eff827",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:55.712425Z",
-     "iopub.status.busy": "2026-04-16T07:03:55.712281Z",
-     "iopub.status.idle": "2026-04-16T07:03:56.171638Z",
-     "shell.execute_reply": "2026-04-16T07:03:56.171245Z"
+     "iopub.execute_input": "2026-06-04T02:50:23.924937Z",
+     "iopub.status.busy": "2026-06-04T02:50:23.924884Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.082990Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.082574Z"
     }
    },
    "outputs": [
@@ -963,7 +963,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Index and Keys Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathop{\\mathtt{keys}}\\left(S\\right);\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\mathop{\\mathtt{keys}}\\left(S\\right)\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\S&\\in \\mathop{\\mathrm{PartialDict}}\\left[N\\times L;\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }N\\times L\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Index and Keys Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathop{\\mathtt{keys}}\\left(S\\right);\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\mathop{\\mathtt{keys}}\\left(S\\right)\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\S&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in L\\right\\};\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in L\\right\\}\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "L&\\text{Category Label}\\end{array}\n",
        "\\end{array}\n",
        "$$"
@@ -972,7 +972,7 @@
        "Problem(name=\"Index and Keys Example\", sense=MINIMIZE, objective=0, constraints=[])"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1047,14 +1047,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "id": "1b8b9adc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:56.172815Z",
-     "iopub.status.busy": "2026-04-16T07:03:56.172757Z",
-     "iopub.status.idle": "2026-04-16T07:03:56.567134Z",
-     "shell.execute_reply": "2026-04-16T07:03:56.566711Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.084007Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.083951Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.193734Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.193454Z"
     }
    },
    "outputs": [
@@ -1069,7 +1069,7 @@
        "Problem(name=\"Sum Example\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1101,14 +1101,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "id": "49336545",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:56.568437Z",
-     "iopub.status.busy": "2026-04-16T07:03:56.568380Z",
-     "iopub.status.idle": "2026-04-16T07:03:56.698518Z",
-     "shell.execute_reply": "2026-04-16T07:03:56.698103Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.194923Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.194868Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.226006Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.225748Z"
     }
    },
    "outputs": [
@@ -1144,14 +1144,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
    "id": "e35b793f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:56.699627Z",
-     "iopub.status.busy": "2026-04-16T07:03:56.699556Z",
-     "iopub.status.idle": "2026-04-16T07:03:57.210870Z",
-     "shell.execute_reply": "2026-04-16T07:03:57.210208Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.226974Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.226917Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.324702Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.324303Z"
     }
    },
    "outputs": [
@@ -1166,7 +1166,7 @@
        "Problem(name=\"Sum Example (Plain)\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1191,14 +1191,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 23,
    "id": "a48f127c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:57.212717Z",
-     "iopub.status.busy": "2026-04-16T07:03:57.212570Z",
-     "iopub.status.idle": "2026-04-16T07:03:57.769718Z",
-     "shell.execute_reply": "2026-04-16T07:03:57.768569Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.325753Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.325699Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.425816Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.425509Z"
     }
    },
    "outputs": [
@@ -1210,10 +1210,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Sum Example (Plain, Alt)\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"Sum Example (Plain, Alt)\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1249,14 +1249,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 24,
    "id": "788d6c0f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:57.775980Z",
-     "iopub.status.busy": "2026-04-16T07:03:57.775613Z",
-     "iopub.status.idle": "2026-04-16T07:03:58.473966Z",
-     "shell.execute_reply": "2026-04-16T07:03:58.472860Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.427027Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.426970Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.577056Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.576738Z"
     }
    },
    "outputs": [
@@ -1271,7 +1271,7 @@
        "Problem(name=\"Even Sum Example\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0)).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1298,14 +1298,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 25,
    "id": "718ac630",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:58.475915Z",
-     "iopub.status.busy": "2026-04-16T07:03:58.475714Z",
-     "iopub.status.idle": "2026-04-16T07:03:58.995704Z",
-     "shell.execute_reply": "2026-04-16T07:03:58.994840Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.578230Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.578175Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.716151Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.715740Z"
     }
    },
    "outputs": [
@@ -1317,10 +1317,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Even Sum Example (Plain)\", sense=MINIMIZE, objective=sum(N.filter(lambda i: i % 2 == 0).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"Even Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0)).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1350,14 +1350,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 26,
    "id": "c5cf959f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:58.996950Z",
-     "iopub.status.busy": "2026-04-16T07:03:58.996858Z",
-     "iopub.status.idle": "2026-04-16T07:03:59.925280Z",
-     "shell.execute_reply": "2026-04-16T07:03:59.924874Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.717102Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.717049Z",
+     "iopub.status.idle": "2026-06-04T02:50:24.875894Z",
+     "shell.execute_reply": "2026-06-04T02:50:24.875552Z"
     }
    },
    "outputs": [
@@ -1372,7 +1372,7 @@
        "Problem(name=\"Double Sum Example\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): M.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1400,14 +1400,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "id": "54bec6e0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:03:59.926786Z",
-     "iopub.status.busy": "2026-04-16T07:03:59.926705Z",
-     "iopub.status.idle": "2026-04-16T07:04:01.216521Z",
-     "shell.execute_reply": "2026-04-16T07:04:01.215347Z"
+     "iopub.execute_input": "2026-06-04T02:50:24.877112Z",
+     "iopub.status.busy": "2026-06-04T02:50:24.877054Z",
+     "iopub.status.idle": "2026-06-04T02:50:25.014738Z",
+     "shell.execute_reply": "2026-06-04T02:50:25.014390Z"
     }
    },
    "outputs": [
@@ -1422,7 +1422,7 @@
        "Problem(name=\"Double Sum Example (Alt)\", sense=MINIMIZE, objective=sum(set(set((N, M))).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1450,14 +1450,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
    "id": "7bd1e8b4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:01.220142Z",
-     "iopub.status.busy": "2026-04-16T07:04:01.219966Z",
-     "iopub.status.idle": "2026-04-16T07:04:01.710462Z",
-     "shell.execute_reply": "2026-04-16T07:04:01.710067Z"
+     "iopub.execute_input": "2026-06-04T02:50:25.015874Z",
+     "iopub.status.busy": "2026-06-04T02:50:25.015824Z",
+     "iopub.status.idle": "2026-06-04T02:50:25.152224Z",
+     "shell.execute_reply": "2026-06-04T02:50:25.151823Z"
     }
    },
    "outputs": [
@@ -1472,7 +1472,7 @@
        "Problem(name=\"Double Sum Example (Alt)\", sense=MINIMIZE, objective=sum(set((N, M)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1502,14 +1502,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 29,
    "id": "b37473be",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:01.711565Z",
-     "iopub.status.busy": "2026-04-16T07:04:01.711505Z",
-     "iopub.status.idle": "2026-04-16T07:04:02.364653Z",
-     "shell.execute_reply": "2026-04-16T07:04:02.364212Z"
+     "iopub.execute_input": "2026-06-04T02:50:25.153210Z",
+     "iopub.status.busy": "2026-06-04T02:50:25.153159Z",
+     "iopub.status.idle": "2026-06-04T02:50:25.360696Z",
+     "shell.execute_reply": "2026-06-04T02:50:25.360287Z"
     }
    },
    "outputs": [
@@ -1524,7 +1524,7 @@
        "Problem(name=\"Filtered Double Sum Example\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): M.map(lambda (j: natural): (i, j))).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1557,14 +1557,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 30,
    "id": "cc27b233",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:02.365890Z",
-     "iopub.status.busy": "2026-04-16T07:04:02.365829Z",
-     "iopub.status.idle": "2026-04-16T07:04:02.966887Z",
-     "shell.execute_reply": "2026-04-16T07:04:02.966497Z"
+     "iopub.execute_input": "2026-06-04T02:50:25.361739Z",
+     "iopub.status.busy": "2026-06-04T02:50:25.361687Z",
+     "iopub.status.idle": "2026-06-04T02:50:25.523378Z",
+     "shell.execute_reply": "2026-06-04T02:50:25.523087Z"
     }
    },
    "outputs": [
@@ -1576,10 +1576,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Filtered Double Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set((N, M)).filter(lambda (i, j): (i + j) % 2 == 0).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
+       "Problem(name=\"Filtered Double Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set(set((N, M)).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1607,14 +1607,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 31,
    "id": "38abd485",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:02.968231Z",
-     "iopub.status.busy": "2026-04-16T07:04:02.968167Z",
-     "iopub.status.idle": "2026-04-16T07:04:03.250766Z",
-     "shell.execute_reply": "2026-04-16T07:04:03.250361Z"
+     "iopub.execute_input": "2026-06-04T02:50:25.524554Z",
+     "iopub.status.busy": "2026-06-04T02:50:25.524498Z",
+     "iopub.status.idle": "2026-06-04T02:50:25.632401Z",
+     "shell.execute_reply": "2026-06-04T02:50:25.632122Z"
     }
    },
    "outputs": [
@@ -1624,10 +1624,10 @@
        "$$\\sum _{i=0}^{N-1}{\\sum _{\\substack{j=0\\\\\\left(i+j\\right)\\bmod 2=0}}^{M-1}{{Q}_{i,j}}}$$"
       ],
       "text/plain": [
-       "Expression(sum(N.flat_map(lambda i: M.map(lambda j: (i, j))).filter(lambda (i, j): (i + j) % 2 == 0).map(lambda (i, j): Q[i, j])))"
+       "Expression(sum(set(N.flat_map(lambda i: M.map(lambda j: (i, j))).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda (i, j): Q[i, j])))"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/docs/en/basics/instance_generation.ipynb b/docs/en/basics/instance_generation.ipynb
index 1e3eb7fe..31b51bdd 100644
--- a/docs/en/basics/instance_generation.ipynb
+++ b/docs/en/basics/instance_generation.ipynb
@@ -30,10 +30,10 @@
    "id": "2c684576",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:14.106336Z",
-     "iopub.status.busy": "2026-03-24T02:05:14.106269Z",
-     "iopub.status.idle": "2026-03-24T02:05:14.479929Z",
-     "shell.execute_reply": "2026-03-24T02:05:14.479587Z"
+     "iopub.execute_input": "2026-06-04T02:50:15.758033Z",
+     "iopub.status.busy": "2026-06-04T02:50:15.757796Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.329492Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.329081Z"
     }
    },
    "outputs": [
@@ -43,11 +43,11 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{Knapsack with Synergy}\\\\\\displaystyle \\max &\\displaystyle \\sum _{i=0}^{N-1}{{v}_{i}\\cdot {x}_{i}}+\\sum _{\\left\\langle i,j\\right\\rangle \\in \\mathop{\\mathtt{keys}}\\left(s\\right)}{{s}_{i,j}\\cdot {x}_{i}\\cdot {x}_{j}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{weight}&\\quad \\displaystyle \\sum _{i=0}^{N-1}{{w}_{i}\\cdot {x}_{i}}\\leq W\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\&&&\\text{Item selection variables}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[N\\times N;\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }N\\times N\\text{, values in }\\mathbb{R}\\\\&&&\\text{Synergy bonus between items}\\\\&&&\\\\v&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Values of the items}\\\\&&&\\\\W&\\in \\mathbb{R}&\\quad &\\text{A scalar placeholder in }\\mathbb{R}\\\\&&&\\text{Weight limit of the problem}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Weights of the items}\\\\\\end{alignedat}\\end{array}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\&&&\\text{Item selection variables}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\};\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\}\\text{, values in }\\mathbb{R}\\\\&&&\\text{Synergy bonus between items}\\\\&&&\\\\v&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Values of the items}\\\\&&&\\\\W&\\in \\mathbb{R}&\\quad &\\text{A scalar placeholder in }\\mathbb{R}\\\\&&&\\text{Weight limit of the problem}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Weights of the items}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack with Synergy\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])) + sum(s.keys().map(lambda ((i, j): ElementOf[set((N, N))]): s[i, j] * x[i] * x[j])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack with Synergy\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])) + sum(set(s.keys()).map(lambda ((i, j): ElementOf[set((N, N))]): s[i, j] * x[i] * x[j])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 1,
@@ -109,10 +109,10 @@
    "id": "0a5c6de3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:14.481204Z",
-     "iopub.status.busy": "2026-03-24T02:05:14.481103Z",
-     "iopub.status.idle": "2026-03-24T02:05:14.483607Z",
-     "shell.execute_reply": "2026-03-24T02:05:14.483299Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.330577Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.330493Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.332797Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.332455Z"
     }
    },
    "outputs": [],
@@ -163,10 +163,10 @@
    "id": "ee4308f1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:14.484698Z",
-     "iopub.status.busy": "2026-03-24T02:05:14.484640Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.313963Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.313614Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.333761Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.333714Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.629273Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.628987Z"
     }
    },
    "outputs": [
@@ -248,10 +248,10 @@
    "id": "6b03e399",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:15.315112Z",
-     "iopub.status.busy": "2026-03-24T02:05:15.315011Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.320236Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.319907Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.630407Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.630319Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.635989Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.635692Z"
     }
    },
    "outputs": [
@@ -455,10 +455,10 @@
    "id": "59256385",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:15.321269Z",
-     "iopub.status.busy": "2026-03-24T02:05:15.321214Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.326594Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.326281Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.636952Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.636899Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.638724Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.638352Z"
     }
    },
    "outputs": [
@@ -492,10 +492,10 @@
    "id": "201474f3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:15.327716Z",
-     "iopub.status.busy": "2026-03-24T02:05:15.327656Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.712228Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.711893Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.639551Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.639502Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.753278Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.752891Z"
     }
    },
    "outputs": [],
@@ -555,10 +555,10 @@
    "id": "90434a42",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:15.713668Z",
-     "iopub.status.busy": "2026-03-24T02:05:15.713595Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.737562Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.737202Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.754467Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.754408Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.791947Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.791670Z"
     }
    },
    "outputs": [
@@ -630,10 +630,10 @@
    "id": "135be9f2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:15.738711Z",
-     "iopub.status.busy": "2026-03-24T02:05:15.738644Z",
-     "iopub.status.idle": "2026-03-24T02:05:15.791763Z",
-     "shell.execute_reply": "2026-03-24T02:05:15.791431Z"
+     "iopub.execute_input": "2026-06-04T02:50:16.793129Z",
+     "iopub.status.busy": "2026-06-04T02:50:16.793072Z",
+     "iopub.status.idle": "2026-06-04T02:50:16.812568Z",
+     "shell.execute_reply": "2026-06-04T02:50:16.812228Z"
     }
    },
    "outputs": [
@@ -818,7 +818,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/basics/modeling.ipynb b/docs/en/basics/modeling.ipynb
index d22916f9..b6d804ba 100644
--- a/docs/en/basics/modeling.ipynb
+++ b/docs/en/basics/modeling.ipynb
@@ -17,10 +17,10 @@
    "id": "b08e6532",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.322485Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.322275Z",
-     "iopub.status.idle": "2026-03-24T02:05:18.331695Z",
-     "shell.execute_reply": "2026-03-24T02:05:18.331323Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.041237Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.041010Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.059305Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.058864Z"
     }
    },
    "outputs": [],
@@ -55,10 +55,10 @@
    "id": "ae36f6cb",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.332840Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.332782Z",
-     "iopub.status.idle": "2026-03-24T02:05:18.383874Z",
-     "shell.execute_reply": "2026-03-24T02:05:18.383231Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.060431Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.060374Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.113880Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.113482Z"
     }
    },
    "outputs": [
@@ -100,10 +100,10 @@
    "id": "2f314ff6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.384853Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.384791Z",
-     "iopub.status.idle": "2026-03-24T02:05:18.406343Z",
-     "shell.execute_reply": "2026-03-24T02:05:18.406018Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.114956Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.114904Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.139144Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.138808Z"
     }
    },
    "outputs": [
@@ -135,8 +135,7 @@
    "id": "e4aecaa3",
    "metadata": {},
    "source": [
-    "You can see that the existing term was not replaced; instead, $y$ was added and the new objective is $x + y$.\n",
-    "If you might need to remove objective terms later, keep a list of terms in Python and set the objective from that list when needed.\n",
+    "You can see that the existing term is not replaced; instead, $y$ is added and the new objective is $x + y$.\n",
     "\n",
     ":::{admonition} Subtracting terms from the objective\n",
     ":class: tip\n",
@@ -144,19 +143,65 @@
     "Since JijModeling 2.3.1, you can also \"subtract\" scalar {py:class}`~jijmodeling.Expression` objects from the objective by using the {py:meth}`-= <jijmodeling.Problem.__isub__>` operator on a {py:class}`~jijmodeling.Problem`.\n",
     ":::\n",
     "\n",
-    "As a more practical example, let's set the objective for the knapsack problem."
+    ":::{admonition} Replacing the objective\n",
+    ":class: tip\n",
+    "Since JijModeling 2.5.0, you can assign an expression directly to `Problem.objective` to discard the previous objective and replace it with a new one.\n",
+    ":::"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
+   "id": "065c9053",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T02:50:19.140173Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.140120Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.159880Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.159476Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Sample}\\\\\\displaystyle \\min &\\displaystyle y\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\y&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"Sample\", sense=MINIMIZE, objective=y, constraints=[])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "problem.objective = y\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec35952c",
+   "metadata": {},
+   "source": [
+    "As a more practical example, let's set the objective for the knapsack problem."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
    "id": "71a3019e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.407562Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.407499Z",
-     "iopub.status.idle": "2026-03-24T02:05:18.505954Z",
-     "shell.execute_reply": "2026-03-24T02:05:18.505541Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.160847Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.160793Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.288070Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.287785Z"
     }
    },
    "outputs": [
@@ -168,10 +213,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints=[])"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -227,14 +272,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "id": "ec207a7d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.507453Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.507378Z",
-     "iopub.status.idle": "2026-03-24T02:05:18.646245Z",
-     "shell.execute_reply": "2026-03-24T02:05:18.645925Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.289257Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.289201Z",
+     "iopub.status.idle": "2026-06-04T02:50:19.433001Z",
+     "shell.execute_reply": "2026-06-04T02:50:19.432684Z"
     }
    },
    "outputs": [
@@ -248,10 +293,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -323,14 +368,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "id": "e9d70317",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:18.647477Z",
-     "iopub.status.busy": "2026-03-24T02:05:18.647411Z",
-     "iopub.status.idle": "2026-03-24T02:05:19.025472Z",
-     "shell.execute_reply": "2026-03-24T02:05:19.025070Z"
+     "iopub.execute_input": "2026-06-04T02:50:19.434342Z",
+     "iopub.status.busy": "2026-06-04T02:50:19.434283Z",
+     "iopub.status.idle": "2026-06-04T02:50:20.104180Z",
+     "shell.execute_reply": "2026-06-04T02:50:20.103796Z"
     }
    },
    "outputs": [
@@ -340,16 +385,16 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{\\#C-1}{\\sum _{i\\in C}{\\sum _{j\\in C}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod \\#C,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{one city}&\\quad \\displaystyle \\sum _{i\\in C}{{x}_{t,i}}=1\\quad \\forall t\\;\\text{s.t.}\\;t\\in \\left\\{0,\\ldots ,\\#C-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle \\sum _{t=0}^{\\#C-1}{{x}_{t,i}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in C\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\#C\\times C;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\#C\\times C\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "C&\\text{Labels of Cities}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(C.count().flat_map(lambda (t: natural): C.map(lambda (i: CategoryLabel(\"C\")): (t, i))).flat_map(lambda ((t, i): Tuple[natural, CategoryLabel(\"C\")]): C.map(lambda (j: CategoryLabel(\"C\")): (t, i, j))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(C.map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(C.count().map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(C.count().flat_map(lambda (t: natural): C.map(lambda (i: CategoryLabel(\"C\")): (t, i))).flat_map(lambda ((t, i): Tuple[natural, CategoryLabel(\"C\")]): C.map(lambda (j: CategoryLabel(\"C\")): (t, i, j)))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(set(C).map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(set(C.count()).map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -391,14 +436,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "id": "a4643a1c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:19.026595Z",
-     "iopub.status.busy": "2026-03-24T02:05:19.026530Z",
-     "iopub.status.idle": "2026-03-24T02:05:19.343648Z",
-     "shell.execute_reply": "2026-03-24T02:05:19.343340Z"
+     "iopub.execute_input": "2026-06-04T02:50:20.105295Z",
+     "iopub.status.busy": "2026-06-04T02:50:20.105237Z",
+     "iopub.status.idle": "2026-06-04T02:50:20.678690Z",
+     "shell.execute_reply": "2026-06-04T02:50:20.678279Z"
     }
    },
    "outputs": [
@@ -408,16 +453,16 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{\\#C-1}{\\sum _{i\\in C}{\\sum _{j\\in C}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod \\#C,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{one city}&\\quad \\displaystyle \\sum _{i\\in C}{{x}_{t,i}}=1\\quad \\forall t\\;\\text{s.t.}\\;t\\in \\left\\{0,\\ldots ,\\#C-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle \\sum _{t=0}^{\\#C-1}{{x}_{t,i}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in C\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\#C\\times C;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\#C\\times C\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "C&\\text{Labels of Cities}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set((C.count(), C, C)).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(C.map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(C.count().map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(set((C.count(), C, C))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(set(C).map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(set(C.count()).map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -467,14 +512,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "id": "8070e0c3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:19.344979Z",
-     "iopub.status.busy": "2026-03-24T02:05:19.344921Z",
-     "iopub.status.idle": "2026-03-24T02:05:19.584042Z",
-     "shell.execute_reply": "2026-03-24T02:05:19.583600Z"
+     "iopub.execute_input": "2026-06-04T02:50:20.679753Z",
+     "iopub.status.busy": "2026-06-04T02:50:20.679699Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.092080Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.091682Z"
     }
    },
    "outputs": [
@@ -483,15 +528,15 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{N-1}{\\sum _{i=0}^{N-1}{\\sum _{j=0}^{N-1}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod N,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{one city}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=1\\\\\\text{one time}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[0\\right]\\right)=1\\end{aligned}\n",
+       "\\text{one city}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[0\\right]\\right)}_{i}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times N;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{Array}}\\left[N\\times N;\\mathbb{R}\\right]&\\quad &2\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\&&&\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\&&&\\text{Number of cities}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (t: natural): N.map(lambda (i: natural): (t, i))).flat_map(lambda ((t, i): Tuple[natural, natural]): N.map(lambda (j: natural): (t, i, j))).map(lambda ((t, i, j): Tuple[natural, natural, natural]): d[i, j] * x[t, i] * x[(t + 1) % N, j])), constraints={one city: [Constraint(name=\"one city\", sense=EQUAL, left=x.sum(1), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],one time: [Constraint(name=\"one time\", sense=EQUAL, left=x.sum(0), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (t: natural): N.map(lambda (i: natural): (t, i))).flat_map(lambda ((t, i): Tuple[natural, natural]): N.map(lambda (j: natural): (t, i, j)))).map(lambda ((t, i, j): Tuple[natural, natural, natural]): d[i, j] * x[t, i] * x[(t + 1) % N, j])), constraints={one city: [Constraint(name=\"one city\", sense=EQUAL, left=x.sum(1), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],one time: [Constraint(name=\"one time\", sense=EQUAL, left=x.sum(0), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/4051608972.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -530,27 +575,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "id": "bd709223",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:19.585023Z",
-     "iopub.status.busy": "2026-03-24T02:05:19.584971Z",
-     "iopub.status.idle": "2026-03-24T02:05:19.599318Z",
-     "shell.execute_reply": "2026-03-24T02:05:19.598886Z"
+     "iopub.execute_input": "2026-06-04T02:50:21.093183Z",
+     "iopub.status.busy": "2026-06-04T02:50:21.093121Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.115502Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.115165Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/latex": [
-       "$$\\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]$$"
+       "$$\\mathop{\\mathrm{Array}}\\left[N;\\mathbb{N}\\right]$$"
       ],
       "text/plain": [
-       "Array[N; binary!]"
+       "Array[N; natural!]"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -582,14 +627,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "id": "e62303cb",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:19.600528Z",
-     "iopub.status.busy": "2026-03-24T02:05:19.600471Z",
-     "iopub.status.idle": "2026-03-24T02:05:19.833831Z",
-     "shell.execute_reply": "2026-03-24T02:05:19.833421Z"
+     "iopub.execute_input": "2026-06-04T02:50:21.116656Z",
+     "iopub.status.busy": "2026-06-04T02:50:21.116596Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.393329Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.392926Z"
     }
    },
    "outputs": [
@@ -606,7 +651,7 @@
        "Problem(name=\"Possibly Overlapping Constraints\", sense=MINIMIZE, objective=0, constraints={constr: [Constraint(name=\"constr\", , lambda i: x[i] >= 1, domain=set(N)),Constraint(name=\"constr\", , lambda i: x[i] <= 2, domain=set(M)),],})"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -635,14 +680,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "id": "b442d9b0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:19.834787Z",
-     "iopub.status.busy": "2026-03-24T02:05:19.834731Z",
-     "iopub.status.idle": "2026-03-24T02:05:21.196547Z",
-     "shell.execute_reply": "2026-03-24T02:05:21.196113Z"
+     "iopub.execute_input": "2026-06-04T02:50:21.394436Z",
+     "iopub.status.busy": "2026-06-04T02:50:21.394383Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.688809Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.688403Z"
     }
    },
    "outputs": [
@@ -754,7 +799,7 @@
        "5       <=0  Linear      {5}  constr        [5]        <NA>"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -778,14 +823,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "id": "9a608594",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:21.197683Z",
-     "iopub.status.busy": "2026-03-24T02:05:21.197558Z",
-     "iopub.status.idle": "2026-03-24T02:05:21.220036Z",
-     "shell.execute_reply": "2026-03-24T02:05:21.219654Z"
+     "iopub.execute_input": "2026-06-04T02:50:21.689924Z",
+     "iopub.status.busy": "2026-06-04T02:50:21.689832Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.715698Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.715459Z"
     }
    },
    "outputs": [
@@ -795,9 +840,9 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while evaluating problem `Problem(name=\"Possibly Overlapping Constraints\", sense=MINIMIZE, objective=0, constraints={constr: [Constraint(name=\"constr\", , lambda i: x[i] >= 1, domain=set(N)),Constraint(name=\"constr\", , lambda i: x[i] <= 2, domain=set(M)),],})',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/316836703.py\", line 1, col 2-55\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/316836703.py\", line 1, col 2-55\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/316836703.py\", line 1, col 2-55:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/316836703.py\", line 1, col 2-55:\n",
       "\n",
       "    1  |  @jm.Problem.define(\"Possibly Overlapping Constraints\")\n",
       "           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
@@ -825,14 +870,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "id": "92176ef9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:21.221047Z",
-     "iopub.status.busy": "2026-03-24T02:05:21.220992Z",
-     "iopub.status.idle": "2026-03-24T02:05:21.263953Z",
-     "shell.execute_reply": "2026-03-24T02:05:21.263607Z"
+     "iopub.execute_input": "2026-06-04T02:50:21.716834Z",
+     "iopub.status.busy": "2026-06-04T02:50:21.716788Z",
+     "iopub.status.idle": "2026-06-04T02:50:21.790146Z",
+     "shell.execute_reply": "2026-06-04T02:50:21.789782Z"
     }
    },
    "outputs": [
@@ -842,18 +887,18 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while adding constraint 'constr',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/2812696639.py\", line 7, col 9-56\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/2812696639.py\", line 7, col 9-56\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/2812696639.py\", line 7, col 9-56:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/2812696639.py\", line 7, col 9-56:\n",
       "\n",
       "    7  |          problem += problem.Constraint(\"constr\", x <= 2)\n",
       "                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
       "\n",
       "Constraint 'constr' has conflicting definition!\n",
       "    existing: Constraint(name=\"constr\", sense=GREATER_THAN_EQUAL, left=x, right=1, shape=Scalar(Integer))\n",
-      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/2812696639.py\", line 6, col 20-56\n",
+      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/2812696639.py\", line 6, col 20-56\n",
       "    new: Constraint(name=\"constr\", sense=LESS_THAN_EQUAL, left=x, right=2, shape=Scalar(Integer))\n",
-      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47870/2812696639.py\", line 7, col 20-56\n"
+      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_4385/2812696639.py\", line 7, col 20-56\n"
      ]
     }
    ],
@@ -897,7 +942,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/basics/overview.ipynb b/docs/en/basics/overview.ipynb
index 623e870a..27abde48 100644
--- a/docs/en/basics/overview.ipynb
+++ b/docs/en/basics/overview.ipynb
@@ -47,7 +47,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/basics/problem.ipynb b/docs/en/basics/problem.ipynb
index 632c008e..4a5abc63 100644
--- a/docs/en/basics/problem.ipynb
+++ b/docs/en/basics/problem.ipynb
@@ -22,10 +22,10 @@
    "id": "7b8759ae",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.724684Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.724622Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.729576Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.729251Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.758395Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.758346Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.764627Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.764168Z"
     }
    },
    "outputs": [],
@@ -50,10 +50,10 @@
    "id": "ee62b49c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.730719Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.730660Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.759990Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.759672Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.766261Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.766176Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.795683Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.795255Z"
     }
    },
    "outputs": [],
@@ -82,10 +82,10 @@
    "id": "7e0217ec",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.761139Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.761071Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.779979Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.779590Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.796829Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.796770Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.814272Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.813900Z"
     }
    },
    "outputs": [
@@ -127,10 +127,10 @@
    "id": "be7ff8c0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.781157Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.781094Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.801351Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.800946Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.815283Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.815228Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.836198Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.835861Z"
     }
    },
    "outputs": [
@@ -195,10 +195,10 @@
    "id": "abd131df",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.802391Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.802334Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.805407Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.804630Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.837173Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.837120Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.838937Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.838670Z"
     }
    },
    "outputs": [
@@ -236,10 +236,10 @@
    "id": "eecf1bff",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.807325Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.807233Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.839924Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.839463Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.839872Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.839817Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.872833Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.872507Z"
     }
    },
    "outputs": [
@@ -280,10 +280,10 @@
    "id": "d3d912cf",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:27.841184Z",
-     "iopub.status.busy": "2026-03-24T02:05:27.841105Z",
-     "iopub.status.idle": "2026-03-24T02:05:27.868184Z",
-     "shell.execute_reply": "2026-03-24T02:05:27.867818Z"
+     "iopub.execute_input": "2026-06-04T02:50:28.873806Z",
+     "iopub.status.busy": "2026-06-04T02:50:28.873756Z",
+     "iopub.status.idle": "2026-06-04T02:50:28.904861Z",
+     "shell.execute_reply": "2026-06-04T02:50:28.904531Z"
     }
    },
    "outputs": [
@@ -355,7 +355,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/basics/variables.ipynb b/docs/en/basics/variables.ipynb
index c6159392..57c67d73 100644
--- a/docs/en/basics/variables.ipynb
+++ b/docs/en/basics/variables.ipynb
@@ -17,10 +17,10 @@
    "id": "6c5a391b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:07.767010Z",
-     "iopub.status.busy": "2026-04-06T08:34:07.766768Z",
-     "iopub.status.idle": "2026-04-06T08:34:07.782300Z",
-     "shell.execute_reply": "2026-04-06T08:34:07.781874Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.701466Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.701403Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.707203Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.706826Z"
     }
    },
    "outputs": [],
@@ -89,10 +89,10 @@
    "id": "051961dc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:07.783709Z",
-     "iopub.status.busy": "2026-04-06T08:34:07.783621Z",
-     "iopub.status.idle": "2026-04-06T08:34:07.971950Z",
-     "shell.execute_reply": "2026-04-06T08:34:07.971484Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.708467Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.708412Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.795471Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.795108Z"
     }
    },
    "outputs": [
@@ -151,10 +151,10 @@
    "id": "4e178bbc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:07.973072Z",
-     "iopub.status.busy": "2026-04-06T08:34:07.972990Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.055172Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.054791Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.796523Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.796467Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.861222Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.860959Z"
     }
    },
    "outputs": [
@@ -244,10 +244,10 @@
    "id": "ce6cc419",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.056308Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.056246Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.154710Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.154322Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.862370Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.862313Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.924375Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.924052Z"
     }
    },
    "outputs": [
@@ -289,10 +289,10 @@
    "id": "1f668218",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.155903Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.155832Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.218475Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.218152Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.925410Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.925357Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.990025Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.989741Z"
     }
    },
    "outputs": [
@@ -352,10 +352,10 @@
    "id": "b84e1374",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.219741Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.219671Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.222777Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.222463Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.991264Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.991205Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.993082Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.992775Z"
     }
    },
    "outputs": [
@@ -380,10 +380,10 @@
    "id": "d3a9f52b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.223834Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.223774Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.226224Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.225934Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.993900Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.993857Z",
+     "iopub.status.idle": "2026-06-04T02:50:26.995483Z",
+     "shell.execute_reply": "2026-06-04T02:50:26.995171Z"
     }
    },
    "outputs": [
@@ -501,10 +501,10 @@
    "id": "5f2e4dc8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.227250Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.227187Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.299835Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.299402Z"
+     "iopub.execute_input": "2026-06-04T02:50:26.996500Z",
+     "iopub.status.busy": "2026-06-04T02:50:26.996453Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.037169Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.036803Z"
     }
    },
    "outputs": [
@@ -558,10 +558,10 @@
    "id": "4ce83fe1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.300975Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.300916Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.349222Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.348834Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.038147Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.038097Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.089793Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.089440Z"
     }
    },
    "outputs": [
@@ -659,10 +659,10 @@
    "id": "7333a2d6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.350358Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.350292Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.402718Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.402382Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.090831Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.090782Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.145896Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.145526Z"
     }
    },
    "outputs": [
@@ -718,10 +718,10 @@
    "id": "34184cce",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.404100Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.403923Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.503497Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.503095Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.146818Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.146770Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.204021Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.203663Z"
     }
    },
    "outputs": [
@@ -778,10 +778,10 @@
    "id": "ffa2feec",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.504651Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.504580Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.552528Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.552117Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.204992Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.204946Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.255490Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.255137Z"
     }
    },
    "outputs": [
@@ -839,10 +839,10 @@
    "id": "f93d902b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.553759Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.553695Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.720127Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.719708Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.256485Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.256429Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.401382Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.401095Z"
     }
    },
    "outputs": [
@@ -854,7 +854,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Partially determined shape\", sense=MINIMIZE, objective=sum(a.len_at(0).flat_map(lambda (i: natural): c.len_at(1).map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): a[i] * c[i, j] * x[i, j])), constraints=[])"
+       "Problem(name=\"Partially determined shape\", sense=MINIMIZE, objective=sum(set(a.len_at(0).flat_map(lambda (i: natural): c.len_at(1).map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): a[i] * c[i, j] * x[i, j])), constraints=[])"
       ]
      },
      "execution_count": 13,
@@ -970,10 +970,10 @@
    "id": "f86e9eac",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.721315Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.721253Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.741837Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.741464Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.402664Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.402611Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.422532Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.422225Z"
     }
    },
    "outputs": [
@@ -1017,10 +1017,10 @@
    "id": "470c7514",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.742967Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.742909Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.800254Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.799816Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.423539Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.423484Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.444123Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.443801Z"
     }
    },
    "outputs": [
@@ -1085,10 +1085,10 @@
    "id": "955b0199",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.801395Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.801334Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.855565Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.855175Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.445131Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.445082Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.584223Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.583859Z"
     }
    },
    "outputs": [
@@ -1096,7 +1096,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Dec Var Keys demonstration}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[L\\times N;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }L\\times N\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Dec Var Keys demonstration}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "L&\\text{Category Label}\\end{array}\n",
        "\\end{array}\n",
        "$$"
@@ -1173,10 +1173,10 @@
    "id": "b3e88831",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.856767Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.856700Z",
-     "iopub.status.idle": "2026-04-06T08:34:08.983512Z",
-     "shell.execute_reply": "2026-04-06T08:34:08.982892Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.585466Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.585414Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.655095Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.654777Z"
     }
    },
    "outputs": [
@@ -1230,10 +1230,10 @@
    "id": "4a1d9f04",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:08.985313Z",
-     "iopub.status.busy": "2026-04-06T08:34:08.985147Z",
-     "iopub.status.idle": "2026-04-06T08:34:09.040495Z",
-     "shell.execute_reply": "2026-04-06T08:34:09.040100Z"
+     "iopub.execute_input": "2026-06-04T02:50:27.656296Z",
+     "iopub.status.busy": "2026-06-04T02:50:27.656222Z",
+     "iopub.status.idle": "2026-06-04T02:50:27.708700Z",
+     "shell.execute_reply": "2026-06-04T02:50:27.708340Z"
     }
    },
    "outputs": [
diff --git a/docs/en/introduction.ipynb b/docs/en/introduction.ipynb
index 42178b73..7c70b128 100644
--- a/docs/en/introduction.ipynb
+++ b/docs/en/introduction.ipynb
@@ -73,10 +73,10 @@
    "id": "bf93e55f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:12.168227Z",
-     "iopub.status.busy": "2026-03-24T02:05:12.168162Z",
-     "iopub.status.idle": "2026-03-24T02:05:12.357614Z",
-     "shell.execute_reply": "2026-03-24T02:05:12.357091Z"
+     "iopub.execute_input": "2026-06-04T02:50:14.282082Z",
+     "iopub.status.busy": "2026-06-04T02:50:14.281577Z",
+     "iopub.status.idle": "2026-06-04T02:50:14.561437Z",
+     "shell.execute_reply": "2026-06-04T02:50:14.561144Z"
     }
    },
    "outputs": [
@@ -90,7 +90,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float), description=\"Total weight does not exceed the capacity\"),],})"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float), description=\"Total weight does not exceed the capacity\"),],})"
       ]
      },
      "execution_count": 1,
@@ -146,10 +146,10 @@
    "id": "3e35cee2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:12.359106Z",
-     "iopub.status.busy": "2026-03-24T02:05:12.359026Z",
-     "iopub.status.idle": "2026-03-24T02:05:12.396417Z",
-     "shell.execute_reply": "2026-03-24T02:05:12.395851Z"
+     "iopub.execute_input": "2026-06-04T02:50:14.562913Z",
+     "iopub.status.busy": "2026-06-04T02:50:14.562854Z",
+     "iopub.status.idle": "2026-06-04T02:50:14.617715Z",
+     "shell.execute_reply": "2026-06-04T02:50:14.617425Z"
     }
    },
    "outputs": [],
@@ -174,10 +174,10 @@
    "id": "d7c62729",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:12.397937Z",
-     "iopub.status.busy": "2026-03-24T02:05:12.397860Z",
-     "iopub.status.idle": "2026-03-24T02:05:12.441146Z",
-     "shell.execute_reply": "2026-03-24T02:05:12.440785Z"
+     "iopub.execute_input": "2026-06-04T02:50:14.619005Z",
+     "iopub.status.busy": "2026-06-04T02:50:14.618949Z",
+     "iopub.status.idle": "2026-06-04T02:50:14.692637Z",
+     "shell.execute_reply": "2026-06-04T02:50:14.692337Z"
     }
    },
    "outputs": [],
@@ -219,17 +219,17 @@
    "id": "05305f86",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:12.442451Z",
-     "iopub.status.busy": "2026-03-24T02:05:12.442393Z",
-     "iopub.status.idle": "2026-03-24T02:05:12.444506Z",
-     "shell.execute_reply": "2026-03-24T02:05:12.444040Z"
+     "iopub.execute_input": "2026-06-04T02:50:14.694006Z",
+     "iopub.status.busy": "2026-06-04T02:50:14.693946Z",
+     "iopub.status.idle": "2026-06-04T02:50:14.695784Z",
+     "shell.execute_reply": "2026-06-04T02:50:14.695499Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'2.3.1'"
+       "'2.5.0'"
       ]
      },
      "execution_count": 4,
@@ -289,7 +289,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/quickstart/openjij.ipynb b/docs/en/quickstart/openjij.ipynb
index da31c033..c2cf9607 100644
--- a/docs/en/quickstart/openjij.ipynb
+++ b/docs/en/quickstart/openjij.ipynb
@@ -94,10 +94,10 @@
    "id": "a9c293f9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:54.140257Z",
-     "iopub.status.busy": "2026-03-24T02:05:54.140176Z",
-     "iopub.status.idle": "2026-03-24T02:05:54.344261Z",
-     "shell.execute_reply": "2026-03-24T02:05:54.343870Z"
+     "iopub.execute_input": "2026-06-04T02:51:02.439272Z",
+     "iopub.status.busy": "2026-06-04T02:51:02.439203Z",
+     "iopub.status.idle": "2026-06-04T02:51:02.701928Z",
+     "shell.execute_reply": "2026-06-04T02:51:02.701586Z"
     }
    },
    "outputs": [
@@ -111,7 +111,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight Limit: [Constraint(name=\"Weight Limit\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight Limit: [Constraint(name=\"Weight Limit\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 1,
@@ -169,10 +169,10 @@
    "id": "4e5f7ef5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:54.345358Z",
-     "iopub.status.busy": "2026-03-24T02:05:54.345291Z",
-     "iopub.status.idle": "2026-03-24T02:05:54.347068Z",
-     "shell.execute_reply": "2026-03-24T02:05:54.346754Z"
+     "iopub.execute_input": "2026-06-04T02:51:02.703414Z",
+     "iopub.status.busy": "2026-06-04T02:51:02.703345Z",
+     "iopub.status.idle": "2026-06-04T02:51:02.705164Z",
+     "shell.execute_reply": "2026-06-04T02:51:02.704887Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "id": "ec59b351",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:54.348084Z",
-     "iopub.status.busy": "2026-03-24T02:05:54.348028Z",
-     "iopub.status.idle": "2026-03-24T02:05:55.318686Z",
-     "shell.execute_reply": "2026-03-24T02:05:55.318251Z"
+     "iopub.execute_input": "2026-06-04T02:51:02.706496Z",
+     "iopub.status.busy": "2026-06-04T02:51:02.706426Z",
+     "iopub.status.idle": "2026-06-04T02:51:03.579539Z",
+     "shell.execute_reply": "2026-06-04T02:51:03.579088Z"
     }
    },
    "outputs": [],
@@ -238,10 +238,10 @@
    "id": "89191aba",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:55.319966Z",
-     "iopub.status.busy": "2026-03-24T02:05:55.319862Z",
-     "iopub.status.idle": "2026-03-24T02:05:55.608844Z",
-     "shell.execute_reply": "2026-03-24T02:05:55.608370Z"
+     "iopub.execute_input": "2026-06-04T02:51:03.580745Z",
+     "iopub.status.busy": "2026-06-04T02:51:03.580654Z",
+     "iopub.status.idle": "2026-06-04T02:51:03.865751Z",
+     "shell.execute_reply": "2026-06-04T02:51:03.865422Z"
     }
    },
    "outputs": [],
@@ -272,10 +272,10 @@
    "id": "7dbff4db",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:55.609979Z",
-     "iopub.status.busy": "2026-03-24T02:05:55.609862Z",
-     "iopub.status.idle": "2026-03-24T02:05:55.618691Z",
-     "shell.execute_reply": "2026-03-24T02:05:55.617915Z"
+     "iopub.execute_input": "2026-06-04T02:51:03.866959Z",
+     "iopub.status.busy": "2026-06-04T02:51:03.866864Z",
+     "iopub.status.idle": "2026-06-04T02:51:03.875919Z",
+     "shell.execute_reply": "2026-06-04T02:51:03.875565Z"
     }
    },
    "outputs": [
@@ -322,19 +322,19 @@
        "      <th>1</th>\n",
        "      <td>x</td>\n",
        "      <td>[1]</td>\n",
-       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>x</td>\n",
        "      <td>[2]</td>\n",
-       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>x</td>\n",
        "      <td>[3]</td>\n",
-       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
@@ -356,9 +356,9 @@
        "   name subscripts  value\n",
        "id                       \n",
        "0     x        [0]    1.0\n",
-       "1     x        [1]    1.0\n",
-       "2     x        [2]    1.0\n",
-       "3     x        [3]    0.0\n",
+       "1     x        [1]    0.0\n",
+       "2     x        [2]    0.0\n",
+       "3     x        [3]    1.0\n",
        "4     x        [4]    0.0\n",
        "5     x        [5]    0.0"
       ]
@@ -413,7 +413,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/quickstart/scip.ipynb b/docs/en/quickstart/scip.ipynb
index 46b9e789..c7a9c55f 100644
--- a/docs/en/quickstart/scip.ipynb
+++ b/docs/en/quickstart/scip.ipynb
@@ -94,10 +94,10 @@
    "id": "0e58428f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:57.033597Z",
-     "iopub.status.busy": "2026-03-24T02:05:57.033524Z",
-     "iopub.status.idle": "2026-03-24T02:05:57.220613Z",
-     "shell.execute_reply": "2026-03-24T02:05:57.220137Z"
+     "iopub.execute_input": "2026-06-04T02:51:05.051422Z",
+     "iopub.status.busy": "2026-06-04T02:51:05.051303Z",
+     "iopub.status.idle": "2026-06-04T02:51:05.297581Z",
+     "shell.execute_reply": "2026-06-04T02:51:05.297172Z"
     }
    },
    "outputs": [
@@ -111,7 +111,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight Limit: [Constraint(name=\"Weight Limit\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight Limit: [Constraint(name=\"Weight Limit\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 1,
@@ -169,10 +169,10 @@
    "id": "9065e4c7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:57.221770Z",
-     "iopub.status.busy": "2026-03-24T02:05:57.221702Z",
-     "iopub.status.idle": "2026-03-24T02:05:57.223631Z",
-     "shell.execute_reply": "2026-03-24T02:05:57.223262Z"
+     "iopub.execute_input": "2026-06-04T02:51:05.298794Z",
+     "iopub.status.busy": "2026-06-04T02:51:05.298738Z",
+     "iopub.status.idle": "2026-06-04T02:51:05.300399Z",
+     "shell.execute_reply": "2026-06-04T02:51:05.300125Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "id": "c7014264",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:57.224565Z",
-     "iopub.status.busy": "2026-03-24T02:05:57.224511Z",
-     "iopub.status.idle": "2026-03-24T02:05:57.823423Z",
-     "shell.execute_reply": "2026-03-24T02:05:57.823067Z"
+     "iopub.execute_input": "2026-06-04T02:51:05.301325Z",
+     "iopub.status.busy": "2026-06-04T02:51:05.301272Z",
+     "iopub.status.idle": "2026-06-04T02:51:05.605029Z",
+     "shell.execute_reply": "2026-06-04T02:51:05.604526Z"
     }
    },
    "outputs": [],
@@ -238,10 +238,10 @@
    "id": "deeb53b7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:57.824990Z",
-     "iopub.status.busy": "2026-03-24T02:05:57.824880Z",
-     "iopub.status.idle": "2026-03-24T02:05:57.897273Z",
-     "shell.execute_reply": "2026-03-24T02:05:57.896862Z"
+     "iopub.execute_input": "2026-06-04T02:51:05.606240Z",
+     "iopub.status.busy": "2026-06-04T02:51:05.606157Z",
+     "iopub.status.idle": "2026-06-04T02:51:05.687394Z",
+     "shell.execute_reply": "2026-06-04T02:51:05.687021Z"
     }
    },
    "outputs": [
@@ -276,10 +276,10 @@
    "id": "bc247e30",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:57.898343Z",
-     "iopub.status.busy": "2026-03-24T02:05:57.898246Z",
-     "iopub.status.idle": "2026-03-24T02:05:57.903584Z",
-     "shell.execute_reply": "2026-03-24T02:05:57.903279Z"
+     "iopub.execute_input": "2026-06-04T02:51:05.688474Z",
+     "iopub.status.busy": "2026-06-04T02:51:05.688380Z",
+     "iopub.status.idle": "2026-06-04T02:51:05.693394Z",
+     "shell.execute_reply": "2026-06-04T02:51:05.693048Z"
     }
    },
    "outputs": [
@@ -406,7 +406,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/references/cheat_sheet.ipynb b/docs/en/references/cheat_sheet.ipynb
index 888467c0..ec41ca12 100644
--- a/docs/en/references/cheat_sheet.ipynb
+++ b/docs/en/references/cheat_sheet.ipynb
@@ -14,10 +14,10 @@
    "id": "58e0d17d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.138769Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.138673Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.144634Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.144172Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.214176Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.213274Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.227045Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.226652Z"
     }
    },
    "outputs": [],
@@ -49,10 +49,10 @@
    "id": "1fa8bcb8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.145935Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.145870Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.208435Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.208052Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.228380Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.228309Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.397625Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.396714Z"
     }
    },
    "outputs": [
@@ -95,10 +95,10 @@
    "id": "01dbd1aa",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.209566Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.209508Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.247617Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.247212Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.399475Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.399314Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.449986Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.449602Z"
     }
    },
    "outputs": [
@@ -150,10 +150,10 @@
    "id": "e544f20f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.248803Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.248745Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.300815Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.300523Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.451162Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.451107Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.518079Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.517682Z"
     }
    },
    "outputs": [
@@ -197,10 +197,10 @@
    "id": "b987d8a2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.302089Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.302028Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.360395Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.360096Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.519061Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.519007Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.600839Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.600496Z"
     }
    },
    "outputs": [
@@ -253,10 +253,10 @@
    "id": "16f43d5e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.361838Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.361761Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.435051Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.434653Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.601921Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.601870Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.691581Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.691216Z"
     }
    },
    "outputs": [
@@ -300,10 +300,10 @@
    "id": "8e08a289",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.436176Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.436111Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.509020Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.508680Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.692626Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.692568Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.792894Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.792594Z"
     }
    },
    "outputs": [
@@ -315,7 +315,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(C.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(set(C).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 7,
@@ -356,10 +356,10 @@
    "id": "cb70d54b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.510225Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.510162Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.583409Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.583111Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.794264Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.794205Z",
+     "iopub.status.idle": "2026-06-04T02:50:56.895649Z",
+     "shell.execute_reply": "2026-06-04T02:50:56.895286Z"
     }
    },
    "outputs": [
@@ -403,10 +403,10 @@
    "id": "99bccede",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.584536Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.584478Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.663348Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.662945Z"
+     "iopub.execute_input": "2026-06-04T02:50:56.896858Z",
+     "iopub.status.busy": "2026-06-04T02:50:56.896792Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.023995Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.023528Z"
     }
    },
    "outputs": [
@@ -418,7 +418,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongEdgeSet\", sense=MINIMIZE, objective=sum(E.map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
+       "Problem(name=\"SumAlongEdgeSet\", sense=MINIMIZE, objective=sum(set(E).map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 9,
@@ -459,10 +459,10 @@
    "id": "0c7a84b9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.664450Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.664393Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.785497Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.785171Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.025005Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.024953Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.199721Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.199437Z"
     }
    },
    "outputs": [
@@ -509,10 +509,10 @@
    "id": "2099890c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.786631Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.786573Z",
-     "iopub.status.idle": "2026-03-24T02:05:49.910277Z",
-     "shell.execute_reply": "2026-03-24T02:05:49.909994Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.200932Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.200881Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.434731Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.434312Z"
     }
    },
    "outputs": [
@@ -524,7 +524,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 11,
@@ -565,10 +565,10 @@
    "id": "b0c6a474",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:49.911529Z",
-     "iopub.status.busy": "2026-03-24T02:05:49.911466Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.007014Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.006612Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.435813Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.435760Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.573730Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.573289Z"
     }
    },
    "outputs": [
@@ -614,10 +614,10 @@
    "id": "ffd9b043",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.008161Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.008096Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.111449Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.111109Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.574821Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.574767Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.722420Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.721985Z"
     }
    },
    "outputs": [
@@ -629,7 +629,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"NonDiagonalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i != j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j])), constraints=[])"
+       "Problem(name=\"NonDiagonalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i != j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j])), constraints=[])"
       ]
      },
      "execution_count": 13,
@@ -669,10 +669,10 @@
    "id": "5136e06e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.112733Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.112670Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.189751Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.189365Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.723607Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.723547Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.824869Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.824540Z"
     }
    },
    "outputs": [
@@ -717,10 +717,10 @@
    "id": "22097eb3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.190859Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.190800Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.294869Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.294439Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.826009Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.825955Z",
+     "iopub.status.idle": "2026-06-04T02:50:57.976202Z",
+     "shell.execute_reply": "2026-06-04T02:50:57.975750Z"
     }
    },
    "outputs": [
@@ -732,7 +732,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"DependentSum\", sense=MINIMIZE, objective=sum(M.flat_map(lambda (i: natural): a[i].map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): x[j])), constraints=[])"
+       "Problem(name=\"DependentSum\", sense=MINIMIZE, objective=sum(set(M.flat_map(lambda (i: natural): a[i].map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): x[j])), constraints=[])"
       ]
      },
      "execution_count": 15,
@@ -776,10 +776,10 @@
    "id": "4c24379f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.296177Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.296114Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.365231Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.364897Z"
+     "iopub.execute_input": "2026-06-04T02:50:57.977263Z",
+     "iopub.status.busy": "2026-06-04T02:50:57.977216Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.061532Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.061218Z"
     }
    },
    "outputs": [
@@ -793,7 +793,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 16,
@@ -824,10 +824,10 @@
    "id": "73fff5dc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.366462Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.366397Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.467014Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.465641Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.062624Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.062567Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.174144Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.173793Z"
