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Rafael-SOWNet merged 1 commit into from
Oct 29, 2026
Merged

The Lambert W function #2202

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17 changes: 16 additions & 1 deletion BREAKING-CHANGES.md
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Expand Up @@ -483,7 +483,7 @@ 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` and `productlog`. Names that will not be functions,
is: `zeta`, `riemannzeta` and `hurwitzzeta`. 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`.
Each name without a bracket is still a variable, and short names such as `beta` and `norm` are still read as products
Expand Down Expand Up @@ -555,6 +555,21 @@ through `digamma` and `polygamma` for a whole `m >= 1`. A negative integer `n` h
| `"harmonicnumber(4)".ToEntity().Simplify()` | `4 * harmonicnumber` | `25/12` |
| `"harmonicnumber(n, 2)".ToEntity()` | throws `UnhandledParseException` | `harmonicnumber(n, 2)` |

### The Lambert W function

**Not silent: `lambertw(z)` and `lambertw(k, z)`, also `productlog`, are the Lambert W function, the solution `w` of
`w e^w = z` on the branch `k`, where they were a product and a parse error.** The branches are those of Corless et
al. (1996), as Mathematica's `ProductLog` and mpmath's `lambertw` have them: `W_0` is real on `[-1/e, +oo)` and `W_(-1)`
on `[-1/e, 0)`. It is exact at `0` and where `z` is `c e^c` for a real `c` the branch takes, so `lambertw(e)` is `1`
and `lambertw(-1/e)` is `-1`, and it is evaluated numerically elsewhere. Its derivative is `e^(-W(z))/(1 + W(z))`
([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"lambertw(e)".ToEntity().Simplify()` | `e * lambertw` | `1` |
| `"productlog(e)".ToEntity().Simplify()` | `e * productlog` | `1` |
| `"lambertw(-1, x)".ToEntity()` | throws `UnhandledParseException` | `lambertw(-1, x)` |

### The Catalan numbers

**Not silent: `catalannumber(n)` is the Catalan number, where it was a product.** It is `binomial(2n, n) / (n + 1)` for
Expand Down
9 changes: 9 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -835,3 +835,12 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed

[Tests/UnitTests/Convenience/ForwardDifferenceTest.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

[AngouriMath/Core/Entity/Continuous/Number/LambertW.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

[AngouriMath/Core/Entity/Continuous/Entity.Continuous.LambertW.Classes.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/LambertWTest.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
8 changes: 8 additions & 0 deletions Sources/AngouriMath/Convenience/MathS.cs
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Expand Up @@ -1631,6 +1631,14 @@ public static Entity VectorLength(Matrix v)
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Entity Digamma(Entity argument) => new Polygammaf(Integer.Zero, argument);

/// <summary>The principal branch of the Lambert W function, the solution <c>w</c> of <c>w e^w = z</c></summary>
/// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
public static Entity LambertW(Entity z) => new LambertWf(Integer.Zero, z);

/// <summary>The branch <paramref name="k"/> of the Lambert W function</summary>
/// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
public static Entity LambertW(Entity k, Entity z) => new LambertWf(k, z);

