From f5f697482ad64702aeaa942ccac2dfb04db7ff9c Mon Sep 17 00:00:00 2001 From: Fanwang Meng Date: Thu, 23 Apr 2026 12:08:41 +0800 Subject: [PATCH 1/3] Fix equation rendering --- README.md | 25 +++++++++++++------------ 1 file changed, 13 insertions(+), 12 deletions(-) diff --git a/README.md b/README.md index 8ba54e2..157b1e0 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -[![Python 3](http://img.shields.io/badge/python-3-blue.svg)](https://docs.python.org/3/) +[![This project supports Python 3.10+](https://img.shields.io/badge/Python-3.10+-blue.svg)](https://python.org/downloads) [![pre-commit](https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white)](https://github.com/theochem/matrix-permanent/actions/workflows/pull_request.yml) [![GNU GPLv3](https://img.shields.io/badge/license-%20%20GNU%20GPLv3%20-green?style=plastic)](https://www.gnu.org/licenses/gpl-3.0.en.html) @@ -37,9 +37,10 @@ Compute the permanent of a matrix using the best algorithm for the shape of the Compute the permanent of a matrix combinatorically. **Formula:** -```math + +$$ \text{per}(A) = \sum_{\sigma \in P(N,M)}{\prod_{i=1}^M{a_{i,{\sigma(i)}}}} -``` +$$ **Parameters:** @@ -55,29 +56,29 @@ Compute the permanent of a matrix combinatorically. **Formula:** -```math +$$ \text{per}(A) = \frac{1}{2^{N-1}} \cdot \sum_{\delta \in \left[\delta_1 = 1,~ \delta_2 \dots \delta_N=\pm1\right]}{ \left(\sum_{k=1}^N{\delta_k}\right){\prod_{j=1}^N{\sum_{i=1}^N{\delta_i a_{i,j}}}}} -``` +$$ **Additional Information:** The original formula has been generalized here to work with $M$-by-$N$ rectangular permanents with $M \leq N$ by use of the following identity (shown here for $M \geq N$): -```math +$$ \text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} \\ \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N}\end{matrix}\right) = \frac{1}{(M - N + 1)!} \cdot \text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} & 1_{1,N+1} & \cdots & 1_{1,M} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N} & 1_{M,N+1} & \cdots & 1_{M,M}\end{matrix}\right) -``` +$$ This can be neatly fit into the original formula by extending the inner sums over $\delta$ from $[1,M]$ to $[1,N]$: -```math +$$ \text{per}(A) = \frac{1}{2^{N-1}} \cdot \frac{1}{(N - M + 1)!}\cdot \sum_{\delta \in \left[\delta_1 = 1,~ \delta_2 \dots \delta_N=\pm1\right]}{ \left(\sum_{k=1}^N{\delta_k}\right) \prod_{j=1}^N{\left( \sum_{i=1}^M{\delta_i a_{i,j}} + \sum_{i=M+1}^N{\delta_i} \right)} } -``` +$$ **Parameters:** @@ -93,7 +94,7 @@ This can be neatly fit into the original formula by extending the inner sums ove **Formula:** -```math +$$ \text{per}(A) = \sum_{k=0}^{M-1}{ {(-1)}^k \binom{N - M + k}{k} @@ -103,7 +104,7 @@ This can be neatly fit into the original formula by extending the inner sums ove } } } -``` +$$ **Parameters:** @@ -181,4 +182,4 @@ is with pip. # License This code is distributed under the GNU General Public License version 3 (GPLv3). -See for more information. \ No newline at end of file +See for more information. From c317963f2fcf7a1469f65b6e4f376602b30cd928 Mon Sep 17 00:00:00 2001 From: Fanwang Meng Date: Thu, 23 Apr 2026 12:17:11 +0800 Subject: [PATCH 2/3] Use https instead of http --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 157b1e0..2979fb3 100644 --- a/README.md +++ b/README.md @@ -182,4 +182,4 @@ is with pip. # License This code is distributed under the GNU General Public License version 3 (GPLv3). -See for more information. +See for more information. From c719bb6092c1f57004681791b526085ccb396d03 Mon Sep 17 00:00:00 2001 From: Fanwang Meng Date: Thu, 23 Apr 2026 12:20:38 +0800 Subject: [PATCH 3/3] Fix the misaligned equations --- README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/README.md b/README.md index 2979fb3..64ce023 100644 --- a/README.md +++ b/README.md @@ -66,7 +66,9 @@ The original formula has been generalized here to work with $M$-by-$N$ rectangul $M \leq N$ by use of the following identity (shown here for $M \geq N$): $$ +\begin{aligned} \text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} \\ \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N}\end{matrix}\right) = \frac{1}{(M - N + 1)!} \cdot \text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} & 1_{1,N+1} & \cdots & 1_{1,M} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N} & 1_{M,N+1} & \cdots & 1_{M,M}\end{matrix}\right) +\end{aligned} $$ This can be neatly fit into the original formula by extending the inner sums over $\delta$ from $[1,M]$ to $[1,N]$: