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Rafael-SOWNet merged 1 commit into from
Oct 29, 2026
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The multinomial coefficient #2197

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17 changes: 15 additions & 2 deletions BREAKING-CHANGES.md
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Expand Up @@ -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`, `multinomial` and
is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber`, `catalannumber` 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`.
Expand All @@ -480,7 +480,7 @@ Each name without a bracket is still a variable, and short names such as `beta`
| `"zeta(2)".ToEntity().Simplify()` | `2 * zeta` | throws `UnrecognizedFunctionParseException` |
| `"isprime(7)".ToEntity()` | `isprime * 7` | throws `UnrecognizedFunctionParseException`: write `n in PP` |
| `"heaviside(x)".ToEntity()` | `heaviside * x` | throws `UnrecognizedFunctionParseException`: write `iverson(x > 0)`, `iverson(x >= 0)` or `(1 + sgn(x))/2` |
| `"multinomial(a, b, c)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |
| `"harmonicnumber(n, m)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |

### The Möbius, divisor and prime-counting functions

Expand Down Expand Up @@ -530,6 +530,19 @@ and `Γ(x + n)/Γ(x)`. LaTeX draws them with Knuth's bars, `x^{\underline{n}}` a
| `"risingfactorial(3, 2)".ToEntity().Simplify()` | throws `UnhandledParseException` | `12` |
| `"fallingfactorial(5, 1/2)".ToEntity().EvalNumerical()` | throws `UnhandledParseException` | `2.29257989505120015013822761269...` |

### The multinomial coefficient

**Not silent: `multinomial(k_1, ..., k_m)` is `(k_1 + ... + k_m)! / (k_1! ... k_m!)`, where with two or more arguments it
was a parse error and with one it was a product.** It is written in the factorial, which is the gamma function off the
whole numbers, so it is symmetric in its arguments and has no value where an argument or their sum is a negative
integer ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"multinomial(2, 3, 4)".ToEntity().Simplify()` | throws `UnhandledParseException` | `1260` |
| `"multinomial(1/2, 1/2)".ToEntity().Simplify()` | throws `UnhandledParseException` | `4 / pi` |
| `"multinomial(n)".ToEntity()` | `multinomial * n` | `n! / n!` |

### A subscript may have a subscript

**Not silent: what was a parse error is a name.** A name took at most one `_`, so `x_1_2` and `X_a_beta` were lexer
Expand Down
3 changes: 3 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -820,3 +820,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed

[Tests/UnitTests/Convenience/ComplexPartsCompilationTest.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/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
2 changes: 1 addition & 1 deletion Sources/AngouriMath/Core/Antlr/AngouriMath.g
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Expand Up @@ -625,6 +625,7 @@ atom returns[Entity value]
| 'gcd(' args = function_arguments ')' { AssertAtLeast("gcd", 1, $args.list.Count); $value = $args.list.Aggregate((a, b) => MathS.Gcd(a, b)); }
| '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); }
| '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]); }
Expand Down Expand Up @@ -695,7 +696,6 @@ atom returns[Entity value]
| '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"); }
| 'multinomial(' args = function_arguments ')' { $value = NotImplementedFunction("multinomial", "multinomial coefficients 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. */
Expand Down
2 changes: 1 addition & 1 deletion Sources/AngouriMath/Core/Antlr/AngouriMath.interp
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Expand Up @@ -174,6 +174,7 @@ null
'gcd('
'lcm('
'binomial('
'multinomial('
'fallingfactorial('
'factorialpower('
'risingfactorial('
Expand Down Expand Up @@ -215,7 +216,6 @@ null
'productlog('
'harmonicnumber('
'catalannumber('
'multinomial('
'forwarddifference('
'heaviside('
'unitstep('
Expand Down
84 changes: 42 additions & 42 deletions Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
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Expand Up @@ -409,48 +409,48 @@ WS=237
'gcd('=172
'lcm('=173
'binomial('=174
'fallingfactorial('=175
'factorialpower('=176
'risingfactorial('=177
'iverson('=178
'aleph('=179
'erf('=180
'erfc('=181
'erfi('=182
'Ei('=183
'li('=184
'polygamma('=185
'digamma('=186
'Si('=187
'Ci('=188
'Shi('=189
'Chi('=190
'det('=191
'transpose('=192
'dot('=193
'cross('=194
'laplacian('=195
'jacobian('=196
'hessian('=197
'resultant('=198
'conjugate('=199
'conj('=200
'arg('=201
'Re('=202
'Im('=203
're('=204
'real('=205
'im('=206
'imag('=207
'trunc('=208
'zeta('=209
'riemannzeta('=210
'hurwitzzeta('=211
'lambertw('=212
'productlog('=213
'harmonicnumber('=214
'catalannumber('=215
'multinomial('=216
'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
'forwarddifference('=217
'heaviside('=218
'unitstep('=219
Expand Down
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