     }
    },
    "outputs": [
@@ -841,7 +841,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 17,
@@ -881,10 +881,10 @@
    "id": "28999f5f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.473756Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.473630Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.574785Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.574354Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.175374Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.175321Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.266036Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.265713Z"
     }
    },
    "outputs": [
@@ -930,10 +930,10 @@
    "id": "7091b61a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.576009Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.575942Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.655183Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.654590Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.267190Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.267134Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.401428Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.400823Z"
     }
    },
    "outputs": [
@@ -988,10 +988,10 @@
    "id": "db92c346",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.656805Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.656716Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.753056Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.752741Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.403203Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.403116Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.563882Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.563581Z"
     }
    },
    "outputs": [
@@ -1000,12 +1000,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{2D K-Hot}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{2d k-hot}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=K\\end{aligned}\n",
+       "\\text{2d k-hot}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}={K}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times M;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{N}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{N}\\\\M&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}N&=\\mathop{\\mathtt{len\\_{}at}}\\left(K,0\\right)&\\quad &\\in \\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
+       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
      "execution_count": 20,
@@ -1038,10 +1038,10 @@
    "id": "60016a39",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.754176Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.754110Z",
-     "iopub.status.idle": "2026-03-24T02:05:50.855294Z",
-     "shell.execute_reply": "2026-03-24T02:05:50.854844Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.565131Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.565072Z",
+     "iopub.status.idle": "2026-06-04T02:50:58.725785Z",
+     "shell.execute_reply": "2026-06-04T02:50:58.725491Z"
     }
    },
    "outputs": [
@@ -1050,12 +1050,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{2D K-Hot}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{2d k-hot}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=K\\end{aligned}\n",
+       "\\text{2d k-hot}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}={K}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times M;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{N}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{N}\\\\M&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}N&=\\mathop{\\mathtt{len\\_{}at}}\\left(K,0\\right)&\\quad &\\in \\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
+       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
      "execution_count": 21,
@@ -1097,10 +1097,10 @@
    "id": "8dbef935",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:50.856482Z",
-     "iopub.status.busy": "2026-03-24T02:05:50.856419Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.037052Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.036766Z"
+     "iopub.execute_input": "2026-06-04T02:50:58.726995Z",
+     "iopub.status.busy": "2026-06-04T02:50:58.726938Z",
+     "iopub.status.idle": "2026-06-04T02:50:59.066308Z",
+     "shell.execute_reply": "2026-06-04T02:50:59.065942Z"
     }
    },
    "outputs": [
@@ -1150,10 +1150,10 @@
    "id": "ccce502f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.038413Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.038340Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.220940Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.220510Z"
+     "iopub.execute_input": "2026-06-04T02:50:59.067431Z",
+     "iopub.status.busy": "2026-06-04T02:50:59.067375Z",
+     "iopub.status.idle": "2026-06-04T02:50:59.303655Z",
+     "shell.execute_reply": "2026-06-04T02:50:59.303356Z"
     }
    },
    "outputs": [
@@ -1167,7 +1167,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(C[a].map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
+       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(set(C[a]).map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
       ]
      },
      "execution_count": 23,
@@ -1212,10 +1212,10 @@
    "id": "3f12d8d7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.222576Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.222483Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.314397Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.313970Z"
+     "iopub.execute_input": "2026-06-04T02:50:59.304991Z",
+     "iopub.status.busy": "2026-06-04T02:50:59.304936Z",
+     "iopub.status.idle": "2026-06-04T02:50:59.418310Z",
+     "shell.execute_reply": "2026-06-04T02:50:59.417959Z"
     }
    },
    "outputs": [
@@ -1262,10 +1262,10 @@
    "id": "d4b89527",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.315599Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.315536Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.412830Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.412389Z"
+     "iopub.execute_input": "2026-06-04T02:50:59.419502Z",
+     "iopub.status.busy": "2026-06-04T02:50:59.419446Z",
+     "iopub.status.idle": "2026-06-04T02:50:59.551122Z",
+     "shell.execute_reply": "2026-06-04T02:50:59.550651Z"
     }
    },
    "outputs": [
@@ -1321,10 +1321,10 @@
    "id": "632c4d8c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.414267Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.414180Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.569044Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.568650Z"
+     "iopub.execute_input": "2026-06-04T02:50:59.552451Z",
+     "iopub.status.busy": "2026-06-04T02:50:59.552385Z",
+     "iopub.status.idle": "2026-06-04T02:50:59.812194Z",
+     "shell.execute_reply": "2026-06-04T02:50:59.811823Z"
     }
    },
    "outputs": [
@@ -1333,12 +1333,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{SOS-1}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{Big-M}&\\quad \\displaystyle a\\leq M\\cdot x\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
+       "\\text{Big-M}&\\quad \\displaystyle {a}_{i}\\leq {\\left(M\\cdot x\\right)}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]\\;\\left(0\\leq {a}_{i}\\leq {M}_{i}\\right)&\\quad &1\\text{-dim continuous variable}\\\\x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}M&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 26,
@@ -1372,10 +1372,10 @@
    "id": "cfcc2cf8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.570194Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.570136Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.730890Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.730482Z"
+     "iopub.execute_input": "2026-06-04T02:50:59.814231Z",
+     "iopub.status.busy": "2026-06-04T02:50:59.814133Z",
+     "iopub.status.idle": "2026-06-04T02:51:00.071507Z",
+     "shell.execute_reply": "2026-06-04T02:51:00.071073Z"
     }
    },
    "outputs": [
@@ -1384,12 +1384,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{SOS-1}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{Big-M}&\\quad \\displaystyle a\\leq M\\cdot x\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
+       "\\text{Big-M}&\\quad \\displaystyle {a}_{i}\\leq {\\left(M\\cdot x\\right)}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]\\;\\left(0\\leq {a}_{i}\\leq {M}_{i}\\right)&\\quad &1\\text{-dim continuous variable}\\\\x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}M&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_49545/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_5522/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 27,
@@ -1432,10 +1432,10 @@
    "id": "29ed161b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.732007Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.731947Z",
-     "iopub.status.idle": "2026-03-24T02:05:51.983084Z",
-     "shell.execute_reply": "2026-03-24T02:05:51.982595Z"
+     "iopub.execute_input": "2026-06-04T02:51:00.072938Z",
+     "iopub.status.busy": "2026-06-04T02:51:00.072867Z",
+     "iopub.status.idle": "2026-06-04T02:51:00.387069Z",
+     "shell.execute_reply": "2026-06-04T02:51:00.386761Z"
     }
    },
    "outputs": [
@@ -1490,10 +1490,10 @@
    "id": "01df2009",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:51.984105Z",
-     "iopub.status.busy": "2026-03-24T02:05:51.984039Z",
-     "iopub.status.idle": "2026-03-24T02:05:52.267729Z",
-     "shell.execute_reply": "2026-03-24T02:05:52.267301Z"
+     "iopub.execute_input": "2026-06-04T02:51:00.388135Z",
+     "iopub.status.busy": "2026-06-04T02:51:00.388075Z",
+     "iopub.status.idle": "2026-06-04T02:51:00.776223Z",
+     "shell.execute_reply": "2026-06-04T02:51:00.775890Z"
     }
    },
    "outputs": [
@@ -1558,7 +1558,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/references/migration_guide_to_jijmodeling2.ipynb b/docs/en/references/migration_guide_to_jijmodeling2.ipynb
index ac8ca450..e8b12518 100644
--- a/docs/en/references/migration_guide_to_jijmodeling2.ipynb
+++ b/docs/en/references/migration_guide_to_jijmodeling2.ipynb
@@ -123,10 +123,10 @@
    "id": "07073ecc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:43.321800Z",
-     "iopub.status.busy": "2026-03-24T02:05:43.321690Z",
-     "iopub.status.idle": "2026-03-24T02:05:43.798175Z",
-     "shell.execute_reply": "2026-03-24T02:05:43.797789Z"
+     "iopub.execute_input": "2026-06-04T02:50:50.168536Z",
+     "iopub.status.busy": "2026-06-04T02:50:50.168354Z",
+     "iopub.status.idle": "2026-06-04T02:50:50.729844Z",
+     "shell.execute_reply": "2026-06-04T02:50:50.729556Z"
     }
    },
    "outputs": [
@@ -140,7 +140,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).flat_map(lambda ((i, j): Tuple[natural, natural]): N.map(lambda (t: natural): (i, j, t))).map(lambda ((i, j, t): Tuple[natural, natural, natural]): d[i, j] * x[i, t] * x[j, (t + 1) % N])), constraints={one-city: [Constraint(name=\"one-city\", , lambda t: sum(N.map(lambda (i: natural): x[i, t])) == 1, domain=set(N), description=\"Exactly one city is visited at each time step\"),],one-time: [Constraint(name=\"one-time\", , lambda i: sum(N.map(lambda (t: natural): x[i, t])) == 1, domain=set(N), description=\"Each city is visited exactly once\"),],})"
+       "Problem(name=\"TSP\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).flat_map(lambda ((i, j): Tuple[natural, natural]): N.map(lambda (t: natural): (i, j, t)))).map(lambda ((i, j, t): Tuple[natural, natural, natural]): d[i, j] * x[i, t] * x[j, (t + 1) % N])), constraints={one-city: [Constraint(name=\"one-city\", , lambda t: sum(set(N).map(lambda (i: natural): x[i, t])) == 1, domain=set(N), description=\"Exactly one city is visited at each time step\"),],one-time: [Constraint(name=\"one-time\", , lambda i: sum(set(N).map(lambda (t: natural): x[i, t])) == 1, domain=set(N), description=\"Each city is visited exactly once\"),],})"
       ]
      },
      "execution_count": 1,
@@ -192,10 +192,10 @@
    "id": "a735444a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:43.799604Z",
-     "iopub.status.busy": "2026-03-24T02:05:43.799490Z",
-     "iopub.status.idle": "2026-03-24T02:05:44.480146Z",
-     "shell.execute_reply": "2026-03-24T02:05:44.479708Z"
+     "iopub.execute_input": "2026-06-04T02:50:50.731155Z",
+     "iopub.status.busy": "2026-06-04T02:50:50.731072Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.096492Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.096053Z"
     }
    },
    "outputs": [
@@ -372,10 +372,10 @@
    "id": "1ff67480",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:44.481185Z",
-     "iopub.status.busy": "2026-03-24T02:05:44.481084Z",
-     "iopub.status.idle": "2026-03-24T02:05:44.483291Z",
-     "shell.execute_reply": "2026-03-24T02:05:44.482927Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.097446Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.097356Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.099304Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.098971Z"
     }
    },
    "outputs": [
@@ -408,10 +408,10 @@
    "id": "e436bcac",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:44.484201Z",
-     "iopub.status.busy": "2026-03-24T02:05:44.484151Z",
-     "iopub.status.idle": "2026-03-24T02:05:44.821125Z",
-     "shell.execute_reply": "2026-03-24T02:05:44.820732Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.100182Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.100132Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.255245Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.254851Z"
     }
    },
    "outputs": [],
@@ -710,10 +710,10 @@
    "id": "4248c879",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:44.822546Z",
-     "iopub.status.busy": "2026-03-24T02:05:44.822476Z",
-     "iopub.status.idle": "2026-03-24T02:05:44.888743Z",
-     "shell.execute_reply": "2026-03-24T02:05:44.888343Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.256469Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.256412Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.351705Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.351413Z"
     }
    },
    "outputs": [
@@ -725,7 +725,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SimpleSum\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SimpleSum\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 5,
@@ -784,10 +784,10 @@
    "id": "70c79151",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:44.889952Z",
-     "iopub.status.busy": "2026-03-24T02:05:44.889891Z",
-     "iopub.status.idle": "2026-03-24T02:05:44.978267Z",
-     "shell.execute_reply": "2026-03-24T02:05:44.977914Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.352903Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.352843Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.494409Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.493973Z"
     }
    },
    "outputs": [
@@ -799,7 +799,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"WeightedSum\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"WeightedSum\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
      "execution_count": 6,
@@ -852,10 +852,10 @@
    "id": "a4897d4a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:44.979404Z",
-     "iopub.status.busy": "2026-03-24T02:05:44.979343Z",
-     "iopub.status.idle": "2026-03-24T02:05:45.071099Z",
-     "shell.execute_reply": "2026-03-24T02:05:45.070806Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.495538Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.495474Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.624174Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.623811Z"
     }
    },
    "outputs": [
@@ -867,7 +867,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(C.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(set(C).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 7,
@@ -920,10 +920,10 @@
    "id": "bbb6f2fc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:45.072441Z",
-     "iopub.status.busy": "2026-03-24T02:05:45.072369Z",
-     "iopub.status.idle": "2026-03-24T02:05:45.163873Z",
-     "shell.execute_reply": "2026-03-24T02:05:45.163453Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.625208Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.625145Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.754842Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.754444Z"
     }
    },
    "outputs": [
@@ -935,7 +935,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"EdgeSum\", sense=MINIMIZE, objective=sum(E.map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
+       "Problem(name=\"EdgeSum\", sense=MINIMIZE, objective=sum(set(E).map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 8,
@@ -981,10 +981,10 @@
    "id": "8407f344",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:45.164965Z",
-     "iopub.status.busy": "2026-03-24T02:05:45.164904Z",
-     "iopub.status.idle": "2026-03-24T02:05:45.284771Z",
-     "shell.execute_reply": "2026-03-24T02:05:45.284467Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.755888Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.755833Z",
+     "iopub.status.idle": "2026-06-04T02:50:51.929172Z",
+     "shell.execute_reply": "2026-06-04T02:50:51.928825Z"
     }
    },
    "outputs": [
@@ -996,7 +996,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"EdgeSumRows\", sense=MINIMIZE, objective=sum(E.rows().map(lambda ((l, r): Array[2; natural]): x[l] * x[r])), constraints=[])"
+       "Problem(name=\"EdgeSumRows\", sense=MINIMIZE, objective=sum(set(E.rows()).map(lambda ((l, r): Array[2; natural]): x[l] * x[r])), constraints=[])"
       ]
      },
      "execution_count": 9,
@@ -1049,10 +1049,10 @@
    "id": "0d391b43",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:45.286019Z",
-     "iopub.status.busy": "2026-03-24T02:05:45.285964Z",
-     "iopub.status.idle": "2026-03-24T02:05:45.434244Z",
-     "shell.execute_reply": "2026-03-24T02:05:45.433890Z"
+     "iopub.execute_input": "2026-06-04T02:50:51.930261Z",
+     "iopub.status.busy": "2026-06-04T02:50:51.930208Z",
+     "iopub.status.idle": "2026-06-04T02:50:52.165288Z",
+     "shell.execute_reply": "2026-06-04T02:50:52.164812Z"
     }
    },
    "outputs": [
@@ -1064,7 +1064,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 10,
@@ -1102,10 +1102,10 @@
    "id": "e3050e27",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:45.435289Z",
-     "iopub.status.busy": "2026-03-24T02:05:45.435233Z",
-     "iopub.status.idle": "2026-03-24T02:05:45.703773Z",
-     "shell.execute_reply": "2026-03-24T02:05:45.703350Z"
+     "iopub.execute_input": "2026-06-04T02:50:52.166704Z",
+     "iopub.status.busy": "2026-06-04T02:50:52.166631Z",
+     "iopub.status.idle": "2026-06-04T02:50:52.393011Z",
+     "shell.execute_reply": "2026-06-04T02:50:52.392455Z"
     }
    },
    "outputs": [
@@ -1117,7 +1117,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 11,
@@ -1155,10 +1155,10 @@
    "id": "d4636310",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:45.704909Z",
-     "iopub.status.busy": "2026-03-24T02:05:45.704842Z",
-     "iopub.status.idle": "2026-03-24T02:05:46.234851Z",
-     "shell.execute_reply": "2026-03-24T02:05:46.234033Z"
+     "iopub.execute_input": "2026-06-04T02:50:52.394361Z",
+     "iopub.status.busy": "2026-06-04T02:50:52.394290Z",
+     "iopub.status.idle": "2026-06-04T02:50:53.436123Z",
+     "shell.execute_reply": "2026-06-04T02:50:53.435717Z"
     }
    },
    "outputs": [
@@ -1168,13 +1168,13 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{QuadraticKnapsackLogistics}\\\\\\displaystyle \\max &\\displaystyle \\sum _{j\\in J}{\\sum _{\\left\\langle i,k\\right\\rangle \\in \\mathop{\\mathtt{keys}}\\left(s\\right)}{{s}_{i,k}\\cdot {x}_{i,j}\\cdot {x}_{k,j}}}+\\sum _{i\\in I}{\\sum _{j\\in J}{{r}_{i}\\cdot {x}_{i,j}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{parcel\\_{}assign}&\\quad \\displaystyle \\sum _{j\\in J}{{x}_{i,j}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in I\\\\\\text{truck\\_{}capacity}&\\quad \\displaystyle \\sum _{i\\in I}{{w}_{i}\\cdot {x}_{i,j}}\\leq {C}_{j}\\quad \\forall j\\;\\text{s.t.}\\;j\\in J\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[I\\times J;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }I\\times J\\\\&&&\\text{x[i,j] = 1 if parcel i is assigned to truck j, else 0}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}C&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{J};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{J}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The capacity of each truck}\\\\&&&\\\\r&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The base revenue of each parcel}\\\\&&&\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\mathrm{I}\\times \\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left(\\mathrm{I},\\mathrm{I}\\right)\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The synergy bonus between pairs of parcels}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The weight of each parcel}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in I,j\\in J\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in I,j\\in J\\right\\}\\\\&&&\\text{x[i,j] = 1 if parcel i is assigned to truck j, else 0}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}C&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{J};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{J}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The capacity of each truck}\\\\&&&\\\\r&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The base revenue of each parcel}\\\\&&&\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\mathrm{I}\\times \\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left(\\mathrm{I},\\mathrm{I}\\right)\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The synergy bonus between pairs of parcels}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{The weight of each parcel}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "I&\\text{The labels of parcels}\\\\J&\\text{The labels of trucks}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"QuadraticKnapsackLogistics\", sense=MAXIMIZE, objective=sum(J.flat_map(lambda (j: CategoryLabel(\"J\")): s.keys().map(lambda ((i, k): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"I\")]): (j, i, k))).map(lambda ((j, i, k): Tuple[CategoryLabel(\"J\"), CategoryLabel(\"I\"), CategoryLabel(\"I\")]): s[i, k] * x[i, j] * x[k, j])) + sum(I.flat_map(lambda (i: CategoryLabel(\"I\")): J.map(lambda (j: CategoryLabel(\"J\")): (i, j))).map(lambda ((i, j): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"J\")]): r[i] * x[i, j])), constraints={parcel_assign: [Constraint(name=\"parcel_assign\", , lambda i: sum(J.map(lambda (j: CategoryLabel(\"J\")): x[i, j])) == 1, domain=I),],truck_capacity: [Constraint(name=\"truck_capacity\", , lambda j: sum(I.map(lambda (i: CategoryLabel(\"I\")): w[i] * x[i, j])) <= C[j], domain=J),],})"
+       "Problem(name=\"QuadraticKnapsackLogistics\", sense=MAXIMIZE, objective=sum(set(J.flat_map(lambda (j: CategoryLabel(\"J\")): s.keys().map(lambda ((i, k): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"I\")]): (j, i, k)))).map(lambda ((j, i, k): Tuple[CategoryLabel(\"J\"), CategoryLabel(\"I\"), CategoryLabel(\"I\")]): s[i, k] * x[i, j] * x[k, j])) + sum(set(I.flat_map(lambda (i: CategoryLabel(\"I\")): J.map(lambda (j: CategoryLabel(\"J\")): (i, j)))).map(lambda ((i, j): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"J\")]): r[i] * x[i, j])), constraints={parcel_assign: [Constraint(name=\"parcel_assign\", , lambda i: sum(set(J).map(lambda (j: CategoryLabel(\"J\")): x[i, j])) == 1, domain=I),],truck_capacity: [Constraint(name=\"truck_capacity\", , lambda j: sum(set(I).map(lambda (i: CategoryLabel(\"I\")): w[i] * x[i, j])) <= C[j], domain=J),],})"
       ]
      },
      "execution_count": 12,
@@ -1257,10 +1257,10 @@
    "id": "164f130e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:46.236868Z",
-     "iopub.status.busy": "2026-03-24T02:05:46.236694Z",
-     "iopub.status.idle": "2026-03-24T02:05:46.762020Z",
-     "shell.execute_reply": "2026-03-24T02:05:46.761647Z"
+     "iopub.execute_input": "2026-06-04T02:50:53.437215Z",
+     "iopub.status.busy": "2026-06-04T02:50:53.437156Z",
+     "iopub.status.idle": "2026-06-04T02:50:53.909945Z",
+     "shell.execute_reply": "2026-06-04T02:50:53.909532Z"
     }
    },
    "outputs": [],
@@ -1318,10 +1318,10 @@
    "id": "60c7c648",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:46.764301Z",
-     "iopub.status.busy": "2026-03-24T02:05:46.764158Z",
-     "iopub.status.idle": "2026-03-24T02:05:46.857048Z",
-     "shell.execute_reply": "2026-03-24T02:05:46.856713Z"
+     "iopub.execute_input": "2026-06-04T02:50:53.911140Z",
+     "iopub.status.busy": "2026-06-04T02:50:53.911082Z",
+     "iopub.status.idle": "2026-06-04T02:50:54.049181Z",
+     "shell.execute_reply": "2026-06-04T02:50:54.048828Z"
     }
    },
    "outputs": [
@@ -1335,7 +1335,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 14,
@@ -1384,10 +1384,10 @@
    "id": "c141cc39",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:46.858358Z",
-     "iopub.status.busy": "2026-03-24T02:05:46.858294Z",
-     "iopub.status.idle": "2026-03-24T02:05:47.052041Z",
-     "shell.execute_reply": "2026-03-24T02:05:47.051690Z"
+     "iopub.execute_input": "2026-06-04T02:50:54.050211Z",
+     "iopub.status.busy": "2026-06-04T02:50:54.050152Z",
+     "iopub.status.idle": "2026-06-04T02:50:54.325223Z",
+     "shell.execute_reply": "2026-06-04T02:50:54.324864Z"
     }
    },
    "outputs": [
@@ -1401,7 +1401,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(C[a].map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
+       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(set(C[a]).map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
       ]
      },
      "execution_count": 15,
@@ -1466,10 +1466,10 @@
    "id": "63466e33",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:47.053191Z",
-     "iopub.status.busy": "2026-03-24T02:05:47.053134Z",
-     "iopub.status.idle": "2026-03-24T02:05:47.619735Z",
-     "shell.execute_reply": "2026-03-24T02:05:47.619326Z"
+     "iopub.execute_input": "2026-06-04T02:50:54.326490Z",
+     "iopub.status.busy": "2026-06-04T02:50:54.326427Z",
+     "iopub.status.idle": "2026-06-04T02:50:54.672700Z",
+     "shell.execute_reply": "2026-06-04T02:50:54.672328Z"
     }
    },
    "outputs": [
@@ -1766,10 +1766,10 @@
    "id": "66f48d43",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:47.621016Z",
-     "iopub.status.busy": "2026-03-24T02:05:47.620953Z",
-     "iopub.status.idle": "2026-03-24T02:05:47.748264Z",
-     "shell.execute_reply": "2026-03-24T02:05:47.747608Z"
+     "iopub.execute_input": "2026-06-04T02:50:54.673921Z",
+     "iopub.status.busy": "2026-06-04T02:50:54.673862Z",
+     "iopub.status.idle": "2026-06-04T02:50:54.868410Z",
+     "shell.execute_reply": "2026-06-04T02:50:54.868102Z"
     }
    },
    "outputs": [
@@ -1781,7 +1781,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"My Problem\", sense=MINIMIZE, objective=sum(N.filter(lambda i: i % 2 == 0).flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): x[i, j])), constraints=[])"
+       "Problem(name=\"My Problem\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0).flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): x[i, j])), constraints=[])"
       ]
      },
      "execution_count": 17,
@@ -1813,10 +1813,10 @@
    "id": "35080ca8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:47.749365Z",
-     "iopub.status.busy": "2026-03-24T02:05:47.749301Z",
-     "iopub.status.idle": "2026-03-24T02:05:47.850728Z",
-     "shell.execute_reply": "2026-03-24T02:05:47.850339Z"
+     "iopub.execute_input": "2026-06-04T02:50:54.869465Z",
+     "iopub.status.busy": "2026-06-04T02:50:54.869406Z",
+     "iopub.status.idle": "2026-06-04T02:50:55.011219Z",
+     "shell.execute_reply": "2026-06-04T02:50:55.010853Z"
     }
    },
    "outputs": [
@@ -1883,7 +1883,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/en/releases/jijmodeling-2.5.0.ipynb b/docs/en/releases/jijmodeling-2.5.0.ipynb
new file mode 100644
index 00000000..410635ea
--- /dev/null
+++ b/docs/en/releases/jijmodeling-2.5.0.ipynb
@@ -0,0 +1,647 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# JijModeling 2.5.0 Release Notes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Feature Enhancements"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Comprehension syntax for `jm.min`, `jm.max`, and `jm.set` in the Decorator API\n",
+    "\n",
+    "Previously, when using the Decorator API, only {py:func}`jm.sum <jijmodeling.sum>` and {py:func}`jm.prod <jijmodeling.prod>` accepted a comprehension (Python generator) expression as their single argument.\n",
+    "\n",
+    "Starting with this version, unary calls to {py:func}`jm.min <jijmodeling.min>`, {py:func}`jm.max <jijmodeling.max>`, and {py:func}`jm.set <jijmodeling.set>` also accept comprehension expressions in the same way."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "32793934",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:23.700701Z",
+     "iopub.status.busy": "2026-06-04T03:14:23.700648Z",
+     "iopub.status.idle": "2026-06-04T03:14:23.968395Z",
+     "shell.execute_reply": "2026-06-04T03:14:23.967965Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{min/max/set comprehension example}\\\\\\displaystyle \\min &\\displaystyle \\min _{i=0}^{N-1}{{x}_{i}}+\\max _{\\substack{i=0\\\\i\\neq 0}}^{N-1}{{x}_{i}}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"min/max/set comprehension example\", sense=MINIMIZE, objective=min(set(N).map(lambda (i: natural): x[i])) + max(set(set(set(N.filter(lambda i: i != 0)).map(lambda (i: natural): i))).map(lambda (i: natural): x[i])), constraints=[])"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"min/max/set comprehension example\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Length()\n",
+    "    x = problem.BinaryVar(shape=N)\n",
+    "\n",
+    "    nonzero = jm.set(i for i in N if i != 0)\n",
+    "    problem += jm.min(x[i] for i in N) + jm.max(x[i] for i in nonzero)\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be77d5e2",
+   "metadata": {},
+   "source": [
+    "### Math output: More readable constraint indices\n",
+    "\n",
+    "Constraints created by directly comparing dictionaries or arrays are now rendered in $\\LaTeX$ output using $\\forall$, improving readability."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "cc7c29a2",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:23.969505Z",
+     "iopub.status.busy": "2026-06-04T03:14:23.969441Z",
+     "iopub.status.idle": "2026-06-04T03:14:24.724589Z",
+     "shell.execute_reply": "2026-06-04T03:14:24.724175Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{container-vs-scalar-comp}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
+       "\\text{dict-vs-dict}&\\quad \\displaystyle {y}_{i,j}\\leq {z}_{i,j}\\quad \\forall \\left(i,j\\right)\\;\\text{s.t.}\\;i\\in L,j\\in \\left\\{0,\\ldots ,N-1-1\\right\\}\\\\\\text{dict-vs-scalar}&\\quad \\displaystyle {y}_{i,j}\\leq 5\\quad \\forall \\left(i,j\\right)\\;\\text{s.t.}\\;i\\in L,j\\in \\left\\{0,\\ldots ,N-1-1\\right\\}\\\\\\text{scalar-vs-tensor}&\\quad \\displaystyle {x}_{i}\\geq 1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{tensor-vs-tensor}&\\quad \\displaystyle {x}_{i}\\leq {x}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\y&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\}\\\\z&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "L&\\text{Category Label}\\end{array}\n",
+       "\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"container-vs-scalar-comp\", sense=MINIMIZE, objective=0, constraints={dict-vs-dict: [Constraint(name=\"dict-vs-dict\", sense=LESS_THAN_EQUAL, left=y, right=z, shape=SameTotalDict { key: Located { inner: ElementOf { set: Located { inner: ToSet { operand: Located { inner: Tuple { components: [Located { inner: IterCategoryLabels { name: \"L\", ext: WithType { type_: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, Located { inner: OverloadedBinaryNumeric { operator: Located { inner: Sub, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, lhs: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) }, rhs: Located { inner: Literal { literal: Located { inner: Integer { value: Located { inner: 1, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: NoSrcSpan }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithTypeAndDictionary { type_: Scalar { mode: Static, kind: Natural }, dictionary: Scalar, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }], ext: WithType { type_: Tuple { components: [Located { inner: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, ext: WithTypeAndDictionary { type_: Set { element: Located { inner: Tuple { components: [Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, src_span: NoSrcSpan } }, dictionary: Product { component_dicts: [Set(CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }), FromNatural] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, value: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan }, scalar: Binary }),],dict-vs-scalar: [Constraint(name=\"dict-vs-scalar\", sense=LESS_THAN_EQUAL, left=y, right=5, shape=TotalDictVsScalar { key: Located { inner: ElementOf { set: Located { inner: ToSet { operand: Located { inner: Tuple { components: [Located { inner: IterCategoryLabels { name: \"L\", ext: WithType { type_: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, Located { inner: OverloadedBinaryNumeric { operator: Located { inner: Sub, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, lhs: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) }, rhs: Located { inner: Literal { literal: Located { inner: Integer { value: Located { inner: 1, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: NoSrcSpan }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithTypeAndDictionary { type_: Scalar { mode: Static, kind: Natural }, dictionary: Scalar, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }], ext: WithType { type_: Tuple { components: [Located { inner: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, ext: WithTypeAndDictionary { type_: Set { element: Located { inner: Tuple { components: [Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, src_span: NoSrcSpan } }, dictionary: Product { component_dicts: [Set(CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }), FromNatural] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, value: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan }, scalar: Natural }),],scalar-vs-tensor: [Constraint(name=\"scalar-vs-tensor\", sense=GREATER_THAN_EQUAL, left=x, right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],tensor-vs-tensor: [Constraint(name=\"tensor-vs-tensor\", sense=LESS_THAN_EQUAL, left=x, right=x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_43978/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],})"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"container-vs-scalar-comp\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Natural()\n",
+    "    L = problem.CategoryLabel()\n",
+    "    x = problem.BinaryVar(shape=N)\n",
+    "    y = problem.BinaryVar(dict_keys=(L, N - 1))\n",
+    "    z = problem.BinaryVar(dict_keys=(L, N - 1))\n",
+    "\n",
+    "    problem += problem.Constraint(\"scalar-vs-tensor\", 1 <= x)\n",
+    "    problem += problem.Constraint(\"tensor-vs-tensor\", x <= x)\n",
+    "    problem += problem.Constraint(\"dict-vs-scalar\", y <= 5)\n",
+    "    problem += problem.Constraint(\"dict-vs-dict\", y <= z)\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8ffaa668",
+   "metadata": {},
+   "source": [
+    "### Bounded naturals and category labels are now allowed as a `Placeholder` `dtype`\n",
+    "\n",
+    "The `dtype` argument of {py:meth}`Problem.Placeholder <jijmodeling.Problem.Placeholder>` (and its shorthands such as `Graph`, `PartialDict`, and `TotalDict`) used to be limited to a `jm.DataType`, a NumPy scalar type, or a tuple built out of those.\n",
+    "Starting with this version, `dtype` additionally accepts:\n",
+    "\n",
+    "- a natural-number expression `n`, declaring that the values are natural numbers strictly less than `n` (i.e. drawn from $\\{0, 1, \\dots, n - 1\\}$); the bound `n` may also be a Python integer literal or another placeholder/named expression of natural-number type.\n",
+    "- a {py:class}`~jijmodeling.CategoryLabel` `L`, declaring that the values are labels drawn from `L`.\n",
+    "- a tuple `(T, T, ...)` whose components are any of the above (or any other accepted `dtype`).\n",
+    "\n",
+    "Along with the additions on `dtype` as described above, the shorthand constructors {py:meth}`Problem.Natural <jijmodeling.Problem.Natural>` (and its aliases: {py:meth}`Problem.Length <jijmodeling.Problem.Length>` and {py:meth}`Problem.Dim <jijmodeling.Problem.Dim>`) now also accept a `less_than=natexpr` keyword argument. This declares the same bounded-natural type placeholder variable as `Placeholder(dtype=natexpr)`, while more clearly communicating the intent of it being a scalar natural placeholder:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f9fbbd9e",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:24.725749Z",
+     "iopub.status.busy": "2026-06-04T03:14:24.725686Z",
+     "iopub.status.idle": "2026-06-04T03:14:24.797481Z",
+     "shell.execute_reply": "2026-06-04T03:14:24.797110Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{bounded natural shorthand}\\\\\\displaystyle \\min &\\displaystyle {x}_{i}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}i&\\in N&\\quad &\\text{A scalar placeholder in }N\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"bounded natural shorthand\", sense=MINIMIZE, objective=x[i], constraints=[])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"bounded natural shorthand\")\n",
+    "N = problem.Natural(\"N\")\n",
+    "i = problem.Natural(\"i\", less_than=N)\n",
+    "x = problem.BinaryVar(\"x\", shape=(N,))\n",
+    "problem += x[i]\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f3bc6378",
+   "metadata": {},
+   "source": [
+    "The same keyword argument is available in the Decorator API:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "d351d778",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:24.798593Z",
+     "iopub.status.busy": "2026-06-04T03:14:24.798534Z",
+     "iopub.status.idle": "2026-06-04T03:14:24.873968Z",
+     "shell.execute_reply": "2026-06-04T03:14:24.873598Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{bounded natural shorthand in Decorator API}\\\\\\displaystyle \\min &\\displaystyle {x}_{i}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}i&\\in N&\\quad &\\text{A scalar placeholder in }N\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"bounded natural shorthand in Decorator API\", sense=MINIMIZE, objective=x[i], constraints=[])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "@jm.Problem.define(\"bounded natural shorthand in Decorator API\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Length()\n",
+    "    i = problem.Dim(less_than=N)\n",
+    "    x = problem.BinaryVar(shape=(N,))\n",
+    "    problem += x[i]\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48e01c2e",
+   "metadata": {},
+   "source": [
+    "For a more complex example, consider the following optimization problem involving an undirected graph $G = (V, E)$. Previously, edge endpoints had to be declared as plain naturals; with this release you can express the intent that they must lie in $[0, V)$:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "bd4e7945",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:24.874913Z",
+     "iopub.status.busy": "2026-06-04T03:14:24.874854Z",
+     "iopub.status.idle": "2026-06-04T03:14:25.079884Z",
+     "shell.execute_reply": "2026-06-04T03:14:25.079570Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{max cut}\\\\\\displaystyle \\max &\\displaystyle \\sum _{\\left\\langle u,v\\right\\rangle \\in E}{{\\left({x}_{u}-{x}_{v}\\right)}^{2}}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[V;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}E&\\in \\mathop{\\mathrm{Array}}\\left[(-);V\\times V\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }V\\times V\\\\V&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"max cut\", sense=MAXIMIZE, objective=sum(E.map(lambda ((u, v): Tuple[V, V]): (x[u] - x[v]) ** 2)), constraints=[])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"max cut\", sense=jm.ProblemSense.MAXIMIZE)\n",
+    "V = problem.Natural(\"V\")\n",
+    "# We can now say that each entry of `E` is a pair of vertices in [0, V)\n",
+    "# (previously we had to write dtype=(jm.DataType.Natural, jm.DataType.Natural)).\n",
+    "# Alternatively, we may write this as problem.graph(\"E\", dtype=V)\n",
+    "E = problem.Placeholder(\"E\", dtype=(V, V), ndim=1)\n",
+    "x = problem.BinaryVar(\"x\", shape=(V,))\n",
+    "problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, E).sum()\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "82d88a43",
+   "metadata": {},
+   "source": [
+    "When the vertices of a graph are named rather than indexed, a {py:class}`~jijmodeling.CategoryLabel` can now be used directly as the `dtype`.\n",
+    "Here is the same problem, written with {py:meth}`Problem.Graph`, but on a graph whose vertices are identified by labels rather than integer indices:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "282beebb",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:25.080968Z",
+     "iopub.status.busy": "2026-06-04T03:14:25.080890Z",
+     "iopub.status.idle": "2026-06-04T03:14:25.637898Z",