/// <summary>The upper incomplete gamma function, <c>Gamma(a, z) = int_z^oo t^(a - 1) e^(-t) dt</c></summary>
/// <param name="parameter">The parameter <c>a</c>, any complex number</param>
/// <param name="lowerLimit">The lower limit <c>z</c>, any complex number; <c>0</c> only where <c>Re a > 0</c></param>
Expand Down
4 changes: 2 additions & 2 deletions Sources/AngouriMath/Core/Antlr/AngouriMath.g
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Expand Up @@ -644,6 +644,8 @@ atom returns[Entity value]
| 'Ei(' args = function_arguments ')' { Assert("Ei", 1, $args.list.Count); $value = MathS.Ei($args.list[0]); }
| 'li(' args = function_arguments ')' { Assert("li", 1, $args.list.Count); $value = MathS.Li($args.list[0]); }
/* The polygamma functions, and the digamma function, which is the one of order 0. https://github.com/asc-community/AngouriMath/issues/171 */
| 'lambertw(' args = function_arguments ')' { if (Assert("lambertw", (2, 1), $args.list.Count)) $value = MathS.LambertW($args.list[0], $args.list[1]); else $value = MathS.LambertW($args.list[0]); }
| 'productlog(' args = function_arguments ')' { if (Assert("productlog", (2, 1), $args.list.Count)) $value = MathS.LambertW($args.list[0], $args.list[1]); else $value = MathS.LambertW($args.list[0]); }
| 'polygamma(' args = function_arguments ')' { Assert("polygamma", 2, $args.list.Count); $value = MathS.Polygamma($args.list[0], $args.list[1]); }
| 'digamma(' args = function_arguments ')' { Assert("digamma", 1, $args.list.Count); $value = MathS.Digamma($args.list[0]); }
/* The trigonometric and hyperbolic integrals. https://github.com/asc-community/AngouriMath/issues/1501 */
Expand Down Expand Up @@ -695,8 +697,6 @@ atom returns[Entity value]
| 'zeta(' args = function_arguments ')' { $value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); }
| 'riemannzeta(' args = function_arguments ')' { $value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); }
| 'hurwitzzeta(' args = function_arguments ')' { $value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); }
| 'lambertw(' args = function_arguments ')' { $value = NotImplementedFunction("lambertw", "Lambert W function yet"); }
| 'productlog(' args = function_arguments ')' { $value = NotImplementedFunction("productlog", "Lambert W function 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. */
| 'heaviside(' args = function_arguments ')' { $value = NotAFunctionHere("heaviside", "its value at 0 is 0, 1/2 or 1 by source; write iverson(x > 0), iverson(x >= 0) or (1 + sgn(x))/2"); }
Expand Down
4 changes: 2 additions & 2 deletions Sources/AngouriMath/Core/Antlr/AngouriMath.interp
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Expand Up @@ -187,6 +187,8 @@ null
'erfi('
'Ei('
'li('
'lambertw('
'productlog('
'polygamma('
'digamma('
'Si('
Expand Down Expand Up @@ -215,8 +217,6 @@ null
'zeta('
'riemannzeta('
'hurwitzzeta('
'lambertw('
'productlog('
'heaviside('
'unitstep('
'isprime('
Expand Down
60 changes: 30 additions & 30 deletions Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
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Expand Up @@ -422,36 +422,36 @@ WS=237
'erfi('=185
'Ei('=186
'li('=187
'polygamma('=188
'digamma('=189
'Si('=190
'Ci('=191
'Shi('=192
'Chi('=193
'det('=194
'transpose('=195
'dot('=196
'cross('=197
'laplacian('=198
'forwarddifference('=199
'jacobian('=200
'hessian('=201
'resultant('=202
'conjugate('=203
'conj('=204
'arg('=205
'Re('=206
'Im('=207
're('=208
'real('=209
'im('=210
'imag('=211
'trunc('=212
'zeta('=213
'riemannzeta('=214
'hurwitzzeta('=215
'lambertw('=216
'productlog('=217
'lambertw('=188
'productlog('=189
'polygamma('=190
'digamma('=191
'Si('=192
'Ci('=193
'Shi('=194
'Chi('=195
'det('=196
'transpose('=197
'dot('=198
'cross('=199
'laplacian('=200
'forwarddifference('=201
'jacobian('=202
'hessian('=203
'resultant('=204
'conjugate('=205
'conj('=206
'arg('=207
'Re('=208
'Im('=209
're('=210
'real('=211
'im('=212
'imag('=213
'trunc('=214
'zeta('=215
'riemannzeta('=216
'hurwitzzeta('=217
'heaviside('=218
'unitstep('=219
'isprime('=220
Expand Down
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