The Catalan numbers

BREAKING-CHANGES.md

@@ -467,7 +467,7 @@ the right shape, written out or once its operations are carried out, throws `Inv
 **Not silent: these names followed by a bracket now throw `UnrecognizedFunctionParseException` where they were read as
 products.** An unknown name followed by a bracket is a product, so `zeta(2)` was `zeta * 2` and simplified to
 `2 * zeta`. The long names of the functions the library is to have are refused until each is implemented, as `trunc`
-is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber`, `catalannumber` and
+is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber` and
 `forwarddifference`. Names that will not be functions,
 because what they mean differs between sources or is already written exactly, are refused with the spelling to use:
 `heaviside`, `unitstep`, `isprime`, `pochhammer`, `doublefactorial`, `factorial2`, `fractionalpart` and `quotient`.
@@ -516,6 +516,18 @@ is ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).
 | `"hessian(x^3 y^2, [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `[[6 * x * y ^ 2, 6 * x ^ 2 * y], [6 * x ^ 2 * y, 2 * x ^ 3]]` |
 | `"jacobian(x y, {x, y})".ToEntity()` | throws `UnhandledParseException` | throws `InvalidArgumentParseException`: a set has no order for the columns |
 
+### The Catalan numbers
+
+**Not silent: `catalannumber(n)` is the Catalan number, where it was a product.** It is `binomial(2n, n) / (n + 1)` for
+a whole `n >= 0`, and `4^n Γ(n + 1/2) / (√π Γ(n + 2))` elsewhere, as SymPy's `catalan` is: `-1/2` at `-1`, `0` at
+every whole number below it, and no value at a negative half-integer
+([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"catalannumber(4)".ToEntity().Simplify()` | `4 * catalannumber` | `14` |
+| `"catalannumber(-1)".ToEntity().Simplify()` | `-catalannumber` | `-1/2` |
+
 ### The falling and the rising factorial
 
 **Not silent: `fallingfactorial(x, n)`, also `factorialpower(x, n)`, and `risingfactorial(x, n)` are functions, where

Sources/.editorconfig

@@ -823,3 +823,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 
 [Tests/UnitTests/Convenience/MultinomialTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+
+[Tests/UnitTests/Convenience/CatalanNumberTest.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

Sources/AngouriMath/Convenience/MathS.cs

@@ -1387,6 +1387,10 @@ public static Entity VectorLength(Matrix v)
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public static Entity Binomial(Entity n, Entity k) => new Binomialf(n, k);
 
+        /// <summary>The Catalan number <c>C_n = binomial(2n, n) / (n + 1)</c></summary>
+        /// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
+        public static Entity CatalanNumber(Entity n) => new CatalanNumberf(n);
+
         /// <summary>The falling factorial <c>x (x - 1) ... (x - n + 1)</c>, <c>x^{\underline{n}}</c></summary>
         /// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
         public static Entity FallingFactorial(Entity x, Entity n) => new FallingFactorialf(x, n);

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -626,6 +626,7 @@ atom returns[Entity value]
     | 'lcm(' args = function_arguments ')' { AssertAtLeast("lcm", 1, $args.list.Count); $value = $args.list.Aggregate((a, b) => MathS.Lcm(a, b)); }
     | 'binomial(' args = function_arguments ')' { Assert("binomial", 2, $args.list.Count); $value = MathS.Binomial($args.list[0], $args.list[1]); }
     | 'multinomial(' args = function_arguments ')' { $value = ParsingHelpers.Multinomial($args.list); }
+    | 'catalannumber(' args = function_arguments ')' { Assert("catalannumber", 1, $args.list.Count); $value = MathS.CatalanNumber($args.list[0]); }
     | 'fallingfactorial(' args = function_arguments ')' { Assert("fallingfactorial", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); }
     | 'factorialpower(' args = function_arguments ')' { Assert("factorialpower", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); }
     | 'risingfactorial(' args = function_arguments ')' { Assert("risingfactorial", 2, $args.list.Count); $value = MathS.RisingFactorial($args.list[0], $args.list[1]); }
@@ -695,7 +696,6 @@ atom returns[Entity value]
     | 'lambertw(' args = function_arguments ')' { $value = NotImplementedFunction("lambertw", "Lambert W function yet"); }
     | 'productlog(' args = function_arguments ')' { $value = NotImplementedFunction("productlog", "Lambert W function yet"); }
     | 'harmonicnumber(' args = function_arguments ')' { $value = NotImplementedFunction("harmonicnumber", "harmonic numbers yet"); }
-    | 'catalannumber(' args = function_arguments ')' { $value = NotImplementedFunction("catalannumber", "Catalan numbers yet"); }
     | 'forwarddifference(' args = function_arguments ')' { $value = NotImplementedFunction("forwarddifference", "forward difference yet"); }
     /* Names that will not be functions, refused with the spelling to use: what they mean is
        ambiguous between sources, or is already written exactly another way. */

Sources/AngouriMath/Core/Antlr/AngouriMath.interp

@@ -175,6 +175,7 @@ null
 'lcm('
 'binomial('
 'multinomial('
+'catalannumber('
 'fallingfactorial('
 'factorialpower('
 'risingfactorial('
@@ -215,7 +216,6 @@ null
 'lambertw('
 'productlog('
 'harmonicnumber('
-'catalannumber('
 'forwarddifference('
 'heaviside('
 'unitstep('

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -410,47 +410,47 @@ WS=237
 'lcm('=173
 'binomial('=174
 'multinomial('=175
-'fallingfactorial('=176
-'factorialpower('=177
-'risingfactorial('=178
-'iverson('=179
-'aleph('=180
-'erf('=181
-'erfc('=182
-'erfi('=183
-'Ei('=184
-'li('=185
-'polygamma('=186
-'digamma('=187
-'Si('=188
-'Ci('=189
-'Shi('=190
-'Chi('=191
-'det('=192
-'transpose('=193
-'dot('=194
-'cross('=195
-'laplacian('=196
-'jacobian('=197
-'hessian('=198
-'resultant('=199
-'conjugate('=200
-'conj('=201
-'arg('=202
-'Re('=203
-'Im('=204
-'re('=205
-'real('=206
-'im('=207
-'imag('=208
-'trunc('=209
-'zeta('=210
-'riemannzeta('=211
-'hurwitzzeta('=212
-'lambertw('=213
-'productlog('=214
-'harmonicnumber('=215
-'catalannumber('=216
+'catalannumber('=176
+'fallingfactorial('=177
+'factorialpower('=178
+'risingfactorial('=179
+'iverson('=180
+'aleph('=181
+'erf('=182
+'erfc('=183
+'erfi('=184
+'Ei('=185
+'li('=186
+'polygamma('=187
+'digamma('=188
+'Si('=189
+'Ci('=190
+'Shi('=191
+'Chi('=192
+'det('=193
+'transpose('=194
+'dot('=195
+'cross('=196
+'laplacian('=197
+'jacobian('=198
+'hessian('=199
+'resultant('=200
+'conjugate('=201
+'conj('=202
+'arg('=203
+'Re('=204
+'Im('=205
+'re('=206
+'real('=207
+'im('=208
+'imag('=209
+'trunc('=210
+'zeta('=211
+'riemannzeta('=212
+'hurwitzzeta('=213
+'lambertw('=214
+'productlog('=215
+'harmonicnumber('=216
 'forwarddifference('=217
 'heaviside('=218
 'unitstep('=219