+     "shell.execute_reply": "2026-06-04T03:14:25.637535Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "problem = jm.Problem(\"max cut on a labeled graph\", sense=jm.ProblemSense.MAXIMIZE)\n",
+    "L = problem.CategoryLabel(\"L\")\n",
+    "edges = problem.Graph(\"edges\", dtype=L)\n",
+    "x = problem.BinaryVar(\"x\", dict_keys=L)\n",
+    "problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, edges).sum()\n",
+    "\n",
+    "compiler = jm.Compiler.from_problem(\n",
+    "    problem,\n",
+    "    {\n",
+    "        \"L\": [\"A\", \"B\", \"C\"],\n",
+    "        \"edges\": [(\"A\", \"B\"), (\"B\", \"C\"), (\"C\", \"A\")],\n",
+    "    },\n",
+    ")\n",
+    "instance = compiler.eval_problem(problem)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b3c0355a",
+   "metadata": {},
+   "source": [
+    "When a value supplied through the instance data is not consistent with the declared `dtype` (for example a vertex index $\\geq V$, or a label not in `L`), the compiler will report an out-of-range error instead of silently accepting the value."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "set-objective-assignment",
+   "metadata": {},
+   "source": [
+    "### Objective functions can now be replaced by assignment\n",
+    "\n",
+    "In this version, you can now replace the objective function directly by assigning to {py:attr}`Problem.objective <jijmodeling.Problem.objective>`.\n",
+    "The same `problem.objective = ...` syntax is also available for {py:class}`~jijmodeling.DecoratedProblem`.\n",
+    "\n",
+    "For example, you can replace an already-defined objective with another expression, or explicitly reset it with `problem.objective = 0`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "set-objective-assignment-example",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:25.639089Z",
+     "iopub.status.busy": "2026-06-04T03:14:25.638983Z",
+     "iopub.status.idle": "2026-06-04T03:14:25.709430Z",
+     "shell.execute_reply": "2026-06-04T03:14:25.709093Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{set objective example}\\\\\\displaystyle \\min &\\displaystyle z\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\y&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\z&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"set objective example\", sense=MINIMIZE, objective=z, constraints=[])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"set objective example\")\n",
+    "x = problem.BinaryVar(\"x\")\n",
+    "y = problem.BinaryVar(\"y\")\n",
+    "\n",
+    "problem.objective = x\n",
+    "problem.objective = y\n",
+    "problem.objective = 0\n",
+    "\n",
+    "\n",
+    "@problem.update\n",
+    "def _(problem: jm.DecoratedProblem):\n",
+    "    z = problem.BinaryVar()\n",
+    "    problem.objective = z\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ff2502fc",
+   "metadata": {},
+   "source": [
+    "### Generating dictionaries with generator functions\n",
+    "\n",
+    "Starting with this version, the {py:func}`~jijmodeling.gendict` function can be used to generate dictionaries by specifying a set of keys and a generator function.\n",
+    "This is similar to the array version {py:func}`~jijmodeling.genarray`, and to NumPy's {py:func}`~numpy.fromfunction`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "d4ea0168",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:25.710355Z",
+     "iopub.status.busy": "2026-06-04T03:14:25.710297Z",
+     "iopub.status.idle": "2026-06-04T03:14:25.811912Z",
+     "shell.execute_reply": "2026-06-04T03:14:25.811322Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{gendict example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{K};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }K\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{K};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{K}\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "K&\\text{Category Label}\\end{array}\n",
+       "\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}Sums&=\\mathop{\\mathtt{gen\\_{}dict}}\\left(\\lambda \\left(k\\in \\mathrm{K}\\right)\\ldotp {a}_{k}\\cdot {x}_{k},K\\right)&\\quad &\\in \\mathop{\\mathrm{TotalDict}}\\left[K;\\mathbb{R}\\right]\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"gendict example\", sense=MINIMIZE, objective=0, constraints=[])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "problem = jm.Problem(\"gendict example\")\n",
+    "K = problem.CategoryLabel(\"K\")\n",
+    "a = problem.Float(\"a\", dict_keys=K)\n",
+    "x = problem.BinaryVar(\"x\", dict_keys=K)\n",
+    "Sums = problem.NamedExpr(\"Sums\", jm.gendict(K, lambda k: a[k] * x[k]))\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "01bc6a3f",
+   "metadata": {},
+   "source": [
+    "Like `genarray`, using comprehensions is supported when using the Decorator API, but only one `for .. in ...` clause is allowed in a comprehension."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "95007f63",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:25.813151Z",
+     "iopub.status.busy": "2026-06-04T03:14:25.813091Z",
+     "iopub.status.idle": "2026-06-04T03:14:25.910339Z",
+     "shell.execute_reply": "2026-06-04T03:14:25.909980Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{gendict example}\\\\\\displaystyle \\min &\\displaystyle 0\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"gendict example\", sense=MINIMIZE, objective=0, constraints=[])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "@jm.Problem.define(\"gendict example\")\n",
+    "def problem(problem):\n",
+    "    problem = jm.Problem(\"gendict example\")\n",
+    "    K = problem.CategoryLabel(\"K\")\n",
+    "    a = problem.Float(\"a\", dict_keys=K)\n",
+    "    x = problem.BinaryVar(\"x\", dict_keys=K)\n",
+    "    Sums = problem.NamedExpr(\"Sums\", jm.gendict(a[k] * x[k] for k in K))\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bug-fixes",
+   "metadata": {},
+   "source": [
+    "## Bug Fixes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8bbdb161",
+   "metadata": {},
+   "source": [
+    "### Fix bug where operations between subscript elements and numeric types failed\n",
+    "\n",
+    "Fixed an issue where numeric operations on `Constraint` subscript elements, as shown below, were incorrectly treated as type errors."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "55a7ce10",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:25.911462Z",
+     "iopub.status.busy": "2026-06-04T03:14:25.911410Z",
+     "iopub.status.idle": "2026-06-04T03:14:26.055197Z",
+     "shell.execute_reply": "2026-06-04T03:14:26.054864Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
+       "\\text{c}&\\quad \\displaystyle k\\cdot x\\leq 0\\quad \\forall k\\;\\text{s.t.}\\;k\\in K\\end{aligned}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"Example\", sense=MINIMIZE, objective=0, constraints={c: [Constraint(name=\"c\", , lambda k: k * x <= 0, domain=set(K)),],})"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"Example\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    K = problem.Float(ndim=1)\n",
+    "    x = problem.BinaryVar()\n",
+    "    problem += problem.Constraint(\"c\", [k * x <= 0 for k in K])\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98fed1a5",
+   "metadata": {},
+   "source": [
+    "### Improved math rendering for expressions involving `product` and `filter`\n",
+    "\n",
+    "Previously, expressions involving `product` and `filter` could be rendered as overly complex formulas in some cases. They are now displayed in a more readable form using comprehension-style notation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "fc510cb5",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:26.056375Z",
+     "iopub.status.busy": "2026-06-04T03:14:26.056311Z",
+     "iopub.status.idle": "2026-06-04T03:14:26.170598Z",
+     "shell.execute_reply": "2026-06-04T03:14:26.170268Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,M-1\\right\\},i=j\\right\\}$$"
+      ],
+      "text/plain": [
+       "Expression(set((N, M)).filter(lambda (i, j): i == j))"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"product and filter example\")\n",
+    "N = problem.Natural(\"N\")\n",
+    "M = problem.Natural(\"M\")\n",
+    "x = problem.BinaryVar(\"x\", shape=(N, M))\n",
+    "jm.product(N, M).filter(lambda i, j: i == j)"
+   ]
+  }
+ ],
+ "metadata": {
+  "jupytext": {
+   "default_lexer": "ipython3"
+  },
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/docs/ja/_toc.yml b/docs/ja/_toc.yml
index 2e6d73ec..dbe6e716 100644
--- a/docs/ja/_toc.yml
+++ b/docs/ja/_toc.yml
@@ -36,6 +36,7 @@ parts:
         title: 典型問題集
   - caption: Release Notes
     chapters:
+      - file: releases/jijmodeling-2.5.0
       - file: releases/jijmodeling-2.4.1
       - file: releases/jijmodeling-2.4.0
       - file: releases/jijmodeling-2.3.2
diff --git a/docs/ja/advanced/generation.ipynb b/docs/ja/advanced/generation.ipynb
index d9f383eb..e38a9915 100644
--- a/docs/ja/advanced/generation.ipynb
+++ b/docs/ja/advanced/generation.ipynb
@@ -40,17 +40,17 @@
    "id": "34020325-4747-42ce-ab64-4114e871dca0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:40.949446Z",
-     "iopub.status.busy": "2026-03-24T02:04:40.949109Z",
-     "iopub.status.idle": "2026-03-24T02:04:41.010745Z",
-     "shell.execute_reply": "2026-03-24T02:04:41.010319Z"
+     "iopub.execute_input": "2026-06-04T02:49:39.212159Z",
+     "iopub.status.busy": "2026-06-04T02:49:39.212089Z",
+     "iopub.status.idle": "2026-06-04T02:49:39.279588Z",
+     "shell.execute_reply": "2026-06-04T02:49:39.279162Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': 6, 'B': 1}"
+       "{'B': 1, 'A': 1}"
       ]
      },
      "execution_count": 1,
@@ -90,17 +90,17 @@
    "id": "9ea06ded-9bc5-4eb9-85c7-837538a5940b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:41.011898Z",
-     "iopub.status.busy": "2026-03-24T02:04:41.011838Z",
-     "iopub.status.idle": "2026-03-24T02:04:41.014289Z",
-     "shell.execute_reply": "2026-03-24T02:04:41.013956Z"
+     "iopub.execute_input": "2026-06-04T02:49:39.280822Z",
+     "iopub.status.busy": "2026-06-04T02:49:39.280766Z",
+     "iopub.status.idle": "2026-06-04T02:49:39.282907Z",
+     "shell.execute_reply": "2026-06-04T02:49:39.282590Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'B': 6, 'A': 81}"
+       "{'A': 64, 'B': 9}"
       ]
      },
      "execution_count": 2,
@@ -126,17 +126,17 @@
    "id": "8fedb42a-12d2-41f6-b3de-c989ea1aa4ab",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:41.015385Z",
-     "iopub.status.busy": "2026-03-24T02:04:41.015329Z",
-     "iopub.status.idle": "2026-03-24T02:04:41.017678Z",
-     "shell.execute_reply": "2026-03-24T02:04:41.017370Z"
+     "iopub.execute_input": "2026-06-04T02:49:39.283752Z",
+     "iopub.status.busy": "2026-06-04T02:49:39.283704Z",
+     "iopub.status.idle": "2026-06-04T02:49:39.285558Z",
+     "shell.execute_reply": "2026-06-04T02:49:39.285283Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': 69, 'B': 1}"
+       "{'B': 3, 'A': 96}"
       ]
      },
      "execution_count": 3,
@@ -164,17 +164,17 @@
    "id": "19a45cfe-40de-4e5e-9cad-62114b225b09",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:41.018524Z",
-     "iopub.status.busy": "2026-03-24T02:04:41.018472Z",
-     "iopub.status.idle": "2026-03-24T02:04:41.071480Z",
-     "shell.execute_reply": "2026-03-24T02:04:41.071114Z"
+     "iopub.execute_input": "2026-06-04T02:49:39.286439Z",
+     "iopub.status.busy": "2026-06-04T02:49:39.286397Z",
+     "iopub.status.idle": "2026-06-04T02:49:39.357918Z",
+     "shell.execute_reply": "2026-06-04T02:49:39.357583Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': array([1, 8, 4, 6, 7, 3, 8, 9, 6, 3], dtype=object)}"
+       "{'A': array([9, 5, 6, 9, 6, 1, 8, 1, 2, 3], dtype=object)}"
       ]
      },
      "execution_count": 4,
@@ -206,18 +206,18 @@
    "id": "ac97241e-47bd-4b5b-b8f6-49d5ddb43254",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:41.072644Z",
-     "iopub.status.busy": "2026-03-24T02:04:41.072558Z",
-     "iopub.status.idle": "2026-03-24T02:04:41.103176Z",
-     "shell.execute_reply": "2026-03-24T02:04:41.102769Z"
+     "iopub.execute_input": "2026-06-04T02:49:39.358992Z",
+     "iopub.status.busy": "2026-06-04T02:49:39.358912Z",
+     "iopub.status.idle": "2026-06-04T02:49:39.414891Z",
+     "shell.execute_reply": "2026-06-04T02:49:39.414576Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'A': array([7.922440851203646, -2.2362166205229705, -1.187315801401505,\n",
-       "        3.8729629770943053, 7.164100076039116], dtype=object)}"
+       "{'A': array([8.695305222150136, 3.42523979686813, 4.812904660791846,\n",
+       "        8.42347332514177], dtype=object)}"
       ]
      },
      "execution_count": 5,
@@ -303,7 +303,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/advanced/named_expr.ipynb b/docs/ja/advanced/named_expr.ipynb
index 5ad1b565..460cbeb3 100644
--- a/docs/ja/advanced/named_expr.ipynb
+++ b/docs/ja/advanced/named_expr.ipynb
@@ -44,10 +44,10 @@
    "id": "fa9c461b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:42.375128Z",
-     "iopub.status.busy": "2026-03-24T02:04:42.374891Z",
-     "iopub.status.idle": "2026-03-24T02:04:42.556974Z",
-     "shell.execute_reply": "2026-03-24T02:04:42.556630Z"
+     "iopub.execute_input": "2026-06-04T02:49:41.020930Z",
+     "iopub.status.busy": "2026-06-04T02:49:41.020870Z",
+     "iopub.status.idle": "2026-06-04T02:49:41.260528Z",
+     "shell.execute_reply": "2026-06-04T02:49:41.260233Z"
     }
    },
    "outputs": [
@@ -61,7 +61,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack (Unnamed)\", sense=MAXIMIZE, objective=sum(w.len_at(0).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(w.len_at(0).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack (Unnamed)\", sense=MAXIMIZE, objective=sum(set(w.len_at(0)).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(set(w.len_at(0)).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 1,
@@ -106,10 +106,10 @@
    "id": "225fa821",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:42.558188Z",
-     "iopub.status.busy": "2026-03-24T02:04:42.558125Z",
-     "iopub.status.idle": "2026-03-24T02:04:42.720393Z",
-     "shell.execute_reply": "2026-03-24T02:04:42.719977Z"
+     "iopub.execute_input": "2026-06-04T02:49:41.261834Z",
+     "iopub.status.busy": "2026-06-04T02:49:41.261774Z",
+     "iopub.status.idle": "2026-06-04T02:49:41.492731Z",
+     "shell.execute_reply": "2026-06-04T02:49:41.492388Z"
     }
    },
    "outputs": [
@@ -123,7 +123,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 2,
@@ -172,10 +172,10 @@
    "id": "21904726",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:42.721549Z",
-     "iopub.status.busy": "2026-03-24T02:04:42.721491Z",
-     "iopub.status.idle": "2026-03-24T02:04:43.863718Z",
-     "shell.execute_reply": "2026-03-24T02:04:43.863251Z"
+     "iopub.execute_input": "2026-06-04T02:49:41.494004Z",
+     "iopub.status.busy": "2026-06-04T02:49:41.493944Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.107794Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.107373Z"
     }
    },
    "outputs": [],
@@ -227,10 +227,10 @@
    "id": "eb75269d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:43.865210Z",
-     "iopub.status.busy": "2026-03-24T02:04:43.865074Z",
-     "iopub.status.idle": "2026-03-24T02:04:43.911678Z",
-     "shell.execute_reply": "2026-03-24T02:04:43.911374Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.109062Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.108959Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.168074Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.167739Z"
     }
    },
    "outputs": [
@@ -238,7 +238,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Scalar}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[5;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}scalar&=\\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}&\\quad &\\in \\left\\{0, 1\\right\\}\\\\&&&\\text{\\texttt{save\\_{}in\\_{}ommx=True}}\\\\\\end{alignedat}\\end{array}\n",
+       "\\text{Problem}\\colon &\\text{Scalar}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[5;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}scalar&=\\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}&\\quad &\\in \\mathbb{N}\\\\&&&\\text{\\texttt{save\\_{}in\\_{}ommx=True}}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
@@ -264,10 +264,10 @@
    "id": "f7b3b6f6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:43.912811Z",
-     "iopub.status.busy": "2026-03-24T02:04:43.912747Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.067702Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.067275Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.169122Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.169062Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.328031Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.327624Z"
     }
    },
    "outputs": [
@@ -302,10 +302,10 @@
    "id": "de572788",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.068809Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.068747Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.182892Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.182488Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.328977Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.328920Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.433280Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.433002Z"
     }
    },
    "outputs": [
@@ -351,10 +351,10 @@
    "id": "e269beca",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.185843Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.185711Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.193369Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.193003Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.434505Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.434453Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.441760Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.441503Z"
     }
    },
    "outputs": [],
@@ -368,10 +368,10 @@
    "id": "0e6ecc43",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.194486Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.194424Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.217104Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.216777Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.442807Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.442748Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.475441Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.475082Z"
     }
    },
    "outputs": [
@@ -398,10 +398,10 @@
    "id": "54225607",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.218549Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.218465Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.234275Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.233610Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.476345Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.476298Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.488952Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.488631Z"
     }
    },
    "outputs": [
@@ -428,10 +428,10 @@
    "id": "6b752e2b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.236620Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.236540Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.260785Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.260296Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.489877Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.489831Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.518566Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.518190Z"
     }
    },
    "outputs": [
@@ -476,10 +476,10 @@
    "id": "defa81a9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.262455Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.262374Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.523826Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.523286Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.519603Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.519557Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.808298Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.807922Z"
     }
    },
    "outputs": [
@@ -493,7 +493,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=total_weight, right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={Weight: [Constraint(name=\"Weight\", sense=LESS_THAN_EQUAL, left=total_weight, right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 11,
@@ -538,10 +538,10 @@
    "id": "9c8d7f15",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.525216Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.525127Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.907968Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.906899Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.809333Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.809276Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.897053Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.896598Z"
     }
    },
    "outputs": [],
@@ -563,10 +563,10 @@
    "id": "19f45fef",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.909993Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.909890Z",
-     "iopub.status.idle": "2026-03-24T02:04:44.921316Z",
-     "shell.execute_reply": "2026-03-24T02:04:44.920680Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.898236Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.898178Z",
+     "iopub.status.idle": "2026-06-04T02:49:42.907293Z",
+     "shell.execute_reply": "2026-06-04T02:49:42.906962Z"
     }
    },
    "outputs": [
@@ -672,10 +672,10 @@
    "id": "f78cf116",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:44.922518Z",
-     "iopub.status.busy": "2026-03-24T02:04:44.922450Z",
-     "iopub.status.idle": "2026-03-24T02:04:45.521929Z",
-     "shell.execute_reply": "2026-03-24T02:04:45.521624Z"
+     "iopub.execute_input": "2026-06-04T02:49:42.908189Z",
+     "iopub.status.busy": "2026-06-04T02:49:42.908142Z",
+     "iopub.status.idle": "2026-06-04T02:49:43.198165Z",
+     "shell.execute_reply": "2026-06-04T02:49:43.197840Z"
     }
    },
    "outputs": [
@@ -720,7 +720,7 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>46.0</td>\n",
+       "      <td>45.0</td>\n",
        "      <td>{0, 1, 2, 3, 4, 5}</td>\n",
        "      <td>total_weight</td>\n",
        "      <td>[]</td>\n",
@@ -734,7 +734,7 @@
       "text/plain": [
        "    value            used_ids          name subscripts  \\\n",
        "id                                                       \n",
-       "0    46.0  {0, 1, 2, 3, 4, 5}  total_weight         []   \n",
+       "0    45.0  {0, 1, 2, 3, 4, 5}  total_weight         []   \n",
        "\n",
        "                              description parameters.subscripts  \n",
        "id                                                               \n",
@@ -788,7 +788,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/advanced/serialize.ipynb b/docs/ja/advanced/serialize.ipynb
index c889da90..78d238b7 100644
--- a/docs/ja/advanced/serialize.ipynb
+++ b/docs/ja/advanced/serialize.ipynb
@@ -16,10 +16,10 @@
    "id": "b5807c3d-8bd3-4d3e-92bd-6cfa802cd625",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:46.910294Z",
-     "iopub.status.busy": "2026-03-24T02:04:46.910240Z",
-     "iopub.status.idle": "2026-03-24T02:04:46.952123Z",
-     "shell.execute_reply": "2026-03-24T02:04:46.951739Z"
+     "iopub.execute_input": "2026-06-04T02:49:44.360966Z",
+     "iopub.status.busy": "2026-06-04T02:49:44.360838Z",
+     "iopub.status.idle": "2026-06-04T02:49:44.418566Z",
+     "shell.execute_reply": "2026-06-04T02:49:44.418161Z"
     }
    },
    "outputs": [],
@@ -48,10 +48,10 @@
    "id": "fb7345c2-2252-4c3a-ae46-9e6318a4fa9a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:46.953331Z",
-     "iopub.status.busy": "2026-03-24T02:04:46.953275Z",
-     "iopub.status.idle": "2026-03-24T02:04:46.958699Z",
-     "shell.execute_reply": "2026-03-24T02:04:46.958422Z"
+     "iopub.execute_input": "2026-06-04T02:49:44.419866Z",
+     "iopub.status.busy": "2026-06-04T02:49:44.419803Z",
+     "iopub.status.idle": "2026-06-04T02:49:44.424309Z",
+     "shell.execute_reply": "2026-06-04T02:49:44.423975Z"
     }
    },
    "outputs": [],
@@ -79,7 +79,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/basics/expressions.ipynb b/docs/ja/basics/expressions.ipynb
index 3007ff72..ff8aa8be 100644
--- a/docs/ja/basics/expressions.ipynb
+++ b/docs/ja/basics/expressions.ipynb
@@ -25,10 +25,10 @@
    "id": "a065d0ee",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:04.740233Z",
-     "iopub.status.busy": "2026-04-16T07:04:04.740139Z",
-     "iopub.status.idle": "2026-04-16T07:04:04.768519Z",
-     "shell.execute_reply": "2026-04-16T07:04:04.764810Z"
+     "iopub.execute_input": "2026-06-04T02:49:31.633340Z",
+     "iopub.status.busy": "2026-06-04T02:49:31.633084Z",
+     "iopub.status.idle": "2026-06-04T02:49:31.646686Z",
+     "shell.execute_reply": "2026-06-04T02:49:31.645836Z"
     }
    },
    "outputs": [],
@@ -57,10 +57,10 @@
    "id": "beaddc39",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:04.775259Z",
-     "iopub.status.busy": "2026-04-16T07:04:04.774997Z",
-     "iopub.status.idle": "2026-04-16T07:04:05.036085Z",
-     "shell.execute_reply": "2026-04-16T07:04:05.035587Z"
+     "iopub.execute_input": "2026-06-04T02:49:31.648009Z",
+     "iopub.status.busy": "2026-06-04T02:49:31.647920Z",
+     "iopub.status.idle": "2026-06-04T02:49:31.753151Z",
+     "shell.execute_reply": "2026-06-04T02:49:31.752828Z"
     },
     "label": "test-problem"
    },
@@ -177,10 +177,10 @@
    "id": "e73538ae",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:05.037667Z",
-     "iopub.status.busy": "2026-04-16T07:04:05.037573Z",
-     "iopub.status.idle": "2026-04-16T07:04:05.092196Z",
-     "shell.execute_reply": "2026-04-16T07:04:05.091774Z"
+     "iopub.execute_input": "2026-06-04T02:49:31.754195Z",
+     "iopub.status.busy": "2026-06-04T02:49:31.754143Z",
+     "iopub.status.idle": "2026-06-04T02:49:31.782889Z",
+     "shell.execute_reply": "2026-06-04T02:49:31.782464Z"
     }
    },
    "outputs": [
@@ -220,10 +220,10 @@
    "id": "b525d6c0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:05.093666Z",
-     "iopub.status.busy": "2026-04-16T07:04:05.093586Z",
-     "iopub.status.idle": "2026-04-16T07:04:05.112806Z",
-     "shell.execute_reply": "2026-04-16T07:04:05.112344Z"
+     "iopub.execute_input": "2026-06-04T02:49:31.783952Z",
+     "iopub.status.busy": "2026-06-04T02:49:31.783879Z",
+     "iopub.status.idle": "2026-06-04T02:49:31.818278Z",
+     "shell.execute_reply": "2026-06-04T02:49:31.817632Z"
     }
    },
    "outputs": [
@@ -233,13 +233,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `x + Located { inner: \"hoge\", src_span: NoSrcSpan }',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/2391251849.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/2391251849.py\", line 3, col 19-29\n",
       "    while inferring the type of expression `x + Located { inner: \"hoge\", src_span: NoSrcSpan }',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/2391251849.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/2391251849.py\", line 3, col 19-29\n",
       "    while checking if types `binary!' and `Literal[\"hoge\"]' can be combined with numeric operator `Add',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/2391251849.py\", line 3, col 19-29\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/2391251849.py\", line 3, col 19-29\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/2391251849.py\", line 3, col 19-29:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/2391251849.py\", line 3, col 19-29:\n",
       "\n",
       "    3  |      problem.infer(x + \"hoge\")\n",
       "                            ^^^^^^^^^^\n",
@@ -312,10 +312,10 @@
    "id": "5de5e593",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:05.114276Z",
-     "iopub.status.busy": "2026-04-16T07:04:05.114194Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.402997Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.402602Z"
+     "iopub.execute_input": "2026-06-04T02:49:31.819446Z",
+     "iopub.status.busy": "2026-06-04T02:49:31.819363Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.121916Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.121482Z"
     }
    },
    "outputs": [
@@ -371,10 +371,10 @@
    "id": "3aa8e74d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.404250Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.404156Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.420719Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.420340Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.123052Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.122973Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.137865Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.137590Z"
     }
    },
    "outputs": [
@@ -402,10 +402,10 @@
    "id": "f7348dfe",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.421767Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.421713Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.511448Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.511111Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.138984Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.138936Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.166617Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.166341Z"
     }
    },
    "outputs": [
@@ -433,10 +433,10 @@
    "id": "200cbd4b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.512517Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.512458Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.607426Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.606963Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.167602Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.167540Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.189346Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.188984Z"
     }
    },
    "outputs": [
@@ -464,10 +464,10 @@
    "id": "e9405fa6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.608524Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.608464Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.703975Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.703612Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.190348Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.190303Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.218367Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.218045Z"
     }
    },
    "outputs": [
@@ -495,10 +495,10 @@
    "id": "1dff7e02",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.705222Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.705161Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.795627Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.795268Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.219327Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.219273Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.240363Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.240092Z"
     }
    },
    "outputs": [
@@ -534,10 +534,10 @@
    "id": "7a5b888f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.796819Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.796744Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.816870Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.816344Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.241444Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.241395Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.255023Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.254752Z"
     }
    },
    "outputs": [
@@ -547,13 +547,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `S * y',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3719066850.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3719066850.py\", line 3, col 19-24\n",
       "    while inferring the type of expression `S * y',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3719066850.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3719066850.py\", line 3, col 19-24\n",
       "    while checking if types `TotalDict[N; float]' and `Array[N, M; int!]' can be combined with numeric operator `Mul',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3719066850.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3719066850.py\", line 3, col 19-24\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3719066850.py\", line 3, col 19-24:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3719066850.py\", line 3, col 19-24:\n",
       "\n",
       "    3  |      problem.infer(S * y)\n",
       "                            ^^^^^\n",
@@ -576,10 +576,10 @@
    "id": "7bf01863",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.819579Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.819047Z",
-     "iopub.status.idle": "2026-04-16T07:04:06.842386Z",
-     "shell.execute_reply": "2026-04-16T07:04:06.842098Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.256028Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.255977Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.270069Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.269802Z"
     }
    },
    "outputs": [
@@ -589,13 +589,13 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while inferring the type of expression `y + z',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3550267328.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3550267328.py\", line 3, col 19-24\n",
       "    while inferring the type of expression `y + z',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3550267328.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3550267328.py\", line 3, col 19-24\n",
       "    while checking if types `Array[N, M; int!]' and `Array[N, M, N; float!]' can be combined with numeric operator `Add',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3550267328.py\", line 3, col 19-24\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3550267328.py\", line 3, col 19-24\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_63555/3550267328.py\", line 3, col 19-24:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2790/3550267328.py\", line 3, col 19-24:\n",
       "\n",
       "    3  |      problem.infer(y + z)\n",
       "                            ^^^^^\n",
@@ -629,10 +629,10 @@
    "id": "8caa0e4b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:06.843768Z",
-     "iopub.status.busy": "2026-04-16T07:04:06.843710Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.112763Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.112429Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.271050Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.271004Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.339579Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.339351Z"
     }
    },
    "outputs": [
@@ -682,10 +682,10 @@
    "id": "eec6742a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.114983Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.114893Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.380626Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.380075Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.340713Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.340665Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.426221Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.425836Z"
     }
    },
    "outputs": [
@@ -737,10 +737,10 @@
    "id": "0683580a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.381879Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.381817Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.395525Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.394961Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.427368Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.427307Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.436284Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.435933Z"
     }
    },
    "outputs": [
@@ -804,14 +804,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "id": "19d6caee",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.515824Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.515737Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.623423Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.622939Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.437265Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.437216Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.465052Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.464744Z"
     }
    },
    "outputs": [
@@ -824,7 +824,7 @@
        "Comparison[binary!, Array[N, M; int!]]"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -835,14 +835,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "id": "0829b0d0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.624679Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.624605Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.642826Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.642439Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.466205Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.466145Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.480981Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.480575Z"
     }
    },
    "outputs": [
@@ -855,7 +855,7 @@
        "bool"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -866,14 +866,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "id": "98865e29",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.644241Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.644068Z",
-     "iopub.status.idle": "2026-04-16T07:04:07.882949Z",
-     "shell.execute_reply": "2026-04-16T07:04:07.882562Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.481909Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.481861Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.522651Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.522249Z"
     }
    },
    "outputs": [
@@ -886,7 +886,7 @@
        "Comparison[Array[N, M; float!], Array[N, M; float!]]"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -931,14 +931,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "id": "6e97e0ff",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:07.884099Z",
-     "iopub.status.busy": "2026-04-16T07:04:07.884041Z",
-     "iopub.status.idle": "2026-04-16T07:04:08.231863Z",
-     "shell.execute_reply": "2026-04-16T07:04:08.231547Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.523638Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.523586Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.679506Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.679208Z"
     }
    },
    "outputs": [
@@ -946,7 +946,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Index and Keys Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathop{\\mathtt{keys}}\\left(S\\right);\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\mathop{\\mathtt{keys}}\\left(S\\right)\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\S&\\in \\mathop{\\mathrm{PartialDict}}\\left[N\\times L;\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }N\\times L\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Index and Keys Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathop{\\mathtt{keys}}\\left(S\\right);\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\mathop{\\mathtt{keys}}\\left(S\\right)\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\S&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in L\\right\\};\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in L\\right\\}\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "L&\\text{Category Label}\\end{array}\n",
        "\\end{array}\n",
        "$$"
@@ -955,7 +955,7 @@
        "Problem(name=\"Index and Keys Example\", sense=MINIMIZE, objective=0, constraints=[])"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1028,14 +1028,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "id": "17eb39a1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:08.233129Z",
-     "iopub.status.busy": "2026-04-16T07:04:08.233060Z",
-     "iopub.status.idle": "2026-04-16T07:04:08.686641Z",
-     "shell.execute_reply": "2026-04-16T07:04:08.686282Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.680642Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.680586Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.794909Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.794595Z"
     }
    },
    "outputs": [
@@ -1050,7 +1050,7 @@
        "Problem(name=\"Sum Example\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1082,14 +1082,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "id": "dffc0a7b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:08.687870Z",
-     "iopub.status.busy": "2026-04-16T07:04:08.687791Z",
-     "iopub.status.idle": "2026-04-16T07:04:08.737062Z",
-     "shell.execute_reply": "2026-04-16T07:04:08.736722Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.796075Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.796016Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.826766Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.826411Z"
     }
    },
    "outputs": [
@@ -1125,14 +1125,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
    "id": "15434b93",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:08.738170Z",
-     "iopub.status.busy": "2026-04-16T07:04:08.738115Z",
-     "iopub.status.idle": "2026-04-16T07:04:09.149340Z",
-     "shell.execute_reply": "2026-04-16T07:04:09.148064Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.827903Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.827854Z",
+     "iopub.status.idle": "2026-06-04T02:49:32.924734Z",
+     "shell.execute_reply": "2026-06-04T02:49:32.924379Z"
     }
    },
    "outputs": [
@@ -1147,7 +1147,7 @@
        "Problem(name=\"Sum Example (Plain)\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1172,14 +1172,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 23,
    "id": "0112b897",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:09.150683Z",
-     "iopub.status.busy": "2026-04-16T07:04:09.150617Z",
-     "iopub.status.idle": "2026-04-16T07:04:09.548851Z",
-     "shell.execute_reply": "2026-04-16T07:04:09.548325Z"
+     "iopub.execute_input": "2026-06-04T02:49:32.925741Z",
+     "iopub.status.busy": "2026-06-04T02:49:32.925683Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.048818Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.048107Z"
     }
    },
    "outputs": [
@@ -1191,10 +1191,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Sum Example (Plain, Alt)\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"Sum Example (Plain, Alt)\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1227,14 +1227,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 24,
    "id": "84a0a84c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:09.550085Z",
-     "iopub.status.busy": "2026-04-16T07:04:09.550015Z",
-     "iopub.status.idle": "2026-04-16T07:04:10.030400Z",
-     "shell.execute_reply": "2026-04-16T07:04:10.029923Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.051356Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.051111Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.257297Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.256962Z"
     }
    },
    "outputs": [
@@ -1249,7 +1249,7 @@
        "Problem(name=\"Even Sum Example\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0)).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1276,14 +1276,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 25,
    "id": "1e520da7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:10.031620Z",
-     "iopub.status.busy": "2026-04-16T07:04:10.031566Z",
-     "iopub.status.idle": "2026-04-16T07:04:10.530312Z",
-     "shell.execute_reply": "2026-04-16T07:04:10.516385Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.258478Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.258424Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.416765Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.416419Z"
     }
    },
    "outputs": [
@@ -1295,10 +1295,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Even Sum Example (Plain)\", sense=MINIMIZE, objective=sum(N.filter(lambda i: i % 2 == 0).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"Even Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0)).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1328,14 +1328,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 26,
    "id": "28b8bad3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:10.534229Z",
-     "iopub.status.busy": "2026-04-16T07:04:10.533832Z",
-     "iopub.status.idle": "2026-04-16T07:04:11.091517Z",
-     "shell.execute_reply": "2026-04-16T07:04:11.091121Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.417937Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.417881Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.576687Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.576362Z"
     }
    },
    "outputs": [
@@ -1350,7 +1350,7 @@
        "Problem(name=\"Double Sum Example\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): M.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1378,14 +1378,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "id": "385cb7b1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:11.092772Z",
-     "iopub.status.busy": "2026-04-16T07:04:11.092711Z",
-     "iopub.status.idle": "2026-04-16T07:04:11.573549Z",
-     "shell.execute_reply": "2026-04-16T07:04:11.573230Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.577819Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.577764Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.716040Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.715666Z"
     }
    },
    "outputs": [
@@ -1400,7 +1400,7 @@
        "Problem(name=\"Double Sum Example (Alt)\", sense=MINIMIZE, objective=sum(set(set((N, M))).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1428,14 +1428,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
    "id": "710245ee",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:11.574879Z",
-     "iopub.status.busy": "2026-04-16T07:04:11.574810Z",
-     "iopub.status.idle": "2026-04-16T07:04:12.098044Z",
-     "shell.execute_reply": "2026-04-16T07:04:12.097699Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.717321Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.717264Z",
+     "iopub.status.idle": "2026-06-04T02:49:33.850140Z",
+     "shell.execute_reply": "2026-06-04T02:49:33.849737Z"
     }
    },
    "outputs": [
@@ -1450,7 +1450,7 @@
        "Problem(name=\"Double Sum Example (Alt)\", sense=MINIMIZE, objective=sum(set((N, M)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1480,14 +1480,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 29,
    "id": "3362f83d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:12.099290Z",
-     "iopub.status.busy": "2026-04-16T07:04:12.099216Z",
-     "iopub.status.idle": "2026-04-16T07:04:13.001106Z",
-     "shell.execute_reply": "2026-04-16T07:04:13.000669Z"
+     "iopub.execute_input": "2026-06-04T02:49:33.851135Z",
+     "iopub.status.busy": "2026-06-04T02:49:33.851076Z",
+     "iopub.status.idle": "2026-06-04T02:49:34.052101Z",
+     "shell.execute_reply": "2026-06-04T02:49:34.051739Z"
     }
    },
    "outputs": [
@@ -1502,7 +1502,7 @@
        "Problem(name=\"Filtered Double Sum Example\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): M.map(lambda (j: natural): (i, j))).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1535,14 +1535,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 30,
    "id": "7c2e2ab9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:13.002348Z",
-     "iopub.status.busy": "2026-04-16T07:04:13.002288Z",
-     "iopub.status.idle": "2026-04-16T07:04:13.610579Z",
-     "shell.execute_reply": "2026-04-16T07:04:13.609824Z"
+     "iopub.execute_input": "2026-06-04T02:49:34.053226Z",
+     "iopub.status.busy": "2026-06-04T02:49:34.053166Z",
+     "iopub.status.idle": "2026-06-04T02:49:34.218018Z",
+     "shell.execute_reply": "2026-06-04T02:49:34.217626Z"
     }
    },
    "outputs": [
@@ -1554,10 +1554,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Filtered Double Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set((N, M)).filter(lambda (i, j): (i + j) % 2 == 0).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
+       "Problem(name=\"Filtered Double Sum Example (Plain)\", sense=MINIMIZE, objective=sum(set(set((N, M)).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda ((i, j): Tuple[natural, natural]): Q[i, j])), constraints=[])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1585,14 +1585,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 31,
    "id": "2027a720",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-16T07:04:13.612856Z",
-     "iopub.status.busy": "2026-04-16T07:04:13.612757Z",
-     "iopub.status.idle": "2026-04-16T07:04:13.993722Z",
-     "shell.execute_reply": "2026-04-16T07:04:13.993261Z"
+     "iopub.execute_input": "2026-06-04T02:49:34.219137Z",
+     "iopub.status.busy": "2026-06-04T02:49:34.219076Z",
+     "iopub.status.idle": "2026-06-04T02:49:34.336602Z",
+     "shell.execute_reply": "2026-06-04T02:49:34.336222Z"
     }
    },
    "outputs": [
@@ -1602,10 +1602,10 @@
        "$$\\sum _{i=0}^{N-1}{\\sum _{\\substack{j=0\\\\\\left(i+j\\right)\\bmod 2=0}}^{M-1}{{Q}_{i,j}}}$$"
       ],
       "text/plain": [
-       "Expression(sum(N.flat_map(lambda i: M.map(lambda j: (i, j))).filter(lambda (i, j): (i + j) % 2 == 0).map(lambda (i, j): Q[i, j])))"
+       "Expression(sum(set(N.flat_map(lambda i: M.map(lambda j: (i, j))).filter(lambda (i, j): (i + j) % 2 == 0)).map(lambda (i, j): Q[i, j])))"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/docs/ja/basics/instance_generation.ipynb b/docs/ja/basics/instance_generation.ipynb
index 3184d81e..380744ea 100644
--- a/docs/ja/basics/instance_generation.ipynb
+++ b/docs/ja/basics/instance_generation.ipynb
@@ -30,10 +30,10 @@
    "id": "2fbc556e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:17.722025Z",
-     "iopub.status.busy": "2026-03-24T02:04:17.721838Z",
-     "iopub.status.idle": "2026-03-24T02:04:18.093380Z",
-     "shell.execute_reply": "2026-03-24T02:04:18.092879Z"
+     "iopub.execute_input": "2026-06-04T02:49:23.099686Z",
+     "iopub.status.busy": "2026-06-04T02:49:23.099628Z",
+     "iopub.status.idle": "2026-06-04T02:49:24.094796Z",
+     "shell.execute_reply": "2026-06-04T02:49:24.094449Z"
     }
    },
    "outputs": [
@@ -43,11 +43,11 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{Knapsack with Synergy}\\\\\\displaystyle \\max &\\displaystyle \\sum _{i=0}^{N-1}{{v}_{i}\\cdot {x}_{i}}+\\sum _{\\left\\langle i,j\\right\\rangle \\in \\mathop{\\mathtt{keys}}\\left(s\\right)}{{s}_{i,j}\\cdot {x}_{i}\\cdot {x}_{j}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{weight}&\\quad \\displaystyle \\sum _{i=0}^{N-1}{{w}_{i}\\cdot {x}_{i}}\\leq W\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\&&&\\text{Item selection variables}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[N\\times N;\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }N\\times N\\text{, values in }\\mathbb{R}\\\\&&&\\text{Synergy bonus between items}\\\\&&&\\\\v&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Values of the items}\\\\&&&\\\\W&\\in \\mathbb{R}&\\quad &\\text{A scalar placeholder in }\\mathbb{R}\\\\&&&\\text{Weight limit of the problem}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Weights of the items}\\\\\\end{alignedat}\\end{array}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\&&&\\text{Item selection variables}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\};\\mathbb{R}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\}\\text{, values in }\\mathbb{R}\\\\&&&\\text{Synergy bonus between items}\\\\&&&\\\\v&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Values of the items}\\\\&&&\\\\W&\\in \\mathbb{R}&\\quad &\\text{A scalar placeholder in }\\mathbb{R}\\\\&&&\\text{Weight limit of the problem}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{Weights of the items}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack with Synergy\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])) + sum(s.keys().map(lambda ((i, j): ElementOf[set((N, N))]): s[i, j] * x[i] * x[j])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack with Synergy\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])) + sum(set(s.keys()).map(lambda ((i, j): ElementOf[set((N, N))]): s[i, j] * x[i] * x[j])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
      "execution_count": 1,
@@ -109,10 +109,10 @@
    "id": "df329286",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:18.094670Z",
-     "iopub.status.busy": "2026-03-24T02:04:18.094567Z",
-     "iopub.status.idle": "2026-03-24T02:04:18.096930Z",
-     "shell.execute_reply": "2026-03-24T02:04:18.096592Z"
+     "iopub.execute_input": "2026-06-04T02:49:24.096676Z",
+     "iopub.status.busy": "2026-06-04T02:49:24.096564Z",
+     "iopub.status.idle": "2026-06-04T02:49:24.098931Z",
+     "shell.execute_reply": "2026-06-04T02:49:24.098533Z"
     }
    },
    "outputs": [],
@@ -161,10 +161,10 @@
    "id": "3688cb57",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:18.098095Z",
-     "iopub.status.busy": "2026-03-24T02:04:18.098029Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.247847Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.247578Z"
+     "iopub.execute_input": "2026-06-04T02:49:24.099965Z",
+     "iopub.status.busy": "2026-06-04T02:49:24.099902Z",
+     "iopub.status.idle": "2026-06-04T02:49:24.875268Z",
+     "shell.execute_reply": "2026-06-04T02:49:24.874869Z"
     }
    },
    "outputs": [
@@ -246,10 +246,10 @@
    "id": "6988c9e0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:19.248932Z",
-     "iopub.status.busy": "2026-03-24T02:04:19.248836Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.254342Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.254093Z"
+     "iopub.execute_input": "2026-06-04T02:49:24.876378Z",
+     "iopub.status.busy": "2026-06-04T02:49:24.876280Z",
+     "iopub.status.idle": "2026-06-04T02:49:24.881506Z",
+     "shell.execute_reply": "2026-06-04T02:49:24.881137Z"
     }
    },
    "outputs": [
@@ -453,10 +453,10 @@
    "id": "ecc3b474",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:19.255357Z",
-     "iopub.status.busy": "2026-03-24T02:04:19.255305Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.257207Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.256957Z"
+     "iopub.execute_input": "2026-06-04T02:49:24.882436Z",
+     "iopub.status.busy": "2026-06-04T02:49:24.882376Z",
+     "iopub.status.idle": "2026-06-04T02:49:24.884776Z",
+     "shell.execute_reply": "2026-06-04T02:49:24.884440Z"
     }
    },
    "outputs": [
@@ -489,10 +489,10 @@
    "id": "fbfe4e07",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:19.258170Z",
-     "iopub.status.busy": "2026-03-24T02:04:19.258115Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.633389Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.632966Z"
+     "iopub.execute_input": "2026-06-04T02:49:24.885665Z",
+     "iopub.status.busy": "2026-06-04T02:49:24.885617Z",
+     "iopub.status.idle": "2026-06-04T02:49:25.007399Z",
+     "shell.execute_reply": "2026-06-04T02:49:25.006916Z"
     }
    },
    "outputs": [],
@@ -540,10 +540,10 @@
    "id": "4cd5670d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:19.634599Z",
-     "iopub.status.busy": "2026-03-24T02:04:19.634535Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.657061Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.656707Z"
+     "iopub.execute_input": "2026-06-04T02:49:25.008513Z",
+     "iopub.status.busy": "2026-06-04T02:49:25.008460Z",
+     "iopub.status.idle": "2026-06-04T02:49:25.047537Z",
+     "shell.execute_reply": "2026-06-04T02:49:25.047168Z"
     }
    },
    "outputs": [
@@ -607,10 +607,10 @@
    "id": "6695be16",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:19.658220Z",
-     "iopub.status.busy": "2026-03-24T02:04:19.658157Z",
-     "iopub.status.idle": "2026-03-24T02:04:19.759410Z",
-     "shell.execute_reply": "2026-03-24T02:04:19.759069Z"
+     "iopub.execute_input": "2026-06-04T02:49:25.048564Z",
+     "iopub.status.busy": "2026-06-04T02:49:25.048509Z",
+     "iopub.status.idle": "2026-06-04T02:49:25.116796Z",
+     "shell.execute_reply": "2026-06-04T02:49:25.116420Z"
     }
    },
    "outputs": [
@@ -786,7 +786,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/basics/modeling.ipynb b/docs/ja/basics/modeling.ipynb
index 4fb2d210..45acf6e9 100644
--- a/docs/ja/basics/modeling.ipynb
+++ b/docs/ja/basics/modeling.ipynb
@@ -17,10 +17,10 @@
    "id": "9fd7135f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.183004Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.182943Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.188766Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.188482Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.474578Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.474391Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.487522Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.486694Z"
     }
    },
    "outputs": [],
@@ -53,10 +53,10 @@
    "id": "4183f019",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.190098Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.190042Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.311617Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.311221Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.490398Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.490294Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.677887Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.677558Z"
     }
    },
    "outputs": [
@@ -68,7 +68,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints=[])"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints=[])"
       ]
      },
      "execution_count": 2,
@@ -115,10 +115,10 @@
    "id": "742666cc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.312593Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.312541Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.337986Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.337551Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.679072Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.679010Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.711229Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.710915Z"
     }
    },
    "outputs": [
@@ -160,10 +160,10 @@
    "id": "c0381225",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.339052Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.338997Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.360171Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.359757Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.712590Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.712519Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.739819Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.738659Z"
     }
    },
    "outputs": [
@@ -195,8 +195,7 @@
    "id": "b31b1155",
    "metadata": {},
    "source": [
-    "既存の項が置き換えられたのではなく、$y$ が加算され $x + y$ が新たな目的関数となっていることが分かります。\n",
-    "目的関数の項を削除したい場合、目的関数の項の一覧を（Python の）リストなどで持っておき、あとからそれを使って目的関数を設定するなどするとよいでしょう。\n",
+    "既存の項が置き換えられるのではなく、$y$ が加算され $x + y$ が新たな目的関数となっていることが分かります。\n",
     "\n",
     ":::{admonition} 目的関数から項を「引く」操作\n",
     ":class: tip\n",
@@ -204,6 +203,52 @@
     "JijModeling 2.3.1 以降では、{py:class}`~jijmodeling.Problem` に対して {py:meth}`-= <jijmodeling.Problem.__isub__>` 演算子を使うことで、数値型の {py:class}`~jijmodeling.Expression` オブジェクトを目的関数から「引く」こともできます。\n",
     ":::\n",
     "\n",
+    ":::{admonition} 目的関数の置き換え\n",
+    ":class: tip\n",
+    "JijModeling 2.5.0 以降では、`Problem.objective` に直接式を代入することで、これまでの目的関数を捨て、新しい目的関数で置き換えることができます。\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "d4d454f4",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T02:49:27.741191Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.741128Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.764932Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.764617Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Sample}\\\\\\displaystyle \\min &\\displaystyle y\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\y&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"Sample\", sense=MINIMIZE, objective=y, constraints=[])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "problem.objective = y\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "398ffa17",
+   "metadata": {},
+   "source": [
     "## 制約条件の設定\n",
     "\n",
     "制約条件の追加も同様に {py:meth}`+= <jijmodeling.Problem.__iadd__>` 演算子を使って行います。\n",
@@ -227,14 +272,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "id": "897c3ce3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.361156Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.361104Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.480471Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.480123Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.766256Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.766198Z",
+     "iopub.status.idle": "2026-06-04T02:49:27.912378Z",
+     "shell.execute_reply": "2026-06-04T02:49:27.911955Z"
     }
    },
    "outputs": [
@@ -248,10 +293,10 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float)),],})"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -320,14 +365,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "id": "bcaea850",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.481601Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.481541Z",
-     "iopub.status.idle": "2026-03-24T02:04:22.865508Z",
-     "shell.execute_reply": "2026-03-24T02:04:22.865057Z"
+     "iopub.execute_input": "2026-06-04T02:49:27.913625Z",
+     "iopub.status.busy": "2026-06-04T02:49:27.913562Z",
+     "iopub.status.idle": "2026-06-04T02:49:28.684956Z",
+     "shell.execute_reply": "2026-06-04T02:49:28.684625Z"
     }
    },
    "outputs": [
@@ -337,16 +382,16 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{\\#C-1}{\\sum _{i\\in C}{\\sum _{j\\in C}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod \\#C,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{one city}&\\quad \\displaystyle \\sum _{i\\in C}{{x}_{t,i}}=1\\quad \\forall t\\;\\text{s.t.}\\;t\\in \\left\\{0,\\ldots ,\\#C-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle \\sum _{t=0}^{\\#C-1}{{x}_{t,i}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in C\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\#C\\times C;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\#C\\times C\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "C&\\text{Labels of Cities}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(C.count().flat_map(lambda (t: natural): C.map(lambda (i: CategoryLabel(\"C\")): (t, i))).flat_map(lambda ((t, i): Tuple[natural, CategoryLabel(\"C\")]): C.map(lambda (j: CategoryLabel(\"C\")): (t, i, j))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(C.map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(C.count().map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(C.count().flat_map(lambda (t: natural): C.map(lambda (i: CategoryLabel(\"C\")): (t, i))).flat_map(lambda ((t, i): Tuple[natural, CategoryLabel(\"C\")]): C.map(lambda (j: CategoryLabel(\"C\")): (t, i, j)))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(set(C).map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(set(C.count()).map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -387,14 +432,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "id": "3824401e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:22.866574Z",
-     "iopub.status.busy": "2026-03-24T02:04:22.866516Z",
-     "iopub.status.idle": "2026-03-24T02:04:23.241303Z",
-     "shell.execute_reply": "2026-03-24T02:04:23.240727Z"
+     "iopub.execute_input": "2026-06-04T02:49:28.686134Z",
+     "iopub.status.busy": "2026-06-04T02:49:28.686072Z",
+     "iopub.status.idle": "2026-06-04T02:49:29.284164Z",
+     "shell.execute_reply": "2026-06-04T02:49:29.283873Z"
     }
    },
    "outputs": [
@@ -404,16 +449,16 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{\\#C-1}{\\sum _{i\\in C}{\\sum _{j\\in C}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod \\#C,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{one city}&\\quad \\displaystyle \\sum _{i\\in C}{{x}_{t,i}}=1\\quad \\forall t\\;\\text{s.t.}\\;t\\in \\left\\{0,\\ldots ,\\#C-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle \\sum _{t=0}^{\\#C-1}{{x}_{t,i}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in C\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\#C\\times C;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\#C\\times C\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,\\#C-1\\right\\},j\\in C\\right\\}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{C}\\times \\mathrm{C};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\left(\\mathrm{C},\\mathrm{C}\\right)\\text{, values in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "C&\\text{Labels of Cities}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set((C.count(), C, C)).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(C.map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(C.count().map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(set((C.count(), C, C))).map(lambda ((t, i, j): Tuple[natural, CategoryLabel(\"C\"), CategoryLabel(\"C\")]): d[i, j] * x[t, i] * x[(t + 1) % C.count(), j])), constraints={one city: [Constraint(name=\"one city\", , lambda t: sum(set(C).map(lambda (i: CategoryLabel(\"C\")): x[t, i])) == 1, domain=set(C.count())),],one time: [Constraint(name=\"one time\", , lambda i: sum(set(C.count()).map(lambda (t: natural): x[t, i])) == 1, domain=C),],})"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -463,14 +508,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "id": "563e6dfe",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:23.243100Z",
-     "iopub.status.busy": "2026-03-24T02:04:23.242948Z",
-     "iopub.status.idle": "2026-03-24T02:04:23.759638Z",
-     "shell.execute_reply": "2026-03-24T02:04:23.758654Z"
+     "iopub.execute_input": "2026-06-04T02:49:29.285402Z",
+     "iopub.status.busy": "2026-06-04T02:49:29.285345Z",
+     "iopub.status.idle": "2026-06-04T02:49:29.682781Z",
+     "shell.execute_reply": "2026-06-04T02:49:29.682480Z"
     }
    },
    "outputs": [
@@ -479,15 +524,15 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{TSP, Decorated}\\\\\\displaystyle \\min &\\displaystyle \\sum _{t=0}^{N-1}{\\sum _{i=0}^{N-1}{\\sum _{j=0}^{N-1}{{d}_{i,j}\\cdot {x}_{t,i}\\cdot {x}_{\\left(t+1\\right)\\bmod N,j}}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{one city}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=1\\\\\\text{one time}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[0\\right]\\right)=1\\end{aligned}\n",
+       "\\text{one city}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{one time}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[0\\right]\\right)}_{i}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times N;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\&&&\\text{$x_{t,i} = 1$ if City $i$ is visited at time $t$}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}d&\\in \\mathop{\\mathrm{Array}}\\left[N\\times N;\\mathbb{R}\\right]&\\quad &2\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\&&&\\text{distance between cities}\\\\&&&\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\&&&\\text{Number of cities}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (t: natural): N.map(lambda (i: natural): (t, i))).flat_map(lambda ((t, i): Tuple[natural, natural]): N.map(lambda (j: natural): (t, i, j))).map(lambda ((t, i, j): Tuple[natural, natural, natural]): d[i, j] * x[t, i] * x[(t + 1) % N, j])), constraints={one city: [Constraint(name=\"one city\", sense=EQUAL, left=x.sum(1), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],one time: [Constraint(name=\"one time\", sense=EQUAL, left=x.sum(0), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],})"
+       "Problem(name=\"TSP, Decorated\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (t: natural): N.map(lambda (i: natural): (t, i))).flat_map(lambda ((t, i): Tuple[natural, natural]): N.map(lambda (j: natural): (t, i, j)))).map(lambda ((t, i, j): Tuple[natural, natural, natural]): d[i, j] * x[t, i] * x[(t + 1) % N, j])), constraints={one city: [Constraint(name=\"one city\", sense=EQUAL, left=x.sum(1), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],one time: [Constraint(name=\"one time\", sense=EQUAL, left=x.sum(0), right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/1513282866.py\", start: SrcLoc { line: 4, column: 8 }, end: SrcLoc { line: 6, column: 5 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -525,27 +570,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "id": "464f8394",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:23.761621Z",
-     "iopub.status.busy": "2026-03-24T02:04:23.761508Z",
-     "iopub.status.idle": "2026-03-24T02:04:23.784763Z",
-     "shell.execute_reply": "2026-03-24T02:04:23.783190Z"
+     "iopub.execute_input": "2026-06-04T02:49:29.684022Z",
+     "iopub.status.busy": "2026-06-04T02:49:29.683969Z",
+     "iopub.status.idle": "2026-06-04T02:49:29.705009Z",
+     "shell.execute_reply": "2026-06-04T02:49:29.704655Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/latex": [
-       "$$\\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]$$"
+       "$$\\mathop{\\mathrm{Array}}\\left[N;\\mathbb{N}\\right]$$"
       ],
       "text/plain": [
-       "Array[N; binary!]"
+       "Array[N; natural!]"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -576,14 +621,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "id": "2a324e3f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:23.786767Z",
-     "iopub.status.busy": "2026-03-24T02:04:23.786691Z",
-     "iopub.status.idle": "2026-03-24T02:04:24.101294Z",
-     "shell.execute_reply": "2026-03-24T02:04:24.100547Z"
+     "iopub.execute_input": "2026-06-04T02:49:29.705977Z",
+     "iopub.status.busy": "2026-06-04T02:49:29.705927Z",
+     "iopub.status.idle": "2026-06-04T02:49:29.983968Z",
+     "shell.execute_reply": "2026-06-04T02:49:29.983624Z"
     }
    },
    "outputs": [
@@ -600,7 +645,7 @@
        "Problem(name=\"Possibly Overlapping Constraints\", sense=MINIMIZE, objective=0, constraints={constr: [Constraint(name=\"constr\", , lambda i: x[i] >= 1, domain=set(N)),Constraint(name=\"constr\", , lambda i: x[i] <= 2, domain=set(M)),],})"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -629,14 +674,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "id": "6fad67a9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:24.102725Z",
-     "iopub.status.busy": "2026-03-24T02:04:24.102644Z",
-     "iopub.status.idle": "2026-03-24T02:04:26.951388Z",
-     "shell.execute_reply": "2026-03-24T02:04:26.950336Z"
+     "iopub.execute_input": "2026-06-04T02:49:29.985053Z",
+     "iopub.status.busy": "2026-06-04T02:49:29.984999Z",
+     "iopub.status.idle": "2026-06-04T02:49:30.337633Z",
+     "shell.execute_reply": "2026-06-04T02:49:30.337285Z"
     }
    },
    "outputs": [
@@ -748,7 +793,7 @@
        "5       <=0  Linear      {5}  constr        [5]        <NA>"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -772,14 +817,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "id": "6d36675b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:26.956946Z",
-     "iopub.status.busy": "2026-03-24T02:04:26.956617Z",
-     "iopub.status.idle": "2026-03-24T02:04:27.008328Z",
-     "shell.execute_reply": "2026-03-24T02:04:27.006957Z"
+     "iopub.execute_input": "2026-06-04T02:49:30.338684Z",
+     "iopub.status.busy": "2026-06-04T02:49:30.338602Z",
+     "iopub.status.idle": "2026-06-04T02:49:30.365276Z",
+     "shell.execute_reply": "2026-06-04T02:49:30.364933Z"
     }
    },
    "outputs": [
@@ -789,9 +834,9 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while evaluating problem `Problem(name=\"Possibly Overlapping Constraints\", sense=MINIMIZE, objective=0, constraints={constr: [Constraint(name=\"constr\", , lambda i: x[i] >= 1, domain=set(N)),Constraint(name=\"constr\", , lambda i: x[i] <= 2, domain=set(M)),],})',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/316836703.py\", line 1, col 2-55\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/316836703.py\", line 1, col 2-55\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/316836703.py\", line 1, col 2-55:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/316836703.py\", line 1, col 2-55:\n",
       "\n",
       "    1  |  @jm.Problem.define(\"Possibly Overlapping Constraints\")\n",
       "           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
@@ -819,14 +864,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "id": "0fc6cb95",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:27.014057Z",
-     "iopub.status.busy": "2026-03-24T02:04:27.013741Z",
-     "iopub.status.idle": "2026-03-24T02:04:27.106031Z",
-     "shell.execute_reply": "2026-03-24T02:04:27.104721Z"
+     "iopub.execute_input": "2026-06-04T02:49:30.366220Z",
+     "iopub.status.busy": "2026-06-04T02:49:30.366174Z",
+     "iopub.status.idle": "2026-06-04T02:49:30.443069Z",
+     "shell.execute_reply": "2026-06-04T02:49:30.442678Z"
     }
    },
    "outputs": [
@@ -836,18 +881,18 @@
      "text": [
       "Traceback (most recent last):\n",
       "    while adding constraint 'constr',\n",
-      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/2812696639.py\", line 7, col 9-56\n",
+      "        defined at File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/2812696639.py\", line 7, col 9-56\n",
       "\n",
-      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/2812696639.py\", line 7, col 9-56:\n",
+      "File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/2812696639.py\", line 7, col 9-56:\n",
       "\n",
       "    7  |          problem += problem.Constraint(\"constr\", x <= 2)\n",
       "                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
       "\n",
       "Constraint 'constr' has conflicting definition!\n",
       "    existing: Constraint(name=\"constr\", sense=GREATER_THAN_EQUAL, left=x, right=1, shape=Scalar(Integer))\n",
-      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/2812696639.py\", line 6, col 20-56\n",
+      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/2812696639.py\", line 6, col 20-56\n",
       "    new: Constraint(name=\"constr\", sense=LESS_THAN_EQUAL, left=x, right=2, shape=Scalar(Integer))\n",
-      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44964/2812696639.py\", line 7, col 20-56\n"
+      "        defined at: File \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_2660/2812696639.py\", line 7, col 20-56\n"
      ]
     }
    ],
@@ -891,7 +936,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/basics/overview.ipynb b/docs/ja/basics/overview.ipynb
index 7ee2fb16..c6eae46a 100644
--- a/docs/ja/basics/overview.ipynb
+++ b/docs/ja/basics/overview.ipynb
@@ -46,7 +46,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/basics/problem.ipynb b/docs/ja/basics/problem.ipynb
index b087dc9b..964f1532 100644
--- a/docs/ja/basics/problem.ipynb
+++ b/docs/ja/basics/problem.ipynb
@@ -22,10 +22,10 @@
    "id": "165d3368",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.481235Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.481151Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.486579Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.486251Z"
+     "iopub.execute_input": "2026-06-04T02:49:37.877181Z",
+     "iopub.status.busy": "2026-06-04T02:49:37.877001Z",
+     "iopub.status.idle": "2026-06-04T02:49:37.888798Z",
+     "shell.execute_reply": "2026-06-04T02:49:37.886233Z"
     }
    },
    "outputs": [],
@@ -50,10 +50,10 @@
    "id": "10c85d99",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.487662Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.487606Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.516261Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.515799Z"
+     "iopub.execute_input": "2026-06-04T02:49:37.891611Z",
+     "iopub.status.busy": "2026-06-04T02:49:37.891419Z",
+     "iopub.status.idle": "2026-06-04T02:49:37.934037Z",
+     "shell.execute_reply": "2026-06-04T02:49:37.933616Z"
     }
    },
    "outputs": [],
@@ -82,10 +82,10 @@
    "id": "a04e9459",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.517575Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.517510Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.536172Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.535834Z"
+     "iopub.execute_input": "2026-06-04T02:49:37.935734Z",
+     "iopub.status.busy": "2026-06-04T02:49:37.935661Z",
+     "iopub.status.idle": "2026-06-04T02:49:37.960094Z",
+     "shell.execute_reply": "2026-06-04T02:49:37.959739Z"
     }
    },
    "outputs": [
@@ -127,10 +127,10 @@
    "id": "797e7f58",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.537333Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.537273Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.557293Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.556897Z"
+     "iopub.execute_input": "2026-06-04T02:49:37.961712Z",
+     "iopub.status.busy": "2026-06-04T02:49:37.961567Z",
+     "iopub.status.idle": "2026-06-04T02:49:37.991128Z",
+     "shell.execute_reply": "2026-06-04T02:49:37.990592Z"
     }
    },
    "outputs": [
@@ -194,10 +194,10 @@
    "id": "ca78cfdb",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.558405Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.558346Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.560278Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.559963Z"
+     "iopub.execute_input": "2026-06-04T02:49:37.992437Z",
+     "iopub.status.busy": "2026-06-04T02:49:37.992361Z",
+     "iopub.status.idle": "2026-06-04T02:49:38.000920Z",
+     "shell.execute_reply": "2026-06-04T02:49:37.994941Z"
     }
    },
    "outputs": [
@@ -234,10 +234,10 @@
    "id": "168be19a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.561288Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.561235Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.587958Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.587593Z"
+     "iopub.execute_input": "2026-06-04T02:49:38.004299Z",
+     "iopub.status.busy": "2026-06-04T02:49:38.003997Z",
+     "iopub.status.idle": "2026-06-04T02:49:38.058205Z",
+     "shell.execute_reply": "2026-06-04T02:49:38.057733Z"
     }
    },
    "outputs": [
@@ -280,10 +280,10 @@
    "id": "ee0af68e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:39.589019Z",
-     "iopub.status.busy": "2026-03-24T02:04:39.588961Z",
-     "iopub.status.idle": "2026-03-24T02:04:39.614115Z",
-     "shell.execute_reply": "2026-03-24T02:04:39.613797Z"
+     "iopub.execute_input": "2026-06-04T02:49:38.059826Z",
+     "iopub.status.busy": "2026-06-04T02:49:38.059678Z",
+     "iopub.status.idle": "2026-06-04T02:49:38.108375Z",
+     "shell.execute_reply": "2026-06-04T02:49:38.107993Z"
     }
    },
    "outputs": [
@@ -355,7 +355,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/basics/variables.ipynb b/docs/ja/basics/variables.ipynb
index d3d162c8..4f7315d4 100644
--- a/docs/ja/basics/variables.ipynb
+++ b/docs/ja/basics/variables.ipynb
@@ -17,10 +17,10 @@
    "id": "e89bdd5d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:09.993119Z",
-     "iopub.status.busy": "2026-04-06T08:34:09.993046Z",
-     "iopub.status.idle": "2026-04-06T08:34:09.998434Z",
-     "shell.execute_reply": "2026-04-06T08:34:09.998003Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.641716Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.641586Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.649045Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.648747Z"
     }
    },
    "outputs": [],
@@ -89,10 +89,10 @@
    "id": "86f46b5b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:09.999579Z",
-     "iopub.status.busy": "2026-04-06T08:34:09.999517Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.133620Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.133214Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.650332Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.650274Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.738977Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.738535Z"
     }
    },
    "outputs": [
@@ -150,10 +150,10 @@
    "id": "de5af628",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.134906Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.134832Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.197613Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.197310Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.740183Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.740121Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.807332Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.806932Z"
     }
    },
    "outputs": [
@@ -242,10 +242,10 @@
    "id": "150009c4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.198875Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.198814Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.293965Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.293618Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.808378Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.808322Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.870920Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.870544Z"
     }
    },
    "outputs": [
@@ -287,10 +287,10 @@
    "id": "076c2f07",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.295227Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.295151Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.357962Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.357507Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.872029Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.871970Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.937162Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.936876Z"
     }
    },
    "outputs": [
@@ -347,10 +347,10 @@
    "id": "243ddb11",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.359094Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.359010Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.361043Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.360635Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.938325Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.938270Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.940048Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.939809Z"
     }
    },
    "outputs": [
@@ -375,10 +375,10 @@
    "id": "f3fb46c2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.361973Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.361884Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.364038Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.363644Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.940874Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.940830Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.942469Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.942162Z"
     }
    },
    "outputs": [
@@ -495,10 +495,10 @@
    "id": "4fd8cbae",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.366194Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.365976Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.442843Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.442376Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.943322Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.943272Z",
+     "iopub.status.idle": "2026-06-04T02:49:35.984358Z",
+     "shell.execute_reply": "2026-06-04T02:49:35.984031Z"
     }
    },
    "outputs": [
@@ -552,10 +552,10 @@
    "id": "472b0803",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.443939Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.443868Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.490118Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.489617Z"
+     "iopub.execute_input": "2026-06-04T02:49:35.985412Z",
+     "iopub.status.busy": "2026-06-04T02:49:35.985361Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.037107Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.036763Z"
     }
    },
    "outputs": [
@@ -653,10 +653,10 @@
    "id": "1c058d80",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.491180Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.491120Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.567887Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.567546Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.038177Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.038126Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.093224Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.092859Z"
     }
    },
    "outputs": [
@@ -712,10 +712,10 @@
    "id": "c45d2550",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.568936Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.568883Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.626649Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.626178Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.094300Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.094247Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.150986Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.150671Z"
     }
    },
    "outputs": [
@@ -771,10 +771,10 @@
    "id": "e456d0b6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.627746Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.627677Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.674813Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.674421Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.152154Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.152100Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.203361Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.203078Z"
     }
    },
    "outputs": [
@@ -831,10 +831,10 @@
    "id": "b1c1fef6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.675970Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.675914Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.842981Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.842445Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.204520Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.204462Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.428845Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.428521Z"
     }
    },
    "outputs": [
@@ -846,7 +846,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Partially determined shape\", sense=MINIMIZE, objective=sum(a.len_at(0).flat_map(lambda (i: natural): c.len_at(1).map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): a[i] * c[i, j] * x[i, j])), constraints=[])"
+       "Problem(name=\"Partially determined shape\", sense=MINIMIZE, objective=sum(set(a.len_at(0).flat_map(lambda (i: natural): c.len_at(1).map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): a[i] * c[i, j] * x[i, j])), constraints=[])"
       ]
      },
      "execution_count": 13,
@@ -962,10 +962,10 @@
    "id": "687f3eb0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.844855Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.844737Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.905863Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.905483Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.431482Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.431384Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.453497Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.453139Z"
     }
    },
    "outputs": [
@@ -1009,10 +1009,10 @@
    "id": "bd19e62f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.907050Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.906987Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.929814Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.929401Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.454704Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.454643Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.477846Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.477396Z"
     }
    },
    "outputs": [
@@ -1077,10 +1077,10 @@
    "id": "ef6bbbbb",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.930938Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.930878Z",
-     "iopub.status.idle": "2026-04-06T08:34:10.980611Z",
-     "shell.execute_reply": "2026-04-06T08:34:10.980184Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.479035Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.478975Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.623080Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.622595Z"
     }
    },
    "outputs": [
@@ -1088,7 +1088,7 @@
      "data": {
       "text/latex": [
        "$$\\begin{array}{rl}\n",
-       "\\text{Problem}\\colon &\\text{Dec Var Keys demonstration}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[L\\times N;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }L\\times N\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Dec Var Keys demonstration}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in \\left\\{0,\\ldots ,N-1\\right\\}\\right\\}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "L&\\text{Category Label}\\end{array}\n",
        "\\end{array}\n",
        "$$"
@@ -1165,10 +1165,10 @@
    "id": "c79c1ab2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:10.981958Z",
-     "iopub.status.busy": "2026-04-06T08:34:10.981873Z",
-     "iopub.status.idle": "2026-04-06T08:34:11.097960Z",
-     "shell.execute_reply": "2026-04-06T08:34:11.095711Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.624065Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.624008Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.697047Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.696736Z"
     }
    },
    "outputs": [
@@ -1222,10 +1222,10 @@
    "id": "9ff00f79",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-04-06T08:34:11.099447Z",
-     "iopub.status.busy": "2026-04-06T08:34:11.099343Z",
-     "iopub.status.idle": "2026-04-06T08:34:11.151088Z",
-     "shell.execute_reply": "2026-04-06T08:34:11.150637Z"
+     "iopub.execute_input": "2026-06-04T02:49:36.698338Z",
+     "iopub.status.busy": "2026-06-04T02:49:36.698258Z",
+     "iopub.status.idle": "2026-06-04T02:49:36.752096Z",
+     "shell.execute_reply": "2026-06-04T02:49:36.751764Z"
     }
    },
    "outputs": [
diff --git a/docs/ja/introduction.ipynb b/docs/ja/introduction.ipynb
index f9d3296d..b7b94789 100644
--- a/docs/ja/introduction.ipynb
+++ b/docs/ja/introduction.ipynb
@@ -71,10 +71,10 @@
    "id": "74189d5c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:15.205105Z",
-     "iopub.status.busy": "2026-03-24T02:04:15.205042Z",
-     "iopub.status.idle": "2026-03-24T02:04:16.572981Z",
-     "shell.execute_reply": "2026-03-24T02:04:16.572590Z"
+     "iopub.execute_input": "2026-06-04T02:49:21.391242Z",
+     "iopub.status.busy": "2026-06-04T02:49:21.391112Z",
+     "iopub.status.idle": "2026-06-04T02:49:21.714160Z",
+     "shell.execute_reply": "2026-06-04T02:49:21.713753Z"
     }
    },
    "outputs": [
@@ -88,7 +88,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float), description=\"重さの総和が耐荷重を越えない\"),],})"
+       "Problem(name=\"Knapsack Problem\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={weight: [Constraint(name=\"weight\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Float), description=\"重さの総和が耐荷重を越えない\"),],})"
       ]
      },
      "execution_count": 1,
@@ -144,10 +144,10 @@
    "id": "9eba20ff",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:16.574176Z",
-     "iopub.status.busy": "2026-03-24T02:04:16.574107Z",
-     "iopub.status.idle": "2026-03-24T02:04:16.605709Z",
-     "shell.execute_reply": "2026-03-24T02:04:16.605332Z"
+     "iopub.execute_input": "2026-06-04T02:49:21.715379Z",
+     "iopub.status.busy": "2026-06-04T02:49:21.715322Z",
+     "iopub.status.idle": "2026-06-04T02:49:21.769996Z",
+     "shell.execute_reply": "2026-06-04T02:49:21.769601Z"
     }
    },
    "outputs": [],
@@ -172,10 +172,10 @@
    "id": "f3a2b9c7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:16.606904Z",
-     "iopub.status.busy": "2026-03-24T02:04:16.606845Z",
-     "iopub.status.idle": "2026-03-24T02:04:16.646075Z",
-     "shell.execute_reply": "2026-03-24T02:04:16.645787Z"
+     "iopub.execute_input": "2026-06-04T02:49:21.771259Z",
+     "iopub.status.busy": "2026-06-04T02:49:21.771207Z",
+     "iopub.status.idle": "2026-06-04T02:49:21.847282Z",
+     "shell.execute_reply": "2026-06-04T02:49:21.846870Z"
     }
    },
    "outputs": [],
@@ -217,17 +217,17 @@
    "id": "94580011",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:16.647281Z",
-     "iopub.status.busy": "2026-03-24T02:04:16.647225Z",
-     "iopub.status.idle": "2026-03-24T02:04:16.649129Z",
-     "shell.execute_reply": "2026-03-24T02:04:16.648825Z"
+     "iopub.execute_input": "2026-06-04T02:49:21.848402Z",
+     "iopub.status.busy": "2026-06-04T02:49:21.848348Z",
+     "iopub.status.idle": "2026-06-04T02:49:21.850188Z",
+     "shell.execute_reply": "2026-06-04T02:49:21.849864Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'2.3.1'"
+       "'2.5.0'"
       ]
      },
      "execution_count": 4,
@@ -287,7 +287,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/quickstart/openjij.ipynb b/docs/ja/quickstart/openjij.ipynb
index aee9b398..62277903 100644
--- a/docs/ja/quickstart/openjij.ipynb
+++ b/docs/ja/quickstart/openjij.ipynb
@@ -94,10 +94,10 @@
    "id": "32b82373",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:06.962341Z",
-     "iopub.status.busy": "2026-03-24T02:05:06.962258Z",
-     "iopub.status.idle": "2026-03-24T02:05:07.169469Z",
-     "shell.execute_reply": "2026-03-24T02:05:07.168917Z"
+     "iopub.execute_input": "2026-06-04T02:50:10.476453Z",
+     "iopub.status.busy": "2026-06-04T02:50:10.476322Z",
+     "iopub.status.idle": "2026-06-04T02:50:10.726353Z",
+     "shell.execute_reply": "2026-06-04T02:50:10.725791Z"
     }
    },
    "outputs": [
@@ -111,7 +111,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={重量制限: [Constraint(name=\"重量制限\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={重量制限: [Constraint(name=\"重量制限\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 1,
@@ -169,10 +169,10 @@
    "id": "65d15a95",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:07.170703Z",
-     "iopub.status.busy": "2026-03-24T02:05:07.170637Z",
-     "iopub.status.idle": "2026-03-24T02:05:07.172767Z",
-     "shell.execute_reply": "2026-03-24T02:05:07.172304Z"
+     "iopub.execute_input": "2026-06-04T02:50:10.728033Z",
+     "iopub.status.busy": "2026-06-04T02:50:10.727950Z",
+     "iopub.status.idle": "2026-06-04T02:50:10.729814Z",
+     "shell.execute_reply": "2026-06-04T02:50:10.729407Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "id": "dc31f40f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:07.173836Z",
-     "iopub.status.busy": "2026-03-24T02:05:07.173767Z",
-     "iopub.status.idle": "2026-03-24T02:05:08.081426Z",
-     "shell.execute_reply": "2026-03-24T02:05:08.080927Z"
+     "iopub.execute_input": "2026-06-04T02:50:10.731267Z",
+     "iopub.status.busy": "2026-06-04T02:50:10.731160Z",
+     "iopub.status.idle": "2026-06-04T02:50:11.020033Z",
+     "shell.execute_reply": "2026-06-04T02:50:11.019614Z"
     }
    },
    "outputs": [],
@@ -238,10 +238,10 @@
    "id": "a715a29a",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:08.082681Z",
-     "iopub.status.busy": "2026-03-24T02:05:08.082558Z",
-     "iopub.status.idle": "2026-03-24T02:05:08.459229Z",
-     "shell.execute_reply": "2026-03-24T02:05:08.458766Z"
+     "iopub.execute_input": "2026-06-04T02:50:11.021264Z",
+     "iopub.status.busy": "2026-06-04T02:50:11.021177Z",
+     "iopub.status.idle": "2026-06-04T02:50:11.308051Z",
+     "shell.execute_reply": "2026-06-04T02:50:11.307582Z"
     }
    },
    "outputs": [],
@@ -272,10 +272,10 @@
    "id": "19debd1b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:08.460468Z",
-     "iopub.status.busy": "2026-03-24T02:05:08.460373Z",
-     "iopub.status.idle": "2026-03-24T02:05:08.470105Z",
-     "shell.execute_reply": "2026-03-24T02:05:08.469582Z"
+     "iopub.execute_input": "2026-06-04T02:50:11.309464Z",
+     "iopub.status.busy": "2026-06-04T02:50:11.309383Z",
+     "iopub.status.idle": "2026-06-04T02:50:11.315492Z",
+     "shell.execute_reply": "2026-06-04T02:50:11.315167Z"
     }
    },
    "outputs": [
@@ -316,7 +316,7 @@
        "      <th>0</th>\n",
        "      <td>x</td>\n",
        "      <td>[0]</td>\n",
-       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
@@ -340,7 +340,7 @@
        "      <th>4</th>\n",
        "      <td>x</td>\n",
        "      <td>[4]</td>\n",
-       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
@@ -355,11 +355,11 @@
       "text/plain": [
        "   name subscripts  value\n",
        "id                       \n",
-       "0     x        [0]    1.0\n",
+       "0     x        [0]    0.0\n",
        "1     x        [1]    0.0\n",
        "2     x        [2]    0.0\n",
        "3     x        [3]    1.0\n",
-       "4     x        [4]    0.0\n",
+       "4     x        [4]    1.0\n",
        "5     x        [5]    0.0"
       ]
      },
@@ -413,7 +413,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/quickstart/scip.ipynb b/docs/ja/quickstart/scip.ipynb
index 424ad008..789cf879 100644
--- a/docs/ja/quickstart/scip.ipynb
+++ b/docs/ja/quickstart/scip.ipynb
@@ -94,10 +94,10 @@
    "id": "cf6f5d6e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:09.855622Z",
-     "iopub.status.busy": "2026-03-24T02:05:09.855545Z",
-     "iopub.status.idle": "2026-03-24T02:05:10.036882Z",
-     "shell.execute_reply": "2026-03-24T02:05:10.036496Z"
+     "iopub.execute_input": "2026-06-04T02:50:12.468615Z",
+     "iopub.status.busy": "2026-06-04T02:50:12.468545Z",
+     "iopub.status.idle": "2026-06-04T02:50:12.717527Z",
+     "shell.execute_reply": "2026-06-04T02:50:12.717173Z"
     }
    },
    "outputs": [
@@ -111,7 +111,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(N.map(lambda (i: natural): v[i] * x[i])), constraints={重量制限: [Constraint(name=\"重量制限\", sense=LESS_THAN_EQUAL, left=sum(N.map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
+       "Problem(name=\"Knapsack\", sense=MAXIMIZE, objective=sum(set(N).map(lambda (i: natural): v[i] * x[i])), constraints={重量制限: [Constraint(name=\"重量制限\", sense=LESS_THAN_EQUAL, left=sum(set(N).map(lambda (i: natural): w[i] * x[i])), right=W, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 1,
@@ -169,10 +169,10 @@
    "id": "4fbe5bb8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:10.038214Z",
-     "iopub.status.busy": "2026-03-24T02:05:10.038151Z",
-     "iopub.status.idle": "2026-03-24T02:05:10.040028Z",
-     "shell.execute_reply": "2026-03-24T02:05:10.039702Z"
+     "iopub.execute_input": "2026-06-04T02:50:12.718672Z",
+     "iopub.status.busy": "2026-06-04T02:50:12.718611Z",
+     "iopub.status.idle": "2026-06-04T02:50:12.720300Z",
+     "shell.execute_reply": "2026-06-04T02:50:12.720017Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "id": "42561c0b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:10.040949Z",
-     "iopub.status.busy": "2026-03-24T02:05:10.040896Z",
-     "iopub.status.idle": "2026-03-24T02:05:10.651143Z",
-     "shell.execute_reply": "2026-03-24T02:05:10.650790Z"
+     "iopub.execute_input": "2026-06-04T02:50:12.721174Z",
+     "iopub.status.busy": "2026-06-04T02:50:12.721124Z",
+     "iopub.status.idle": "2026-06-04T02:50:13.004029Z",
+     "shell.execute_reply": "2026-06-04T02:50:13.003717Z"
     }
    },
    "outputs": [],
@@ -238,10 +238,10 @@
    "id": "557ed3a4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:10.652545Z",
-     "iopub.status.busy": "2026-03-24T02:05:10.652442Z",
-     "iopub.status.idle": "2026-03-24T02:05:10.722754Z",
-     "shell.execute_reply": "2026-03-24T02:05:10.722390Z"
+     "iopub.execute_input": "2026-06-04T02:50:13.005328Z",
+     "iopub.status.busy": "2026-06-04T02:50:13.005238Z",
+     "iopub.status.idle": "2026-06-04T02:50:13.075289Z",
+     "shell.execute_reply": "2026-06-04T02:50:13.074876Z"
     }
    },
    "outputs": [
@@ -276,10 +276,10 @@
    "id": "a5afa9c8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:10.723995Z",
-     "iopub.status.busy": "2026-03-24T02:05:10.723897Z",
-     "iopub.status.idle": "2026-03-24T02:05:10.729677Z",
-     "shell.execute_reply": "2026-03-24T02:05:10.729303Z"
+     "iopub.execute_input": "2026-06-04T02:50:13.076293Z",
+     "iopub.status.busy": "2026-06-04T02:50:13.076207Z",
+     "iopub.status.idle": "2026-06-04T02:50:13.080906Z",
+     "shell.execute_reply": "2026-06-04T02:50:13.080597Z"
     }
    },
    "outputs": [
@@ -406,7 +406,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/references/cheat_sheet.ipynb b/docs/ja/references/cheat_sheet.ipynb
index ad2e07e0..f89a2f5d 100644
--- a/docs/ja/references/cheat_sheet.ipynb
+++ b/docs/ja/references/cheat_sheet.ipynb
@@ -14,10 +14,10 @@
    "id": "d4a18618",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.429331Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.429269Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.438422Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.438044Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.216438Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.216292Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.227738Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.227079Z"
     }
    },
    "outputs": [],
@@ -49,10 +49,10 @@
    "id": "79e10997",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.440036Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.439958Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.544052Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.543307Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.229970Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.229817Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.299932Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.299562Z"
     }
    },
    "outputs": [
@@ -95,10 +95,10 @@
    "id": "0b287866",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.545904Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.545790Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.613176Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.611337Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.301069Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.301012Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.348556Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.348202Z"
     }
    },
    "outputs": [
@@ -150,10 +150,10 @@
    "id": "ed7db663",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.615861Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.615567Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.693506Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.693054Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.349772Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.349716Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.418664Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.418281Z"
     }
    },
    "outputs": [
@@ -197,10 +197,10 @@
    "id": "45474fb8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.695344Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.695262Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.753298Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.752745Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.419778Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.419718Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.491592Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.491322Z"
     }
    },
    "outputs": [
@@ -253,10 +253,10 @@
    "id": "08771e03",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.755210Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.755126Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.878464Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.877614Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.492834Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.492781Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.584539Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.584176Z"
     }
    },
    "outputs": [
@@ -300,10 +300,10 @@
    "id": "eff6ac1d",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.880046Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.879916Z",
-     "iopub.status.idle": "2026-03-24T02:05:01.973491Z",
-     "shell.execute_reply": "2026-03-24T02:05:01.973065Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.585657Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.585599Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.686685Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.686325Z"
     }
    },
    "outputs": [
@@ -315,7 +315,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(C.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(set(C).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 7,
@@ -356,10 +356,10 @@
    "id": "3088b3ca",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:01.974620Z",
-     "iopub.status.busy": "2026-03-24T02:05:01.974558Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.056888Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.056548Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.687751Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.687692Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.793280Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.792648Z"
     }
    },
    "outputs": [
@@ -403,10 +403,10 @@
    "id": "547a6ead",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.058019Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.057960Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.140216Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.139888Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.794990Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.794909Z",
+     "iopub.status.idle": "2026-06-04T02:50:05.908975Z",
+     "shell.execute_reply": "2026-06-04T02:50:05.908590Z"
     }
    },
    "outputs": [
@@ -418,7 +418,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongEdgeSet\", sense=MINIMIZE, objective=sum(E.map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
+       "Problem(name=\"SumAlongEdgeSet\", sense=MINIMIZE, objective=sum(set(E).map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 9,
@@ -459,10 +459,10 @@
    "id": "cfdecd72",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.141314Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.141259Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.322713Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.321830Z"
+     "iopub.execute_input": "2026-06-04T02:50:05.910084Z",
+     "iopub.status.busy": "2026-06-04T02:50:05.910028Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.082466Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.082157Z"
     }
    },
    "outputs": [
@@ -509,10 +509,10 @@
    "id": "28c3c3b5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.323836Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.323757Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.477603Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.477115Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.083500Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.083449Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.274392Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.274003Z"
     }
    },
    "outputs": [
@@ -524,7 +524,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 11,
@@ -565,10 +565,10 @@
    "id": "1d285a01",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.478786Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.478725Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.587107Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.586705Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.275485Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.275430Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.409426Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.409038Z"
     }
    },
    "outputs": [
@@ -614,10 +614,10 @@
    "id": "7d1c8a03",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.588091Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.588039Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.740181Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.739815Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.410517Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.410462Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.560991Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.560705Z"
     }
    },
    "outputs": [
@@ -629,7 +629,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"NonDiagonalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i != j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j])), constraints=[])"
+       "Problem(name=\"NonDiagonalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i != j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j])), constraints=[])"
       ]
      },
      "execution_count": 13,
@@ -669,10 +669,10 @@
    "id": "75703ca2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.741675Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.741453Z",
-     "iopub.status.idle": "2026-03-24T02:05:02.901239Z",
-     "shell.execute_reply": "2026-03-24T02:05:02.900893Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.562096Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.562042Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.665910Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.665531Z"
     }
    },
    "outputs": [
@@ -717,10 +717,10 @@
    "id": "0c4e9205",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:02.904014Z",
-     "iopub.status.busy": "2026-03-24T02:05:02.903914Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.021032Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.020218Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.666878Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.666827Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.820613Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.820131Z"
     }
    },
    "outputs": [
@@ -732,7 +732,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"DependentSum\", sense=MINIMIZE, objective=sum(M.flat_map(lambda (i: natural): a[i].map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): x[j])), constraints=[])"
+       "Problem(name=\"DependentSum\", sense=MINIMIZE, objective=sum(set(M.flat_map(lambda (i: natural): a[i].map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): x[j])), constraints=[])"
       ]
      },
      "execution_count": 15,
@@ -775,10 +775,10 @@
    "id": "fc24d108",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.022220Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.022147Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.106428Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.106052Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.821935Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.821862Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.906546Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.906206Z"
     }
    },
    "outputs": [
@@ -792,7 +792,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 16,
@@ -823,10 +823,10 @@
    "id": "dc6c8635",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.107498Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.107440Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.193860Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.193469Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.907616Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.907560Z",
+     "iopub.status.idle": "2026-06-04T02:50:06.998589Z",
+     "shell.execute_reply": "2026-06-04T02:50:06.998296Z"
     }
    },
    "outputs": [
@@ -840,7 +840,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 17,
@@ -880,10 +880,10 @@
    "id": "e94c1845",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.196589Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.196463Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.301828Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.301368Z"
+     "iopub.execute_input": "2026-06-04T02:50:06.999751Z",
+     "iopub.status.busy": "2026-06-04T02:50:06.999699Z",
+     "iopub.status.idle": "2026-06-04T02:50:07.131103Z",
+     "shell.execute_reply": "2026-06-04T02:50:07.130645Z"
     }
    },
    "outputs": [
@@ -929,10 +929,10 @@
    "id": "cf2136d1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.303543Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.303449Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.405151Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.404690Z"
+     "iopub.execute_input": "2026-06-04T02:50:07.132205Z",
+     "iopub.status.busy": "2026-06-04T02:50:07.132141Z",
+     "iopub.status.idle": "2026-06-04T02:50:07.230454Z",
+     "shell.execute_reply": "2026-06-04T02:50:07.230148Z"
     }
    },
    "outputs": [
@@ -987,10 +987,10 @@
    "id": "34f681bc",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.406238Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.406175Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.532199Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.529504Z"
+     "iopub.execute_input": "2026-06-04T02:50:07.231650Z",
+     "iopub.status.busy": "2026-06-04T02:50:07.231597Z",
+     "iopub.status.idle": "2026-06-04T02:50:07.383729Z",
+     "shell.execute_reply": "2026-06-04T02:50:07.383436Z"
     }
    },
    "outputs": [
@@ -999,12 +999,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{2D K-Hot}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{2d k-hot}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=K\\end{aligned}\n",
+       "\\text{2d k-hot}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}={K}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times M;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{N}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{N}\\\\M&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}N&=\\mathop{\\mathtt{len\\_{}at}}\\left(K,0\\right)&\\quad &\\in \\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
+       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1184867636.py\", start: SrcLoc { line: 5, column: 4 }, end: SrcLoc { line: 5, column: 40 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
      "execution_count": 20,
@@ -1037,10 +1037,10 @@
    "id": "3abc03a3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.536814Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.536639Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.647317Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.646932Z"
+     "iopub.execute_input": "2026-06-04T02:50:07.384909Z",
+     "iopub.status.busy": "2026-06-04T02:50:07.384854Z",
+     "iopub.status.idle": "2026-06-04T02:50:07.546207Z",
+     "shell.execute_reply": "2026-06-04T02:50:07.545859Z"
     }
    },
    "outputs": [
@@ -1049,12 +1049,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{2D K-Hot}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{2d k-hot}&\\quad \\displaystyle x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)=K\\end{aligned}\n",
+       "\\text{2d k-hot}&\\quad \\displaystyle {x.\\mathop{\\mathtt{sum}}\\left(\\mathtt{axis}=\\left[1\\right]\\right)}_{i}={K}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N\\times M;\\left\\{0, 1\\right\\}\\right]&\\quad &2\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{N}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{N}\\\\M&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}N&=\\mathop{\\mathtt{len\\_{}at}}\\left(K,0\\right)&\\quad &\\in \\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
+       "Problem(name=\"2D K-Hot\", sense=MINIMIZE, objective=0, constraints={2d k-hot: [Constraint(name=\"2d k-hot\", sense=EQUAL, left=x.sum(1), right=K, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1629874504.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 39 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Natural }, src_span: NoSrcSpan } }), scalar: Natural }),],})"
       ]
      },
      "execution_count": 21,
@@ -1096,10 +1096,10 @@
    "id": "25789023",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.648461Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.648398Z",
-     "iopub.status.idle": "2026-03-24T02:05:03.820160Z",
-     "shell.execute_reply": "2026-03-24T02:05:03.819817Z"
+     "iopub.execute_input": "2026-06-04T02:50:07.547498Z",
+     "iopub.status.busy": "2026-06-04T02:50:07.547445Z",
+     "iopub.status.idle": "2026-06-04T02:50:07.785459Z",
+     "shell.execute_reply": "2026-06-04T02:50:07.785056Z"
     }
    },
    "outputs": [
@@ -1149,10 +1149,10 @@
    "id": "cf7c27cd",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:03.821411Z",
-     "iopub.status.busy": "2026-03-24T02:05:03.821356Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.007530Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.007215Z"
+     "iopub.execute_input": "2026-06-04T02:50:07.786458Z",
+     "iopub.status.busy": "2026-06-04T02:50:07.786399Z",
+     "iopub.status.idle": "2026-06-04T02:50:08.009746Z",
+     "shell.execute_reply": "2026-06-04T02:50:08.009405Z"
     }
    },
    "outputs": [
@@ -1166,7 +1166,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(C[a].map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
+       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(set(C[a]).map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
       ]
      },
      "execution_count": 23,
@@ -1211,10 +1211,10 @@
    "id": "c404bee8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.008611Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.008548Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.102020Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.101644Z"
+     "iopub.execute_input": "2026-06-04T02:50:08.010902Z",
+     "iopub.status.busy": "2026-06-04T02:50:08.010845Z",
+     "iopub.status.idle": "2026-06-04T02:50:08.121759Z",
+     "shell.execute_reply": "2026-06-04T02:50:08.121380Z"
     }
    },
    "outputs": [
@@ -1261,10 +1261,10 @@
    "id": "3d6ef1a1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.103112Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.103050Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.201445Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.200875Z"
+     "iopub.execute_input": "2026-06-04T02:50:08.122805Z",
+     "iopub.status.busy": "2026-06-04T02:50:08.122749Z",
+     "iopub.status.idle": "2026-06-04T02:50:08.250734Z",
+     "shell.execute_reply": "2026-06-04T02:50:08.250363Z"
     }
    },
    "outputs": [
@@ -1320,10 +1320,10 @@
    "id": "33bd2f32",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.202936Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.202858Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.379090Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.378607Z"
+     "iopub.execute_input": "2026-06-04T02:50:08.252025Z",
+     "iopub.status.busy": "2026-06-04T02:50:08.251969Z",
+     "iopub.status.idle": "2026-06-04T02:50:08.484805Z",
+     "shell.execute_reply": "2026-06-04T02:50:08.484430Z"
     }
    },
    "outputs": [
@@ -1332,12 +1332,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{SOS-1}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{Big-M}&\\quad \\displaystyle a\\leq M\\cdot x\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
+       "\\text{Big-M}&\\quad \\displaystyle {a}_{i}\\leq {\\left(M\\cdot x\\right)}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]\\;\\left(0\\leq {a}_{i}\\leq {M}_{i}\\right)&\\quad &1\\text{-dim continuous variable}\\\\x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}M&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/1199227916.py\", start: SrcLoc { line: 2, column: 4 }, end: SrcLoc { line: 2, column: 24 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 26,
@@ -1371,10 +1371,10 @@
    "id": "9f91dea8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.380332Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.380263Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.585189Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.584802Z"
+     "iopub.execute_input": "2026-06-04T02:50:08.485997Z",
+     "iopub.status.busy": "2026-06-04T02:50:08.485939Z",
+     "iopub.status.idle": "2026-06-04T02:50:08.723451Z",
+     "shell.execute_reply": "2026-06-04T02:50:08.722973Z"
     }
    },
    "outputs": [
@@ -1383,12 +1383,12 @@
       "text/latex": [
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{SOS-1}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
-       "\\text{Big-M}&\\quad \\displaystyle a\\leq M\\cdot x\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
+       "\\text{Big-M}&\\quad \\displaystyle {a}_{i}\\leq {\\left(M\\cdot x\\right)}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{SOS1}&\\quad \\displaystyle \\sum _{\\vec{\\imath }}{{{\\left(x\\right)}}_{\\vec{\\imath }}}\\leq 1\\end{aligned}\n",
        "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]\\;\\left(0\\leq {a}_{i}\\leq {M}_{i}\\right)&\\quad &1\\text{-dim continuous variable}\\\\x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}M&\\in \\mathop{\\mathrm{Array}}\\left[N;\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_47001/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"SOS-1\", sense=MINIMIZE, objective=0, constraints={Big-M: [Constraint(name=\"Big-M\", sense=LESS_THAN_EQUAL, left=a, right=M * x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_3974/3596302424.py\", start: SrcLoc { line: 3, column: 8 }, end: SrcLoc { line: 3, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Float }, src_span: NoSrcSpan } }), scalar: Float }),],SOS1: [Constraint(name=\"SOS1\", sense=LESS_THAN_EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 27,
@@ -1431,10 +1431,10 @@
    "id": "a62ab168",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.586397Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.586340Z",
-     "iopub.status.idle": "2026-03-24T02:05:04.868405Z",
-     "shell.execute_reply": "2026-03-24T02:05:04.867931Z"
+     "iopub.execute_input": "2026-06-04T02:50:08.724656Z",
+     "iopub.status.busy": "2026-06-04T02:50:08.724594Z",
+     "iopub.status.idle": "2026-06-04T02:50:09.044380Z",
+     "shell.execute_reply": "2026-06-04T02:50:09.043924Z"
     }
    },
    "outputs": [
@@ -1489,10 +1489,10 @@
    "id": "a86d8c29",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:05:04.869562Z",
-     "iopub.status.busy": "2026-03-24T02:05:04.869487Z",
-     "iopub.status.idle": "2026-03-24T02:05:05.200776Z",
-     "shell.execute_reply": "2026-03-24T02:05:05.200293Z"
+     "iopub.execute_input": "2026-06-04T02:50:09.045514Z",
+     "iopub.status.busy": "2026-06-04T02:50:09.045460Z",
+     "iopub.status.idle": "2026-06-04T02:50:09.417735Z",
+     "shell.execute_reply": "2026-06-04T02:50:09.417395Z"
     }
    },
    "outputs": [
@@ -1557,7 +1557,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/references/migration_guide_to_jijmodeling2.ipynb b/docs/ja/references/migration_guide_to_jijmodeling2.ipynb
index 2ccb871f..35246183 100644
--- a/docs/ja/references/migration_guide_to_jijmodeling2.ipynb
+++ b/docs/ja/references/migration_guide_to_jijmodeling2.ipynb
@@ -126,10 +126,10 @@
    "id": "5c1c13b4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:55.169692Z",
-     "iopub.status.busy": "2026-03-24T02:04:55.169605Z",
-     "iopub.status.idle": "2026-03-24T02:04:55.620482Z",
-     "shell.execute_reply": "2026-03-24T02:04:55.619991Z"
+     "iopub.execute_input": "2026-06-04T02:49:59.552035Z",
+     "iopub.status.busy": "2026-06-04T02:49:59.551883Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.132790Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.132332Z"
     }
    },
    "outputs": [
@@ -143,7 +143,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"TSP\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).flat_map(lambda ((i, j): Tuple[natural, natural]): N.map(lambda (t: natural): (i, j, t))).map(lambda ((i, j, t): Tuple[natural, natural, natural]): d[i, j] * x[i, t] * x[j, (t + 1) % N])), constraints={one-city: [Constraint(name=\"one-city\", , lambda t: sum(N.map(lambda (i: natural): x[i, t])) == 1, domain=set(N), description=\"各時刻にちょうど1つの都市を訪問\"),],one-time: [Constraint(name=\"one-time\", , lambda i: sum(N.map(lambda (t: natural): x[i, t])) == 1, domain=set(N), description=\"各都市はちょうど1回訪問される\"),],})"
+       "Problem(name=\"TSP\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).flat_map(lambda ((i, j): Tuple[natural, natural]): N.map(lambda (t: natural): (i, j, t)))).map(lambda ((i, j, t): Tuple[natural, natural, natural]): d[i, j] * x[i, t] * x[j, (t + 1) % N])), constraints={one-city: [Constraint(name=\"one-city\", , lambda t: sum(set(N).map(lambda (i: natural): x[i, t])) == 1, domain=set(N), description=\"各時刻にちょうど1つの都市を訪問\"),],one-time: [Constraint(name=\"one-time\", , lambda i: sum(set(N).map(lambda (t: natural): x[i, t])) == 1, domain=set(N), description=\"各都市はちょうど1回訪問される\"),],})"
       ]
      },
      "execution_count": 1,
@@ -195,10 +195,10 @@
    "id": "d1f405cd",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:55.621608Z",
-     "iopub.status.busy": "2026-03-24T02:04:55.621531Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.272954Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.272500Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.134044Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.133957Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.482930Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.482625Z"
     }
    },
    "outputs": [
@@ -375,10 +375,10 @@
    "id": "5ef8c8b3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.274019Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.273898Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.276712Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.275995Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.484054Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.483957Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.485971Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.485653Z"
     }
    },
    "outputs": [
@@ -411,10 +411,10 @@
    "id": "9ae594ce",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.282239Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.281653Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.679808Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.679395Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.486897Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.486847Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.640185Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.639847Z"
     }
    },
    "outputs": [],
@@ -718,10 +718,10 @@
    "id": "1e9ca71e",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.680935Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.680879Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.764686Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.764308Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.641462Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.641407Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.739834Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.739530Z"
     }
    },
    "outputs": [
@@ -733,7 +733,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SimpleSum\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SimpleSum\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 5,
@@ -792,10 +792,10 @@
    "id": "66868142",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.766601Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.766493Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.888085Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.887705Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.740959Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.740899Z",
+     "iopub.status.idle": "2026-06-04T02:50:00.874797Z",
+     "shell.execute_reply": "2026-06-04T02:50:00.874444Z"
     }
    },
    "outputs": [
@@ -807,7 +807,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"WeightedSum\", sense=MINIMIZE, objective=sum(N.map(lambda (i: natural): a[i] * x[i])), constraints=[])"
+       "Problem(name=\"WeightedSum\", sense=MINIMIZE, objective=sum(set(N).map(lambda (i: natural): a[i] * x[i])), constraints=[])"
       ]
      },
      "execution_count": 6,
@@ -860,10 +860,10 @@
    "id": "3a042c35",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.889056Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.888999Z",
-     "iopub.status.idle": "2026-03-24T02:04:56.989045Z",
-     "shell.execute_reply": "2026-03-24T02:04:56.988765Z"
+     "iopub.execute_input": "2026-06-04T02:50:00.875898Z",
+     "iopub.status.busy": "2026-06-04T02:50:00.875841Z",
+     "iopub.status.idle": "2026-06-04T02:50:01.022113Z",
+     "shell.execute_reply": "2026-06-04T02:50:01.021728Z"
     }
    },
    "outputs": [
@@ -875,7 +875,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(C.map(lambda (i: natural): x[i])), constraints=[])"
+       "Problem(name=\"SumAlongSet\", sense=MINIMIZE, objective=sum(set(C).map(lambda (i: natural): x[i])), constraints=[])"
       ]
      },
      "execution_count": 7,
@@ -928,10 +928,10 @@
    "id": "73042539",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:56.990163Z",
-     "iopub.status.busy": "2026-03-24T02:04:56.990097Z",
-     "iopub.status.idle": "2026-03-24T02:04:57.107395Z",
-     "shell.execute_reply": "2026-03-24T02:04:57.106889Z"
+     "iopub.execute_input": "2026-06-04T02:50:01.023203Z",
+     "iopub.status.busy": "2026-06-04T02:50:01.023143Z",
+     "iopub.status.idle": "2026-06-04T02:50:01.165122Z",
+     "shell.execute_reply": "2026-06-04T02:50:01.164673Z"
     }
    },
    "outputs": [
@@ -943,7 +943,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"EdgeSum\", sense=MINIMIZE, objective=sum(E.map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
+       "Problem(name=\"EdgeSum\", sense=MINIMIZE, objective=sum(set(E).map(lambda ((i, j): Tuple[natural, natural]): x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 8,
@@ -988,10 +988,10 @@
    "id": "77c29124",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:57.109068Z",
-     "iopub.status.busy": "2026-03-24T02:04:57.108950Z",
-     "iopub.status.idle": "2026-03-24T02:04:57.259231Z",
-     "shell.execute_reply": "2026-03-24T02:04:57.258498Z"
+     "iopub.execute_input": "2026-06-04T02:50:01.166100Z",
+     "iopub.status.busy": "2026-06-04T02:50:01.166046Z",
+     "iopub.status.idle": "2026-06-04T02:50:01.334665Z",
+     "shell.execute_reply": "2026-06-04T02:50:01.334292Z"
     }
    },
    "outputs": [
@@ -1003,7 +1003,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"EdgeSumRows\", sense=MINIMIZE, objective=sum(E.rows().map(lambda ((l, r): Array[2; natural]): x[l] * x[r])), constraints=[])"
+       "Problem(name=\"EdgeSumRows\", sense=MINIMIZE, objective=sum(set(E.rows()).map(lambda ((l, r): Array[2; natural]): x[l] * x[r])), constraints=[])"
       ]
      },
      "execution_count": 9,
@@ -1056,10 +1056,10 @@
    "id": "26009ba5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:57.261020Z",
-     "iopub.status.busy": "2026-03-24T02:04:57.260913Z",
-     "iopub.status.idle": "2026-03-24T02:04:57.431214Z",
-     "shell.execute_reply": "2026-03-24T02:04:57.430925Z"
+     "iopub.execute_input": "2026-06-04T02:50:01.335934Z",
+     "iopub.status.busy": "2026-06-04T02:50:01.335876Z",
+     "iopub.status.idle": "2026-06-04T02:50:01.576555Z",
+     "shell.execute_reply": "2026-06-04T02:50:01.576155Z"
     }
    },
    "outputs": [
@@ -1071,7 +1071,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): N.map(lambda (j: natural): (i, j))).filter(lambda (i, j): i > j)).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 10,
@@ -1109,10 +1109,10 @@
    "id": "18aba181",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:57.433370Z",
-     "iopub.status.busy": "2026-03-24T02:04:57.433244Z",
-     "iopub.status.idle": "2026-03-24T02:04:57.572388Z",
-     "shell.execute_reply": "2026-03-24T02:04:57.572079Z"
+     "iopub.execute_input": "2026-06-04T02:50:01.577674Z",
+     "iopub.status.busy": "2026-06-04T02:50:01.577617Z",
+     "iopub.status.idle": "2026-06-04T02:50:01.779797Z",
+     "shell.execute_reply": "2026-06-04T02:50:01.779400Z"
     }
    },
    "outputs": [
@@ -1124,7 +1124,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(N.flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
+       "Problem(name=\"ConditionalSum\", sense=MINIMIZE, objective=sum(set(N.flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): J[i, j] * x[i] * x[j])), constraints=[])"
       ]
      },
      "execution_count": 11,
@@ -1162,10 +1162,10 @@
    "id": "4ed5b544",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:57.573609Z",
-     "iopub.status.busy": "2026-03-24T02:04:57.573545Z",
-     "iopub.status.idle": "2026-03-24T02:04:58.125109Z",
-     "shell.execute_reply": "2026-03-24T02:04:58.124647Z"
+     "iopub.execute_input": "2026-06-04T02:50:01.780902Z",
+     "iopub.status.busy": "2026-06-04T02:50:01.780848Z",
+     "iopub.status.idle": "2026-06-04T02:50:02.762192Z",
+     "shell.execute_reply": "2026-06-04T02:50:02.761796Z"
     }
    },
    "outputs": [
@@ -1175,13 +1175,13 @@
        "$$\\begin{array}{rl}\n",
        "\\text{Problem}\\colon &\\text{QuadraticKnapsackLogistics}\\\\\\displaystyle \\max &\\displaystyle \\sum _{j\\in J}{\\sum _{\\left\\langle i,k\\right\\rangle \\in \\mathop{\\mathtt{keys}}\\left(s\\right)}{{s}_{i,k}\\cdot {x}_{i,j}\\cdot {x}_{k,j}}}+\\sum _{i\\in I}{\\sum _{j\\in J}{{r}_{i}\\cdot {x}_{i,j}}}\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
        "\\text{parcel\\_{}assign}&\\quad \\displaystyle \\sum _{j\\in J}{{x}_{i,j}}=1\\quad \\forall i\\;\\text{s.t.}\\;i\\in I\\\\\\text{truck\\_{}capacity}&\\quad \\displaystyle \\sum _{i\\in I}{{w}_{i}\\cdot {x}_{i,j}}\\leq {C}_{j}\\quad \\forall j\\;\\text{s.t.}\\;j\\in J\\end{aligned}\n",
-       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[I\\times J;\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }I\\times J\\\\&&&\\text{荷物iをトラックjに割り当てる場合x[i,j] = 1、そうでない場合0}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}C&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{J};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{J}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各トラックの荷重容量}\\\\&&&\\\\r&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各荷物の基本利益}\\\\&&&\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\mathrm{I}\\times \\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left(\\mathrm{I},\\mathrm{I}\\right)\\text{, values in }\\mathbb{Z}\\\\&&&\\text{荷物のペア間のシナジーボーナス}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各荷物の重さ}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in I,j\\in J\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in I,j\\in J\\right\\}\\\\&&&\\text{荷物iをトラックjに割り当てる場合x[i,j] = 1、そうでない場合0}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}C&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{J};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{J}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各トラックの荷重容量}\\\\&&&\\\\r&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各荷物の基本利益}\\\\&&&\\\\s&\\in \\mathop{\\mathrm{PartialDict}}\\left[\\mathrm{I}\\times \\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A partial dictionary of placeholders with keys }\\left(\\mathrm{I},\\mathrm{I}\\right)\\text{, values in }\\mathbb{Z}\\\\&&&\\text{荷物のペア間のシナジーボーナス}\\\\&&&\\\\w&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{I};\\mathbb{Z}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{I}\\text{, values in }\\mathbb{Z}\\\\&&&\\text{各荷物の重さ}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
        "I&\\text{荷物のラベル}\\\\J&\\text{トラックのラベル}\\end{array}\n",
        "\\end{array}\n",
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"QuadraticKnapsackLogistics\", sense=MAXIMIZE, objective=sum(J.flat_map(lambda (j: CategoryLabel(\"J\")): s.keys().map(lambda ((i, k): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"I\")]): (j, i, k))).map(lambda ((j, i, k): Tuple[CategoryLabel(\"J\"), CategoryLabel(\"I\"), CategoryLabel(\"I\")]): s[i, k] * x[i, j] * x[k, j])) + sum(I.flat_map(lambda (i: CategoryLabel(\"I\")): J.map(lambda (j: CategoryLabel(\"J\")): (i, j))).map(lambda ((i, j): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"J\")]): r[i] * x[i, j])), constraints={parcel_assign: [Constraint(name=\"parcel_assign\", , lambda i: sum(J.map(lambda (j: CategoryLabel(\"J\")): x[i, j])) == 1, domain=I),],truck_capacity: [Constraint(name=\"truck_capacity\", , lambda j: sum(I.map(lambda (i: CategoryLabel(\"I\")): w[i] * x[i, j])) <= C[j], domain=J),],})"
+       "Problem(name=\"QuadraticKnapsackLogistics\", sense=MAXIMIZE, objective=sum(set(J.flat_map(lambda (j: CategoryLabel(\"J\")): s.keys().map(lambda ((i, k): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"I\")]): (j, i, k)))).map(lambda ((j, i, k): Tuple[CategoryLabel(\"J\"), CategoryLabel(\"I\"), CategoryLabel(\"I\")]): s[i, k] * x[i, j] * x[k, j])) + sum(set(I.flat_map(lambda (i: CategoryLabel(\"I\")): J.map(lambda (j: CategoryLabel(\"J\")): (i, j)))).map(lambda ((i, j): Tuple[CategoryLabel(\"I\"), CategoryLabel(\"J\")]): r[i] * x[i, j])), constraints={parcel_assign: [Constraint(name=\"parcel_assign\", , lambda i: sum(set(J).map(lambda (j: CategoryLabel(\"J\")): x[i, j])) == 1, domain=I),],truck_capacity: [Constraint(name=\"truck_capacity\", , lambda j: sum(set(I).map(lambda (i: CategoryLabel(\"I\")): w[i] * x[i, j])) <= C[j], domain=J),],})"
       ]
      },
      "execution_count": 12,
@@ -1264,10 +1264,10 @@
    "id": "1480ae56",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:58.126253Z",
-     "iopub.status.busy": "2026-03-24T02:04:58.126188Z",
-     "iopub.status.idle": "2026-03-24T02:04:58.627107Z",
-     "shell.execute_reply": "2026-03-24T02:04:58.626640Z"
+     "iopub.execute_input": "2026-06-04T02:50:02.763194Z",
+     "iopub.status.busy": "2026-06-04T02:50:02.763138Z",
+     "iopub.status.idle": "2026-06-04T02:50:02.982007Z",
+     "shell.execute_reply": "2026-06-04T02:50:02.981670Z"
     }
    },
    "outputs": [],
@@ -1325,10 +1325,10 @@
    "id": "7ba11d75",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:58.628501Z",
-     "iopub.status.busy": "2026-03-24T02:04:58.628434Z",
-     "iopub.status.idle": "2026-03-24T02:04:58.730997Z",
-     "shell.execute_reply": "2026-03-24T02:04:58.730627Z"
+     "iopub.execute_input": "2026-06-04T02:50:02.983348Z",
+     "iopub.status.busy": "2026-06-04T02:50:02.983293Z",
+     "iopub.status.idle": "2026-06-04T02:50:03.097086Z",
+     "shell.execute_reply": "2026-06-04T02:50:03.096752Z"
     }
    },
    "outputs": [
@@ -1342,7 +1342,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Binary)),],})"
+       "Problem(name=\"OneHot\", sense=MINIMIZE, objective=0, constraints={onehot: [Constraint(name=\"onehot\", sense=EQUAL, left=sum(x), right=1, shape=Scalar(Natural)),],})"
       ]
      },
      "execution_count": 14,
@@ -1391,10 +1391,10 @@
    "id": "568c762c",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:58.732526Z",
-     "iopub.status.busy": "2026-03-24T02:04:58.732445Z",
-     "iopub.status.idle": "2026-03-24T02:04:58.943372Z",
-     "shell.execute_reply": "2026-03-24T02:04:58.942971Z"
+     "iopub.execute_input": "2026-06-04T02:50:03.098383Z",
+     "iopub.status.busy": "2026-06-04T02:50:03.098323Z",
+     "iopub.status.idle": "2026-06-04T02:50:03.361793Z",
+     "shell.execute_reply": "2026-06-04T02:50:03.361355Z"
     }
    },
    "outputs": [
@@ -1408,7 +1408,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(C[a].map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
+       "Problem(name=\"KHotOverSet\", sense=MINIMIZE, objective=0, constraints={k-hot_constraint: [Constraint(name=\"k-hot_constraint\", , lambda a: sum(set(C[a]).map(lambda (i: natural): x[i])) == K[a], domain=set(M)),],})"
       ]
      },
      "execution_count": 15,
@@ -1473,10 +1473,10 @@
    "id": "2decc57b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:58.944556Z",
-     "iopub.status.busy": "2026-03-24T02:04:58.944496Z",
-     "iopub.status.idle": "2026-03-24T02:04:59.455793Z",
-     "shell.execute_reply": "2026-03-24T02:04:59.455480Z"
+     "iopub.execute_input": "2026-06-04T02:50:03.363441Z",
+     "iopub.status.busy": "2026-06-04T02:50:03.363357Z",
+     "iopub.status.idle": "2026-06-04T02:50:03.711592Z",
+     "shell.execute_reply": "2026-06-04T02:50:03.711205Z"
     }
    },
    "outputs": [
@@ -1778,10 +1778,10 @@
    "id": "d50b156f",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:59.457088Z",
-     "iopub.status.busy": "2026-03-24T02:04:59.457034Z",
-     "iopub.status.idle": "2026-03-24T02:04:59.590593Z",
-     "shell.execute_reply": "2026-03-24T02:04:59.590182Z"
+     "iopub.execute_input": "2026-06-04T02:50:03.712672Z",
+     "iopub.status.busy": "2026-06-04T02:50:03.712618Z",
+     "iopub.status.idle": "2026-06-04T02:50:03.908662Z",
+     "shell.execute_reply": "2026-06-04T02:50:03.908310Z"
     }
    },
    "outputs": [
@@ -1793,7 +1793,7 @@
        "$$"
       ],
       "text/plain": [
-       "Problem(name=\"My Problem\", sense=MINIMIZE, objective=sum(N.filter(lambda i: i % 2 == 0).flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j))).map(lambda ((i, j): Tuple[natural, natural]): x[i, j])), constraints=[])"
+       "Problem(name=\"My Problem\", sense=MINIMIZE, objective=sum(set(N.filter(lambda i: i % 2 == 0).flat_map(lambda (i: natural): i.map(lambda (j: natural): (i, j)))).map(lambda ((i, j): Tuple[natural, natural]): x[i, j])), constraints=[])"
       ]
      },
      "execution_count": 17,
@@ -1825,10 +1825,10 @@
    "id": "7da928f9",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-03-24T02:04:59.591623Z",
-     "iopub.status.busy": "2026-03-24T02:04:59.591562Z",
-     "iopub.status.idle": "2026-03-24T02:04:59.696371Z",
-     "shell.execute_reply": "2026-03-24T02:04:59.695995Z"
+     "iopub.execute_input": "2026-06-04T02:50:03.909714Z",
+     "iopub.status.busy": "2026-06-04T02:50:03.909655Z",
+     "iopub.status.idle": "2026-06-04T02:50:04.050522Z",
+     "shell.execute_reply": "2026-06-04T02:50:04.050187Z"
     }
    },
    "outputs": [
@@ -1896,7 +1896,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.11"
+   "version": "3.11.14"
   }
  },
  "nbformat": 4,
diff --git a/docs/ja/releases/jijmodeling-2.5.0.ipynb b/docs/ja/releases/jijmodeling-2.5.0.ipynb
new file mode 100644
index 00000000..c999fbde
--- /dev/null
+++ b/docs/ja/releases/jijmodeling-2.5.0.ipynb
@@ -0,0 +1,645 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# JijModeling 2.5.0 リリースノート"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 機能強化"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Decorator API における `jm.min`、`jm.max`、`jm.set` の内包表記サポート\n",
+    "\n",
+    "旧来は、Decorator API を利用する際に内包表記（Python のジェネレータ式）を引数として受け取れるのは {py:func}`jm.sum <jijmodeling.sum>` と {py:func}`jm.prod <jijmodeling.prod>` のみでした。\n",
+    "\n",
+    "本バージョンから、{py:func}`jm.min <jijmodeling.min>`、{py:func}`jm.max <jijmodeling.max>`、{py:func}`jm.set <jijmodeling.set>` の一引数呼び出しでも、同様に内包表記を受け取れるようになりました。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "f89d0a5d",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:26.923762Z",
+     "iopub.status.busy": "2026-06-04T03:14:26.923697Z",
+     "iopub.status.idle": "2026-06-04T03:14:27.119114Z",
+     "shell.execute_reply": "2026-06-04T03:14:27.118785Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{min/max/set comprehension example}\\\\\\displaystyle \\min &\\displaystyle \\min _{i=0}^{N-1}{{x}_{i}}+\\max _{\\substack{i=0\\\\i\\neq 0}}^{N-1}{{x}_{i}}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"min/max/set comprehension example\", sense=MINIMIZE, objective=min(set(N).map(lambda (i: natural): x[i])) + max(set(set(set(N.filter(lambda i: i != 0)).map(lambda (i: natural): i))).map(lambda (i: natural): x[i])), constraints=[])"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"min/max/set comprehension example\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Length()\n",
+    "    x = problem.BinaryVar(shape=N)\n",
+    "\n",
+    "    nonzero = jm.set(i for i in N if i != 0)\n",
+    "    problem += jm.min(x[i] for i in N) + jm.max(x[i] for i in nonzero)\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d74afece",
+   "metadata": {},
+   "source": [
+    "### 数式出力：制約の添え字が読みやすく\n",
+    "\n",
+    "辞書や配列同士の直接比較による制約条件が、$\\LaTeX$ 出力では $\\forall$ を使って出力されるようになり、可読性が向上しました。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "2380843f",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:27.120281Z",
+     "iopub.status.busy": "2026-06-04T03:14:27.120221Z",
+     "iopub.status.idle": "2026-06-04T03:14:27.922643Z",
+     "shell.execute_reply": "2026-06-04T03:14:27.922331Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{container-vs-scalar-comp}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
+       "\\text{dict-vs-dict}&\\quad \\displaystyle {y}_{i,j}\\leq {z}_{i,j}\\quad \\forall \\left(i,j\\right)\\;\\text{s.t.}\\;i\\in L,j\\in \\left\\{0,\\ldots ,N-1-1\\right\\}\\\\\\text{dict-vs-scalar}&\\quad \\displaystyle {y}_{i,j}\\leq 5\\quad \\forall \\left(i,j\\right)\\;\\text{s.t.}\\;i\\in L,j\\in \\left\\{0,\\ldots ,N-1-1\\right\\}\\\\\\text{scalar-vs-tensor}&\\quad \\displaystyle {x}_{i}\\geq 1\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\\\\\text{tensor-vs-tensor}&\\quad \\displaystyle {x}_{i}\\leq {x}_{i}\\quad \\forall i\\;\\text{s.t.}\\;i\\in \\left\\{0,\\ldots ,N-1\\right\\}\\end{aligned}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\y&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\}\\\\z&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in L,j\\in N-1\\right\\}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "L&\\text{Category Label}\\end{array}\n",
+       "\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"container-vs-scalar-comp\", sense=MINIMIZE, objective=0, constraints={dict-vs-dict: [Constraint(name=\"dict-vs-dict\", sense=LESS_THAN_EQUAL, left=y, right=z, shape=SameTotalDict { key: Located { inner: ElementOf { set: Located { inner: ToSet { operand: Located { inner: Tuple { components: [Located { inner: IterCategoryLabels { name: \"L\", ext: WithType { type_: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, Located { inner: OverloadedBinaryNumeric { operator: Located { inner: Sub, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, lhs: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) }, rhs: Located { inner: Literal { literal: Located { inner: Integer { value: Located { inner: 1, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: NoSrcSpan }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithTypeAndDictionary { type_: Scalar { mode: Static, kind: Natural }, dictionary: Scalar, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }], ext: WithType { type_: Tuple { components: [Located { inner: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, ext: WithTypeAndDictionary { type_: Set { element: Located { inner: Tuple { components: [Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, src_span: NoSrcSpan } }, dictionary: Product { component_dicts: [Set(CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }), FromNatural] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, value: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan }, scalar: Binary }),],dict-vs-scalar: [Constraint(name=\"dict-vs-scalar\", sense=LESS_THAN_EQUAL, left=y, right=5, shape=TotalDictVsScalar { key: Located { inner: ElementOf { set: Located { inner: ToSet { operand: Located { inner: Tuple { components: [Located { inner: IterCategoryLabels { name: \"L\", ext: WithType { type_: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, Located { inner: OverloadedBinaryNumeric { operator: Located { inner: Sub, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, lhs: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) }, rhs: Located { inner: Literal { literal: Located { inner: Integer { value: Located { inner: 1, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: NoSrcSpan }, ext: WithType { type_: Scalar { mode: Static, kind: Binary }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }, ext: WithTypeAndDictionary { type_: Scalar { mode: Static, kind: Natural }, dictionary: Scalar, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 40 }, end: SrcLoc { line: 9, column: 45 } }) }], ext: WithType { type_: Tuple { components: [Located { inner: Set { element: Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) }, ext: WithTypeAndDictionary { type_: Set { element: Located { inner: Tuple { components: [Located { inner: CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, Located { inner: Scalar { mode: Static, kind: Natural }, src_span: NoSrcSpan }] }, src_span: NoSrcSpan } }, dictionary: Product { component_dicts: [Set(CategoryLabel { name: Located { inner: \"L\", src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }), FromNatural] }, inner: LaTeXMetadata { custom_latex: None, set_style: None, subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 9, column: 8 }, end: SrcLoc { line: 9, column: 47 } }) } }, src_span: NoSrcSpan }, value: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan }, scalar: Natural }),],scalar-vs-tensor: [Constraint(name=\"scalar-vs-tensor\", sense=GREATER_THAN_EQUAL, left=x, right=1, shape=TensorLikeVsScalar { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],tensor-vs-tensor: [Constraint(name=\"tensor-vs-tensor\", sense=LESS_THAN_EQUAL, left=x, right=x, shape=SameTensorLike { spec: Tensor(TensorSpec { shape: [Specified(Located { inner: RangeNat { upper_bound: Located { inner: FVar { name: \"N\", ext: WithType { type_: Scalar { mode: Static, kind: Natural }, inner: LaTeXMetadata { custom_latex: None, set_style: Some(SetStyle { element: None, kind: Natural }), subscript_styles: [] } } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) } }, src_span: Real(RealSrcSpan { filename: \"/var/folders/mg/mg6st30d18s7pxjjrk6pkxym0000gn/T/ipykernel_44063/4122996662.py\", start: SrcLoc { line: 6, column: 8 }, end: SrcLoc { line: 6, column: 25 } }) })], element: Located { inner: Scalar { mode: Dynamic, kind: Binary }, src_span: NoSrcSpan } }), scalar: Binary }),],})"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"container-vs-scalar-comp\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Natural()\n",
+    "    L = problem.CategoryLabel()\n",
+    "    x = problem.BinaryVar(shape=N)\n",
+    "    y = problem.BinaryVar(dict_keys=(L, N - 1))\n",
+    "    z = problem.BinaryVar(dict_keys=(L, N - 1))\n",
+    "\n",
+    "    problem += problem.Constraint(\"scalar-vs-tensor\", 1 <= x)\n",
+    "    problem += problem.Constraint(\"tensor-vs-tensor\", x <= x)\n",
+    "    problem += problem.Constraint(\"dict-vs-scalar\", y <= 5)\n",
+    "    problem += problem.Constraint(\"dict-vs-dict\", y <= z)\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8079b7de",
+   "metadata": {},
+   "source": [
+    "### `Placeholder` の `dtype` に上限付き自然数とカテゴリーラベルを指定できるように\n",
+    "\n",
+    "{py:meth}`Problem.Placeholder <jijmodeling.Problem.Placeholder>`（および `Graph`、`PartialDict`、`TotalDict` などの型付き構築子）の `dtype` 引数は、これまで `jm.DataType`、NumPy のスカラー型、あるいはそれらから構成されるタプルに限られていました。\n",
+    "本バージョンから、`dtype` には次のものも追加で指定できるようになりました：\n",
+    "\n",
+    "- 自然数式 `n`：値が `n` より真に小さい自然数（すなわち $\\{0, 1, \\dots, n - 1\\}$ のいずれか）であることを表します。`n` には Python の整数リテラルのほか、自然数型の他のプレースホルダーや {py:class}`~jijmodeling.NamedExpr` などの式も渡せます。\n",
+    "- {py:class}`~jijmodeling.CategoryLabel` `L`：値が `L` のラベルのうちのいずれかであることを表します。\n",
+    "- 上記（あるいは他の指定可能な `dtype`）を要素とするタプル `(T, T, ...)`。\n",
+    "\n",
+    "上記の `dtype` に関する追加に合わせて、型付き構築子である {py:meth}`Problem.Natural <jijmodeling.Problem.Natural>`（およびそのエイリアスである {py:meth}`Problem.Length <jijmodeling.Problem.Length>` と {py:meth}`Problem.Dim <jijmodeling.Problem.Dim>`）でも `less_than=natexpr` キーワード引数を指定できるようになりました。これは `Placeholder(dtype=natexpr)` と同じく上限付き自然数型のプレースホルダーを宣言するもので、自然数値のプレースホルダーであるという意図をより明瞭に表現する書き方です。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "7f152946",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:27.923761Z",
+     "iopub.status.busy": "2026-06-04T03:14:27.923698Z",
+     "iopub.status.idle": "2026-06-04T03:14:27.992682Z",
+     "shell.execute_reply": "2026-06-04T03:14:27.992284Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{bounded natural shorthand}\\\\\\displaystyle \\min &\\displaystyle {x}_{i}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}i&\\in N&\\quad &\\text{A scalar placeholder in }N\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"bounded natural shorthand\", sense=MINIMIZE, objective=x[i], constraints=[])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"bounded natural shorthand\")\n",
+    "N = problem.Natural(\"N\")\n",
+    "i = problem.Natural(\"i\", less_than=N)\n",
+    "x = problem.BinaryVar(\"x\", shape=(N,))\n",
+    "problem += x[i]\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "116eef82",
+   "metadata": {},
+   "source": [
+    "Decorator API でも同じキーワード引数を利用できます。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "9eb0de5b",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:27.994506Z",
+     "iopub.status.busy": "2026-06-04T03:14:27.994428Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.068682Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.068298Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{bounded natural shorthand in Decorator API}\\\\\\displaystyle \\min &\\displaystyle {x}_{i}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[N;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}i&\\in N&\\quad &\\text{A scalar placeholder in }N\\\\N&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"bounded natural shorthand in Decorator API\", sense=MINIMIZE, objective=x[i], constraints=[])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "@jm.Problem.define(\"bounded natural shorthand in Decorator API\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    N = problem.Length()\n",
+    "    i = problem.Dim(less_than=N)\n",
+    "    x = problem.BinaryVar(shape=(N,))\n",
+    "    problem += x[i]\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8fdfd33",
+   "metadata": {},
+   "source": [
+    "より複雑な例として、以下の、無向グラフ $G = (V, E)$ についての最適化問題を考えます。以前のバージョンでは辺の端点の型は単なる自然数として宣言する必要がありましたが、本リリースから、端点が $[0, V)$ の範囲に収まることを `dtype` を通じて表現できるようになりました："
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "7109b6c5",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.069633Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.069578Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.240888Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.240532Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{max cut}\\\\\\displaystyle \\max &\\displaystyle \\sum _{\\left\\langle u,v\\right\\rangle \\in E}{{\\left({x}_{u}-{x}_{v}\\right)}^{2}}\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{Array}}\\left[V;\\left\\{0, 1\\right\\}\\right]&\\quad &1\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}E&\\in \\mathop{\\mathrm{Array}}\\left[(-);V\\times V\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }V\\times V\\\\V&\\in \\mathbb{N}&\\quad &\\text{A scalar placeholder in }\\mathbb{N}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"max cut\", sense=MAXIMIZE, objective=sum(E.map(lambda ((u, v): Tuple[V, V]): (x[u] - x[v]) ** 2)), constraints=[])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"max cut\", sense=jm.ProblemSense.MAXIMIZE)\n",
+    "V = problem.Natural(\"V\")\n",
+    "# `E` の各要素が `[0, V)` のペアであることを直接宣言できるようになりました\n",
+    "# （従来は dtype=(jm.DataType.Natural, jm.DataType.Natural) と書く必要がありました）。\n",
+    "# この宣言は、 `problem.graph(\"E\", dtype=V)` と書くこともできます。\n",
+    "E = problem.Placeholder(\"E\", dtype=(V, V), ndim=1)\n",
+    "x = problem.BinaryVar(\"x\", shape=(V,))\n",
+    "problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, E).sum()\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7117bf2d",
+   "metadata": {},
+   "source": [
+    "また、グラフの頂点にラベルを用いる場合を想定して、{py:class}`~jijmodeling.CategoryLabel` をそのまま `dtype` として指定することもできるようになりました。\n",
+    "以下の例は、ラベルが頂点として使われるグラフの上で（{py:meth}`Problem.Graph` を用いて）同じ問題を定義するものです。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "94a7c425",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.241975Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.241900Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.635269Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.634858Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "problem = jm.Problem(\"max cut on a labeled graph\", sense=jm.ProblemSense.MAXIMIZE)\n",
+    "L = problem.CategoryLabel(\"L\")\n",
+    "edges = problem.Graph(\"edges\", dtype=L)\n",
+    "x = problem.BinaryVar(\"x\", dict_keys=L)\n",
+    "problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, edges).sum()\n",
+    "\n",
+    "compiler = jm.Compiler.from_problem(\n",
+    "    problem,\n",
+    "    {\n",
+    "        \"L\": [\"A\", \"B\", \"C\"],\n",
+    "        \"edges\": [(\"A\", \"B\"), (\"B\", \"C\"), (\"C\", \"A\")],\n",
+    "    },\n",
+    ")\n",
+    "instance = compiler.eval_problem(problem)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "67fa5ca1",
+   "metadata": {},
+   "source": [
+    "インスタンスデータとして与えられた値が宣言された `dtype` と整合しない場合（たとえば、頂点インデックスが `V` 以上であったり、`L` に含まれないラベルが渡されたりした場合）、コンパイラは範囲外エラーを報告します。"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 目的関数を代入で再設定できるように\n",
+    "\n",
+    "本バージョンから {py:attr}`Problem.objective <jijmodeling.Problem.objective>` に直接代入して置き換えられるようになりました。\n",
+    "{py:class}`~jijmodeling.DecoratedProblem` でも同じように `problem.objective = ...` と書けます。\n",
+    "\n",
+    "たとえば、一度設定した目的関数を別の式に置き換えたり、`problem.objective = 0` として目的関数を明示的にリセットしたりできます。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.636518Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.636430Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.706288Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.705979Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{set objective example}\\\\\\displaystyle \\min &\\displaystyle z\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\y&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\z&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"set objective example\", sense=MINIMIZE, objective=z, constraints=[])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"set objective example\")\n",
+    "x = problem.BinaryVar(\"x\")\n",
+    "y = problem.BinaryVar(\"y\")\n",
+    "\n",
+    "problem.objective = x\n",
+    "problem.objective = y\n",
+    "problem.objective = 0\n",
+    "\n",
+    "\n",
+    "@problem.update\n",
+    "def _(problem: jm.DecoratedProblem):\n",
+    "    z = problem.BinaryVar()\n",
+    "    problem.objective = z\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "937e1f3d",
+   "metadata": {},
+   "source": [
+    "### 生成関数による辞書の生成\n",
+    "\n",
+    "本バージョンから、{py:func}`~jijmodeling.gendict` 関数により、キー集合と生成関数を指定して配列を生成できるようになりました。\n",
+    "これは配列の {py:func}`~jijmodeling.genarray` や numpy の {py:func}`~numpy.fromfunction` と類似の機能です。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "fe75848f",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.707329Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.707269Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.806463Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.805959Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{gendict example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{K};\\left\\{0, 1\\right\\}\\right]&\\quad &\\text{a dictionary of }\\text{binary}\\text{ variables with key }K\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}a&\\in \\mathop{\\mathrm{TotalDict}}\\left[\\mathrm{K};\\mathbb{R}\\right]&\\quad &\\text{A total dictionary of placeholders with keys }\\mathrm{K}\\text{, values in }\\mathbb{R}\\\\\\end{alignedat}\\\\&\\\\&\\text{Category Labels:}\\\\&\\qquad \\begin{array}{rl}\n",
+       "K&\\text{Category Label}\\end{array}\n",
+       "\\\\&\\\\&\\text{Named Expressions:}\\\\&\\qquad \\begin{alignedat}{2}Sums&=\\mathop{\\mathtt{gen\\_{}dict}}\\left(\\lambda \\left(k\\in \\mathrm{K}\\right)\\ldotp {a}_{k}\\cdot {x}_{k},K\\right)&\\quad &\\in \\mathop{\\mathrm{TotalDict}}\\left[K;\\mathbb{R}\\right]\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"gendict example\", sense=MINIMIZE, objective=0, constraints=[])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "problem = jm.Problem(\"gendict example\")\n",
+    "K = problem.CategoryLabel(\"K\")\n",
+    "a = problem.Float(\"a\", dict_keys=K)\n",
+    "x = problem.BinaryVar(\"x\", dict_keys=K)\n",
+    "Sums = problem.NamedExpr(\"Sums\", jm.gendict(K, lambda k: a[k] * x[k]))\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16268a26",
+   "metadata": {},
+   "source": [
+    "また、`jm.genarray` と同じように、Decorator API を利用している場合、内包表記を用いることもできます。ただし、`for .. in ...` は一つしか許容されません。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "9bd10a27",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.807608Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.807546Z",
+     "iopub.status.idle": "2026-06-04T03:14:28.903833Z",
+     "shell.execute_reply": "2026-06-04T03:14:28.903486Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{gendict example}\\\\\\displaystyle \\min &\\displaystyle 0\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"gendict example\", sense=MINIMIZE, objective=0, constraints=[])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "@jm.Problem.define(\"gendict example\")\n",
+    "def problem(problem):\n",
+    "    problem = jm.Problem(\"gendict example\")\n",
+    "    K = problem.CategoryLabel(\"K\")\n",
+    "    a = problem.Float(\"a\", dict_keys=K)\n",
+    "    x = problem.BinaryVar(\"x\", dict_keys=K)\n",
+    "    Sums = problem.NamedExpr(\"Sums\", jm.gendict(a[k] * x[k] for k in K))\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5cac4033",
+   "metadata": {},
+   "source": [
+    "## バグ修正"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "85257ae8",
+   "metadata": {},
+   "source": [
+    "### 添え字の要素と数値型の演算に失敗していたバグの修正\n",
+    "\n",
+    "以下のように `Constraint` の添え字の要素に対する数値演算が誤って型エラーとして判定されていた問題を修正しました。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "34eef060",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:28.904893Z",
+     "iopub.status.busy": "2026-06-04T03:14:28.904839Z",
+     "iopub.status.idle": "2026-06-04T03:14:29.049894Z",
+     "shell.execute_reply": "2026-06-04T03:14:29.049606Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\begin{array}{rl}\n",
+       "\\text{Problem}\\colon &\\text{Example}\\\\\\displaystyle \\min &\\displaystyle 0\\\\&\\\\\\text{s.t.}&\\\\&\\begin{aligned}\n",
+       "\\text{c}&\\quad \\displaystyle k\\cdot x\\leq 0\\quad \\forall k\\;\\text{s.t.}\\;k\\in K\\end{aligned}\n",
+       "\\\\&\\\\\\text{where}&\\\\&\\text{Decision Variables:}\\\\&\\qquad \\begin{alignedat}{2}x&\\in \\left\\{0, 1\\right\\}&\\quad &0\\text{-dim binary variable}\\\\\\end{alignedat}\\\\&\\\\&\\text{Placeholders:}\\\\&\\qquad \\begin{alignedat}{2}K&\\in \\mathop{\\mathrm{Array}}\\left[(-);\\mathbb{R}\\right]&\\quad &1\\text{-dimensional array of placeholders with elements in }\\mathbb{R}\\\\\\end{alignedat}\\end{array}\n",
+       "$$"
+      ],
+      "text/plain": [
+       "Problem(name=\"Example\", sense=MINIMIZE, objective=0, constraints={c: [Constraint(name=\"c\", , lambda k: k * x <= 0, domain=set(K)),],})"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "\n",
+    "@jm.Problem.define(\"Example\")\n",
+    "def problem(problem: jm.DecoratedProblem):\n",
+    "    K = problem.Float(ndim=1)\n",
+    "    x = problem.BinaryVar()\n",
+    "    problem += problem.Constraint(\"c\", [k * x <= 0 for k in K])\n",
+    "\n",
+    "\n",
+    "problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8ca7e0bf",
+   "metadata": {},
+   "source": [
+    "### `product` や `filter` の絡む数式出力を改善\n",
+    "\n",
+    "旧来は `product` や `filter` などを含む式が場合によって複雑な式として表示されていましたが、内包表記を使った読みやすい出力がされるようになりました。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "8a32b31a",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-06-04T03:14:29.051025Z",
+     "iopub.status.busy": "2026-06-04T03:14:29.050968Z",
+     "iopub.status.idle": "2026-06-04T03:14:29.168549Z",
+     "shell.execute_reply": "2026-06-04T03:14:29.168245Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$$\\left\\{\\left\\langle i,j\\right\\rangle \\mid i\\in \\left\\{0,\\ldots ,N-1\\right\\},j\\in \\left\\{0,\\ldots ,M-1\\right\\},i=j\\right\\}$$"
+      ],
+      "text/plain": [
+       "Expression(set((N, M)).filter(lambda (i, j): i == j))"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jijmodeling as jm\n",
+    "\n",
+    "problem = jm.Problem(\"product and filter example\")\n",
+    "N = problem.Natural(\"N\")\n",
+    "M = problem.Natural(\"M\")\n",
+    "x = problem.BinaryVar(\"x\", shape=(N, M))\n",
+    "jm.product(N, M).filter(lambda i, j: i == j)"
+   ]
+  }
+ ],
+ "metadata": {
+  "jupytext": {
+   "default_lexer": "ipython3"
+  },
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/markdowns/en/advanced/generation.md b/markdowns/en/advanced/generation.md
index 0a387ff6..39ee6fba 100644
--- a/markdowns/en/advanced/generation.md
+++ b/markdowns/en/advanced/generation.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/en/advanced/named_expr.md b/markdowns/en/advanced/named_expr.md
index 6265f7cd..9002591f 100644
--- a/markdowns/en/advanced/named_expr.md
+++ b/markdowns/en/advanced/named_expr.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/advanced/serialize.md b/markdowns/en/advanced/serialize.md
index 01ac8e9c..32d0fdcc 100644
--- a/markdowns/en/advanced/serialize.md
+++ b/markdowns/en/advanced/serialize.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/en/basics/expressions.md b/markdowns/en/basics/expressions.md
index cad0f7da..8df8f815 100644
--- a/markdowns/en/basics/expressions.md
+++ b/markdowns/en/basics/expressions.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/basics/instance_generation.md b/markdowns/en/basics/instance_generation.md
index b4813771..a6ed8c34 100644
--- a/markdowns/en/basics/instance_generation.md
+++ b/markdowns/en/basics/instance_generation.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/basics/modeling.md b/markdowns/en/basics/modeling.md
index c31cdad4..7c0f787c 100644
--- a/markdowns/en/basics/modeling.md
+++ b/markdowns/en/basics/modeling.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
@@ -52,8 +52,7 @@ problem += y
 problem
 ```
 
-You can see that the existing term was not replaced; instead, $y$ was added and the new objective is $x + y$.
-If you might need to remove objective terms later, keep a list of terms in Python and set the objective from that list when needed.
+You can see that the existing term is not replaced; instead, $y$ is added and the new objective is $x + y$.
 
 :::{admonition} Subtracting terms from the objective
 :class: tip
@@ -61,6 +60,17 @@ If you might need to remove objective terms later, keep a list of terms in Pytho
 Since JijModeling 2.3.1, you can also "subtract" scalar {py:class}`~jijmodeling.Expression` objects from the objective by using the {py:meth}`-= <jijmodeling.Problem.__isub__>` operator on a {py:class}`~jijmodeling.Problem`.
 :::
 
+:::{admonition} Replacing the objective
+:class: tip
+Since JijModeling 2.5.0, you can assign an expression directly to `Problem.objective` to discard the previous objective and replace it with a new one.
+:::
+
+```{code-cell} ipython3
+problem.objective = y
+
+problem
+```
+
 As a more practical example, let's set the objective for the knapsack problem.
 
 ```{code-cell} ipython3
diff --git a/markdowns/en/basics/overview.md b/markdowns/en/basics/overview.md
index a4f38bf8..47a6e541 100644
--- a/markdowns/en/basics/overview.md
+++ b/markdowns/en/basics/overview.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/basics/problem.md b/markdowns/en/basics/problem.md
index 08a6313a..059f46e7 100644
--- a/markdowns/en/basics/problem.md
+++ b/markdowns/en/basics/problem.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/basics/variables.md b/markdowns/en/basics/variables.md
index 5a7d6020..667d9ef4 100644
--- a/markdowns/en/basics/variables.md
+++ b/markdowns/en/basics/variables.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/introduction.md b/markdowns/en/introduction.md
index 73385c0c..2c328852 100644
--- a/markdowns/en/introduction.md
+++ b/markdowns/en/introduction.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/en/quickstart/openjij.md b/markdowns/en/quickstart/openjij.md
index da977041..dbfaffce 100644
--- a/markdowns/en/quickstart/openjij.md
+++ b/markdowns/en/quickstart/openjij.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/en/quickstart/scip.md b/markdowns/en/quickstart/scip.md
index a3e3f4ed..16a3a2f9 100644
--- a/markdowns/en/quickstart/scip.md
+++ b/markdowns/en/quickstart/scip.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/references/cheat_sheet.md b/markdowns/en/references/cheat_sheet.md
index 0eba9e93..252be0fb 100644
--- a/markdowns/en/references/cheat_sheet.md
+++ b/markdowns/en/references/cheat_sheet.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/en/references/migration_guide_to_jijmodeling2.md b/markdowns/en/references/migration_guide_to_jijmodeling2.md
index 096f7bc2..a1a63d26 100644
--- a/markdowns/en/references/migration_guide_to_jijmodeling2.md
+++ b/markdowns/en/references/migration_guide_to_jijmodeling2.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.0.0.md b/markdowns/en/releases/jijmodeling-2.0.0.md
index fa633b16..881a6395 100644
--- a/markdowns/en/releases/jijmodeling-2.0.0.md
+++ b/markdowns/en/releases/jijmodeling-2.0.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.1.0.md b/markdowns/en/releases/jijmodeling-2.1.0.md
index 81ba87f4..1e00f753 100644
--- a/markdowns/en/releases/jijmodeling-2.1.0.md
+++ b/markdowns/en/releases/jijmodeling-2.1.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.2.0.md b/markdowns/en/releases/jijmodeling-2.2.0.md
index 6283362e..6e6107a8 100644
--- a/markdowns/en/releases/jijmodeling-2.2.0.md
+++ b/markdowns/en/releases/jijmodeling-2.2.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.3.1.md b/markdowns/en/releases/jijmodeling-2.3.1.md
index 7bea273e..14856032 100644
--- a/markdowns/en/releases/jijmodeling-2.3.1.md
+++ b/markdowns/en/releases/jijmodeling-2.3.1.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.3.2.md b/markdowns/en/releases/jijmodeling-2.3.2.md
index ca6aaf39..7f51c8fe 100644
--- a/markdowns/en/releases/jijmodeling-2.3.2.md
+++ b/markdowns/en/releases/jijmodeling-2.3.2.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.4.0.md b/markdowns/en/releases/jijmodeling-2.4.0.md
index b1ad3582..c937a886 100644
--- a/markdowns/en/releases/jijmodeling-2.4.0.md
+++ b/markdowns/en/releases/jijmodeling-2.4.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.4.1.md b/markdowns/en/releases/jijmodeling-2.4.1.md
index 69c712bc..0856dde2 100644
--- a/markdowns/en/releases/jijmodeling-2.4.1.md
+++ b/markdowns/en/releases/jijmodeling-2.4.1.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/en/releases/jijmodeling-2.5.0.md b/markdowns/en/releases/jijmodeling-2.5.0.md
new file mode 100644
index 00000000..bbeb128d
--- /dev/null
+++ b/markdowns/en/releases/jijmodeling-2.5.0.md
@@ -0,0 +1,243 @@
+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.19.3
+kernelspec:
+  display_name: .venv
+  language: python
+  name: python3
+---
+
+# JijModeling 2.5.0 Release Notes
+
++++
+
+## Feature Enhancements
+
++++
+
+### Comprehension syntax for `jm.min`, `jm.max`, and `jm.set` in the Decorator API
+
+Previously, when using the Decorator API, only {py:func}`jm.sum <jijmodeling.sum>` and {py:func}`jm.prod <jijmodeling.prod>` accepted a comprehension (Python generator) expression as their single argument.
+
+Starting with this version, unary calls to {py:func}`jm.min <jijmodeling.min>`, {py:func}`jm.max <jijmodeling.max>`, and {py:func}`jm.set <jijmodeling.set>` also accept comprehension expressions in the same way.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("min/max/set comprehension example")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Length()
+    x = problem.BinaryVar(shape=N)
+
+    nonzero = jm.set(i for i in N if i != 0)
+    problem += jm.min(x[i] for i in N) + jm.max(x[i] for i in nonzero)
+
+
+problem
+```
+
+### Math output: More readable constraint indices
+
+Constraints created by directly comparing dictionaries or arrays are now rendered in $\LaTeX$ output using $\forall$, improving readability.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("container-vs-scalar-comp")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Natural()
+    L = problem.CategoryLabel()
+    x = problem.BinaryVar(shape=N)
+    y = problem.BinaryVar(dict_keys=(L, N - 1))
+    z = problem.BinaryVar(dict_keys=(L, N - 1))
+
+    problem += problem.Constraint("scalar-vs-tensor", 1 <= x)
+    problem += problem.Constraint("tensor-vs-tensor", x <= x)
+    problem += problem.Constraint("dict-vs-scalar", y <= 5)
+    problem += problem.Constraint("dict-vs-dict", y <= z)
+
+
+problem
+```
+
+### Bounded naturals and category labels are now allowed as a `Placeholder` `dtype`
+
+The `dtype` argument of {py:meth}`Problem.Placeholder <jijmodeling.Problem.Placeholder>` (and its shorthands such as `Graph`, `PartialDict`, and `TotalDict`) used to be limited to a `jm.DataType`, a NumPy scalar type, or a tuple built out of those.
+Starting with this version, `dtype` additionally accepts:
+
+- a natural-number expression `n`, declaring that the values are natural numbers strictly less than `n` (i.e. drawn from $\{0, 1, \dots, n - 1\}$); the bound `n` may also be a Python integer literal or another placeholder/named expression of natural-number type.
+- a {py:class}`~jijmodeling.CategoryLabel` `L`, declaring that the values are labels drawn from `L`.
+- a tuple `(T, T, ...)` whose components are any of the above (or any other accepted `dtype`).
+
+Along with the additions on `dtype` as described above, the shorthand constructors {py:meth}`Problem.Natural <jijmodeling.Problem.Natural>` (and its aliases: {py:meth}`Problem.Length <jijmodeling.Problem.Length>` and {py:meth}`Problem.Dim <jijmodeling.Problem.Dim>`) now also accept a `less_than=natexpr` keyword argument. This declares the same bounded-natural type placeholder variable as `Placeholder(dtype=natexpr)`, while more clearly communicating the intent of it being a scalar natural placeholder:
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("bounded natural shorthand")
+N = problem.Natural("N")
+i = problem.Natural("i", less_than=N)
+x = problem.BinaryVar("x", shape=(N,))
+problem += x[i]
+
+problem
+```
+
+The same keyword argument is available in the Decorator API:
+
+```{code-cell} ipython3
+@jm.Problem.define("bounded natural shorthand in Decorator API")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Length()
+    i = problem.Dim(less_than=N)
+    x = problem.BinaryVar(shape=(N,))
+    problem += x[i]
+
+
+problem
+```
+
+For a more complex example, consider the following optimization problem involving an undirected graph $G = (V, E)$. Previously, edge endpoints had to be declared as plain naturals; with this release you can express the intent that they must lie in $[0, V)$:
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("max cut", sense=jm.ProblemSense.MAXIMIZE)
+V = problem.Natural("V")
+# We can now say that each entry of `E` is a pair of vertices in [0, V)
+# (previously we had to write dtype=(jm.DataType.Natural, jm.DataType.Natural)).
+# Alternatively, we may write this as problem.graph("E", dtype=V)
+E = problem.Placeholder("E", dtype=(V, V), ndim=1)
+x = problem.BinaryVar("x", shape=(V,))
+problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, E).sum()
+
+problem
+```
+
+When the vertices of a graph are named rather than indexed, a {py:class}`~jijmodeling.CategoryLabel` can now be used directly as the `dtype`.
+Here is the same problem, written with {py:meth}`Problem.Graph`, but on a graph whose vertices are identified by labels rather than integer indices:
+
+```{code-cell} ipython3
+problem = jm.Problem("max cut on a labeled graph", sense=jm.ProblemSense.MAXIMIZE)
+L = problem.CategoryLabel("L")
+edges = problem.Graph("edges", dtype=L)
+x = problem.BinaryVar("x", dict_keys=L)
+problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, edges).sum()
+
+compiler = jm.Compiler.from_problem(
+    problem,
+    {
+        "L": ["A", "B", "C"],
+        "edges": [("A", "B"), ("B", "C"), ("C", "A")],
+    },
+)
+instance = compiler.eval_problem(problem)
+```
+
+When a value supplied through the instance data is not consistent with the declared `dtype` (for example a vertex index $\geq V$, or a label not in `L`), the compiler will report an out-of-range error instead of silently accepting the value.
+
++++
+
+### Objective functions can now be replaced by assignment
+
+In this version, you can now replace the objective function directly by assigning to {py:attr}`Problem.objective <jijmodeling.Problem.objective>`.
+The same `problem.objective = ...` syntax is also available for {py:class}`~jijmodeling.DecoratedProblem`.
+
+For example, you can replace an already-defined objective with another expression, or explicitly reset it with `problem.objective = 0`.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("set objective example")
+x = problem.BinaryVar("x")
+y = problem.BinaryVar("y")
+
+problem.objective = x
+problem.objective = y
+problem.objective = 0
+
+
+@problem.update
+def _(problem: jm.DecoratedProblem):
+    z = problem.BinaryVar()
+    problem.objective = z
+
+
+problem
+```
+
+### Generating dictionaries with generator functions
+
+Starting with this version, the {py:func}`~jijmodeling.gendict` function can be used to generate dictionaries by specifying a set of keys and a generator function.
+This is similar to the array version {py:func}`~jijmodeling.genarray`, and to NumPy's {py:func}`~numpy.fromfunction`.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+problem = jm.Problem("gendict example")
+K = problem.CategoryLabel("K")
+a = problem.Float("a", dict_keys=K)
+x = problem.BinaryVar("x", dict_keys=K)
+Sums = problem.NamedExpr("Sums", jm.gendict(K, lambda k: a[k] * x[k]))
+
+
+problem
+```
+
+Like `genarray`, using comprehensions is supported when using the Decorator API, but only one `for .. in ...` clause is allowed in a comprehension.
+
+```{code-cell} ipython3
+@jm.Problem.define("gendict example")
+def problem(problem):
+    problem = jm.Problem("gendict example")
+    K = problem.CategoryLabel("K")
+    a = problem.Float("a", dict_keys=K)
+    x = problem.BinaryVar("x", dict_keys=K)
+    Sums = problem.NamedExpr("Sums", jm.gendict(a[k] * x[k] for k in K))
+
+
+problem
+```
+
+## Bug Fixes
+
++++
+
+### Fix bug where operations between subscript elements and numeric types failed
+
+Fixed an issue where numeric operations on `Constraint` subscript elements, as shown below, were incorrectly treated as type errors.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("Example")
+def problem(problem: jm.DecoratedProblem):
+    K = problem.Float(ndim=1)
+    x = problem.BinaryVar()
+    problem += problem.Constraint("c", [k * x <= 0 for k in K])
+
+
+problem
+```
+
+### Improved math rendering for expressions involving `product` and `filter`
+
+Previously, expressions involving `product` and `filter` could be rendered as overly complex formulas in some cases. They are now displayed in a more readable form using comprehension-style notation.
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("product and filter example")
+N = problem.Natural("N")
+M = problem.Natural("M")
+x = problem.BinaryVar("x", shape=(N, M))
+jm.product(N, M).filter(lambda i, j: i == j)
+```
diff --git a/markdowns/ja/advanced/generation.md b/markdowns/ja/advanced/generation.md
index e0d79e1f..648bd3d0 100644
--- a/markdowns/ja/advanced/generation.md
+++ b/markdowns/ja/advanced/generation.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/ja/advanced/named_expr.md b/markdowns/ja/advanced/named_expr.md
index 28b57d8a..08a2cff5 100644
--- a/markdowns/ja/advanced/named_expr.md
+++ b/markdowns/ja/advanced/named_expr.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/advanced/serialize.md b/markdowns/ja/advanced/serialize.md
index 68fa0e72..c6bfebb7 100644
--- a/markdowns/ja/advanced/serialize.md
+++ b/markdowns/ja/advanced/serialize.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/ja/basics/expressions.md b/markdowns/ja/basics/expressions.md
index 2bdee086..3bee5ee9 100644
--- a/markdowns/ja/basics/expressions.md
+++ b/markdowns/ja/basics/expressions.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/basics/instance_generation.md b/markdowns/ja/basics/instance_generation.md
index 44ab2805..26fa5361 100644
--- a/markdowns/ja/basics/instance_generation.md
+++ b/markdowns/ja/basics/instance_generation.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/basics/modeling.md b/markdowns/ja/basics/modeling.md
index 7ceec201..2ec4e3e0 100644
--- a/markdowns/ja/basics/modeling.md
+++ b/markdowns/ja/basics/modeling.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
@@ -77,8 +77,7 @@ problem += y
 problem
 ```
 
-既存の項が置き換えられたのではなく、$y$ が加算され $x + y$ が新たな目的関数となっていることが分かります。
-目的関数の項を削除したい場合、目的関数の項の一覧を（Python の）リストなどで持っておき、あとからそれを使って目的関数を設定するなどするとよいでしょう。
+既存の項が置き換えられるのではなく、$y$ が加算され $x + y$ が新たな目的関数となっていることが分かります。
 
 :::{admonition} 目的関数から項を「引く」操作
 :class: tip
@@ -86,6 +85,17 @@ problem
 JijModeling 2.3.1 以降では、{py:class}`~jijmodeling.Problem` に対して {py:meth}`-= <jijmodeling.Problem.__isub__>` 演算子を使うことで、数値型の {py:class}`~jijmodeling.Expression` オブジェクトを目的関数から「引く」こともできます。
 :::
 
+:::{admonition} 目的関数の置き換え
+:class: tip
+JijModeling 2.5.0 以降では、`Problem.objective` に直接式を代入することで、これまでの目的関数を捨て、新しい目的関数で置き換えることができます。
+:::
+
+```{code-cell} ipython3
+problem.objective = y
+
+problem
+```
+
 ## 制約条件の設定
 
 制約条件の追加も同様に {py:meth}`+= <jijmodeling.Problem.__iadd__>` 演算子を使って行います。
diff --git a/markdowns/ja/basics/overview.md b/markdowns/ja/basics/overview.md
index 33068f84..52459f55 100644
--- a/markdowns/ja/basics/overview.md
+++ b/markdowns/ja/basics/overview.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/basics/problem.md b/markdowns/ja/basics/problem.md
index 24d284b8..95609c48 100644
--- a/markdowns/ja/basics/problem.md
+++ b/markdowns/ja/basics/problem.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/basics/variables.md b/markdowns/ja/basics/variables.md
index cc54c5a0..aade197f 100644
--- a/markdowns/ja/basics/variables.md
+++ b/markdowns/ja/basics/variables.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/introduction.md b/markdowns/ja/introduction.md
index ba013955..5332d556 100644
--- a/markdowns/ja/introduction.md
+++ b/markdowns/ja/introduction.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/ja/quickstart/openjij.md b/markdowns/ja/quickstart/openjij.md
index ac97f185..ab4a209b 100644
--- a/markdowns/ja/quickstart/openjij.md
+++ b/markdowns/ja/quickstart/openjij.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/ja/quickstart/scip.md b/markdowns/ja/quickstart/scip.md
index ac4cb51f..64c4157d 100644
--- a/markdowns/ja/quickstart/scip.md
+++ b/markdowns/ja/quickstart/scip.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/references/cheat_sheet.md b/markdowns/ja/references/cheat_sheet.md
index 1eb54ae4..3f233cfc 100644
--- a/markdowns/ja/references/cheat_sheet.md
+++ b/markdowns/ja/references/cheat_sheet.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: jijmodeling-tutorial
   language: python
diff --git a/markdowns/ja/references/migration_guide_to_jijmodeling2.md b/markdowns/ja/references/migration_guide_to_jijmodeling2.md
index de13385d..78b2d723 100644
--- a/markdowns/ja/references/migration_guide_to_jijmodeling2.md
+++ b/markdowns/ja/references/migration_guide_to_jijmodeling2.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.0.0.md b/markdowns/ja/releases/jijmodeling-2.0.0.md
index 8da2158d..7d78a1d0 100644
--- a/markdowns/ja/releases/jijmodeling-2.0.0.md
+++ b/markdowns/ja/releases/jijmodeling-2.0.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.1.0.md b/markdowns/ja/releases/jijmodeling-2.1.0.md
index 5d4f45fb..263ce5f1 100644
--- a/markdowns/ja/releases/jijmodeling-2.1.0.md
+++ b/markdowns/ja/releases/jijmodeling-2.1.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.2.0.md b/markdowns/ja/releases/jijmodeling-2.2.0.md
index 84708482..3b709cb3 100644
--- a/markdowns/ja/releases/jijmodeling-2.2.0.md
+++ b/markdowns/ja/releases/jijmodeling-2.2.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.3.1.md b/markdowns/ja/releases/jijmodeling-2.3.1.md
index 2f674915..311a48f5 100644
--- a/markdowns/ja/releases/jijmodeling-2.3.1.md
+++ b/markdowns/ja/releases/jijmodeling-2.3.1.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.3.2.md b/markdowns/ja/releases/jijmodeling-2.3.2.md
index 4280850f..f2e73810 100644
--- a/markdowns/ja/releases/jijmodeling-2.3.2.md
+++ b/markdowns/ja/releases/jijmodeling-2.3.2.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.4.0.md b/markdowns/ja/releases/jijmodeling-2.4.0.md
index 95138200..c5a917f7 100644
--- a/markdowns/ja/releases/jijmodeling-2.4.0.md
+++ b/markdowns/ja/releases/jijmodeling-2.4.0.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.4.1.md b/markdowns/ja/releases/jijmodeling-2.4.1.md
index e8dfd2c3..7dfe0142 100644
--- a/markdowns/ja/releases/jijmodeling-2.4.1.md
+++ b/markdowns/ja/releases/jijmodeling-2.4.1.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.19.1
+    jupytext_version: 1.19.3
 kernelspec:
   display_name: .venv
   language: python
diff --git a/markdowns/ja/releases/jijmodeling-2.5.0.md b/markdowns/ja/releases/jijmodeling-2.5.0.md
new file mode 100644
index 00000000..2dd39033
--- /dev/null
+++ b/markdowns/ja/releases/jijmodeling-2.5.0.md
@@ -0,0 +1,243 @@
+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.19.3
+kernelspec:
+  display_name: .venv
+  language: python
+  name: python3
+---
+
+# JijModeling 2.5.0 リリースノート
+
++++
+
+## 機能強化
+
++++
+
+### Decorator API における `jm.min`、`jm.max`、`jm.set` の内包表記サポート
+
+旧来は、Decorator API を利用する際に内包表記（Python のジェネレータ式）を引数として受け取れるのは {py:func}`jm.sum <jijmodeling.sum>` と {py:func}`jm.prod <jijmodeling.prod>` のみでした。
+
+本バージョンから、{py:func}`jm.min <jijmodeling.min>`、{py:func}`jm.max <jijmodeling.max>`、{py:func}`jm.set <jijmodeling.set>` の一引数呼び出しでも、同様に内包表記を受け取れるようになりました。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("min/max/set comprehension example")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Length()
+    x = problem.BinaryVar(shape=N)
+
+    nonzero = jm.set(i for i in N if i != 0)
+    problem += jm.min(x[i] for i in N) + jm.max(x[i] for i in nonzero)
+
+
+problem
+```
+
+### 数式出力：制約の添え字が読みやすく
+
+辞書や配列同士の直接比較による制約条件が、$\LaTeX$ 出力では $\forall$ を使って出力されるようになり、可読性が向上しました。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("container-vs-scalar-comp")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Natural()
+    L = problem.CategoryLabel()
+    x = problem.BinaryVar(shape=N)
+    y = problem.BinaryVar(dict_keys=(L, N - 1))
+    z = problem.BinaryVar(dict_keys=(L, N - 1))
+
+    problem += problem.Constraint("scalar-vs-tensor", 1 <= x)
+    problem += problem.Constraint("tensor-vs-tensor", x <= x)
+    problem += problem.Constraint("dict-vs-scalar", y <= 5)
+    problem += problem.Constraint("dict-vs-dict", y <= z)
+
+
+problem
+```
+
+### `Placeholder` の `dtype` に上限付き自然数とカテゴリーラベルを指定できるように
+
+{py:meth}`Problem.Placeholder <jijmodeling.Problem.Placeholder>`（および `Graph`、`PartialDict`、`TotalDict` などの型付き構築子）の `dtype` 引数は、これまで `jm.DataType`、NumPy のスカラー型、あるいはそれらから構成されるタプルに限られていました。
+本バージョンから、`dtype` には次のものも追加で指定できるようになりました：
+
+- 自然数式 `n`：値が `n` より真に小さい自然数（すなわち $\{0, 1, \dots, n - 1\}$ のいずれか）であることを表します。`n` には Python の整数リテラルのほか、自然数型の他のプレースホルダーや {py:class}`~jijmodeling.NamedExpr` などの式も渡せます。
+- {py:class}`~jijmodeling.CategoryLabel` `L`：値が `L` のラベルのうちのいずれかであることを表します。
+- 上記（あるいは他の指定可能な `dtype`）を要素とするタプル `(T, T, ...)`。
+
+上記の `dtype` に関する追加に合わせて、型付き構築子である {py:meth}`Problem.Natural <jijmodeling.Problem.Natural>`（およびそのエイリアスである {py:meth}`Problem.Length <jijmodeling.Problem.Length>` と {py:meth}`Problem.Dim <jijmodeling.Problem.Dim>`）でも `less_than=natexpr` キーワード引数を指定できるようになりました。これは `Placeholder(dtype=natexpr)` と同じく上限付き自然数型のプレースホルダーを宣言するもので、自然数値のプレースホルダーであるという意図をより明瞭に表現する書き方です。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("bounded natural shorthand")
+N = problem.Natural("N")
+i = problem.Natural("i", less_than=N)
+x = problem.BinaryVar("x", shape=(N,))
+problem += x[i]
+
+problem
+```
+
+Decorator API でも同じキーワード引数を利用できます。
+
+```{code-cell} ipython3
+@jm.Problem.define("bounded natural shorthand in Decorator API")
+def problem(problem: jm.DecoratedProblem):
+    N = problem.Length()
+    i = problem.Dim(less_than=N)
+    x = problem.BinaryVar(shape=(N,))
+    problem += x[i]
+
+
+problem
+```
+
+より複雑な例として、以下の、無向グラフ $G = (V, E)$ についての最適化問題を考えます。以前のバージョンでは辺の端点の型は単なる自然数として宣言する必要がありましたが、本リリースから、端点が $[0, V)$ の範囲に収まることを `dtype` を通じて表現できるようになりました：
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("max cut", sense=jm.ProblemSense.MAXIMIZE)
+V = problem.Natural("V")
+# `E` の各要素が `[0, V)` のペアであることを直接宣言できるようになりました
+# （従来は dtype=(jm.DataType.Natural, jm.DataType.Natural) と書く必要がありました）。
+# この宣言は、 `problem.graph("E", dtype=V)` と書くこともできます。
+E = problem.Placeholder("E", dtype=(V, V), ndim=1)
+x = problem.BinaryVar("x", shape=(V,))
+problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, E).sum()
+
+problem
+```
+
+また、グラフの頂点にラベルを用いる場合を想定して、{py:class}`~jijmodeling.CategoryLabel` をそのまま `dtype` として指定することもできるようになりました。
+以下の例は、ラベルが頂点として使われるグラフの上で（{py:meth}`Problem.Graph` を用いて）同じ問題を定義するものです。
+
+```{code-cell} ipython3
+problem = jm.Problem("max cut on a labeled graph", sense=jm.ProblemSense.MAXIMIZE)
+L = problem.CategoryLabel("L")
+edges = problem.Graph("edges", dtype=L)
+x = problem.BinaryVar("x", dict_keys=L)
+problem += jm.map(lambda u, v: (x[u] - x[v]) ** 2, edges).sum()
+
+compiler = jm.Compiler.from_problem(
+    problem,
+    {
+        "L": ["A", "B", "C"],
+        "edges": [("A", "B"), ("B", "C"), ("C", "A")],
+    },
+)
+instance = compiler.eval_problem(problem)
+```
+
+インスタンスデータとして与えられた値が宣言された `dtype` と整合しない場合（たとえば、頂点インデックスが `V` 以上であったり、`L` に含まれないラベルが渡されたりした場合）、コンパイラは範囲外エラーを報告します。
+
++++
+
+### 目的関数を代入で再設定できるように
+
+本バージョンから {py:attr}`Problem.objective <jijmodeling.Problem.objective>` に直接代入して置き換えられるようになりました。
+{py:class}`~jijmodeling.DecoratedProblem` でも同じように `problem.objective = ...` と書けます。
+
+たとえば、一度設定した目的関数を別の式に置き換えたり、`problem.objective = 0` として目的関数を明示的にリセットしたりできます。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("set objective example")
+x = problem.BinaryVar("x")
+y = problem.BinaryVar("y")
+
+problem.objective = x
+problem.objective = y
+problem.objective = 0
+
+
+@problem.update
+def _(problem: jm.DecoratedProblem):
+    z = problem.BinaryVar()
+    problem.objective = z
+
+
+problem
+```
+
+### 生成関数による辞書の生成
+
+本バージョンから、{py:func}`~jijmodeling.gendict` 関数により、キー集合と生成関数を指定して配列を生成できるようになりました。
+これは配列の {py:func}`~jijmodeling.genarray` や numpy の {py:func}`~numpy.fromfunction` と類似の機能です。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+problem = jm.Problem("gendict example")
+K = problem.CategoryLabel("K")
+a = problem.Float("a", dict_keys=K)
+x = problem.BinaryVar("x", dict_keys=K)
+Sums = problem.NamedExpr("Sums", jm.gendict(K, lambda k: a[k] * x[k]))
+
+
+problem
+```
+
+また、`jm.genarray` と同じように、Decorator API を利用している場合、内包表記を用いることもできます。ただし、`for .. in ...` は一つしか許容されません。
+
+```{code-cell} ipython3
+@jm.Problem.define("gendict example")
+def problem(problem):
+    problem = jm.Problem("gendict example")
+    K = problem.CategoryLabel("K")
+    a = problem.Float("a", dict_keys=K)
+    x = problem.BinaryVar("x", dict_keys=K)
+    Sums = problem.NamedExpr("Sums", jm.gendict(a[k] * x[k] for k in K))
+
+
+problem
+```
+
+## バグ修正
+
++++
+
+### 添え字の要素と数値型の演算に失敗していたバグの修正
+
+以下のように `Constraint` の添え字の要素に対する数値演算が誤って型エラーとして判定されていた問題を修正しました。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+
+@jm.Problem.define("Example")
+def problem(problem: jm.DecoratedProblem):
+    K = problem.Float(ndim=1)
+    x = problem.BinaryVar()
+    problem += problem.Constraint("c", [k * x <= 0 for k in K])
+
+
+problem
+```
+
+### `product` や `filter` の絡む数式出力を改善
+
+旧来は `product` や `filter` などを含む式が場合によって複雑な式として表示されていましたが、内包表記を使った読みやすい出力がされるようになりました。
+
+```{code-cell} ipython3
+import jijmodeling as jm
+
+problem = jm.Problem("product and filter example")
+N = problem.Natural("N")
+M = problem.Natural("M")
+x = problem.BinaryVar("x", shape=(N, M))
+jm.product(N, M).filter(lambda i, j: i == j)
+```
diff --git a/requirements.txt b/requirements.txt
index 209c079f..8fa51c6d 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -6,7 +6,7 @@ dimod==0.12.21
     #   openjij
 jij-cimod==1.7.3
     # via openjij
-jijmodeling==2.4.0
+jijmodeling==2.5.0
     # via jijmodeling-tutorial (pyproject.toml)
 numpy==2.3.5
     # via
@@ -18,19 +18,19 @@ numpy==2.3.5
     #   pandas
     #   pyscipopt
     #   scipy
-ommx==2.5.2
+ommx==2.6.1
     # via
     #   jijmodeling-tutorial (pyproject.toml)
     #   jijmodeling
     #   ommx-openjij-adapter
     #   ommx-pyscipopt-adapter
-ommx-openjij-adapter==2.5.2
+ommx-openjij-adapter==2.6.1
     # via jijmodeling-tutorial (pyproject.toml)
-ommx-pyscipopt-adapter==2.5.2
+ommx-pyscipopt-adapter==2.6.1
     # via jijmodeling-tutorial (pyproject.toml)
 openjij==0.11.6
     # via ommx-openjij-adapter
-orjson==3.11.8
+orjson==3.11.9
     # via jijmodeling
 pandas==2.3.3
     # via
@@ -40,13 +40,13 @@ protobuf==5.29.6
     # via ommx
 pyarrow==22.0.0
     # via ommx
-pyscipopt==6.1.0
+pyscipopt==6.2.1
     # via ommx-pyscipopt-adapter
 python-dateutil==2.9.0.post0
     # via
     #   ommx
     #   pandas
-pytz==2026.1.post1
+pytz==2026.2
     # via pandas
 scipy==1.15.3
     # via jij-cimod
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