From 05c077c0c558c91808cb59fc69e787c50f561657 Mon Sep 17 00:00:00 2001 From: Rafael Vuijk Date: Thu, 29 Oct 2026 13:55:16 +0000 Subject: [PATCH] The Lambert W function lambertw(z) and lambertw(k, z), also productlog, Mathematica's name, were reserved by name in #2184 and are now Entity.LambertWf, built by MathS.LambertW: the solution w of w e^w = z on the branch k, a whole number, and the principal branch without one. The branches are those of Corless, Gonnet, Hare, Jeffrey and Knuth (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), both are -1 at -1/e, and a value on a cut is the one approached from above. It is exact at 0, which is 0 on the principal branch and -oo off it as ln 0 is, and where z is c e^c for a real number c the branch takes: lambertw(e) is 1, lambertw(-1/e) is -1 and lambertw(-1, -2 e^(-2)) is -2. Elsewhere it is evaluated at the working precision, in Number.LambertW. The branch is found in double precision: from the series in p = sqrt(2 (e z + 1)) about the branch point, from ln(1 + z) on the principal branch short of |z| = 3, and from ln z + 2 pi i k - ln(ln z + 2 pi i k) otherwise, each taken to a root by Halley's iteration. That root is refined by the same iteration on decimal pairs at the working precision, which triples the digits with each step and does not leave the branch. Near the branch point, where double precision cannot resolve z + 1/e, the series is evaluated at the working precision instead. Forty-five points on branches -2 to 2, and 700 random ones on -3 to 3 on and about the cuts, agree with mpmath to 1e-25. Its derivative is e^(-W(z)) / (1 + W(z)), which is 1 at 0 where W(z) / (z (1 + W(z))) is 0/0. It prints as lambertw(z) and lambertw(k, z), draws as \operatorname{W}_{k}, and exports to SymPy's LambertW. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura --- BREAKING-CHANGES.md | 17 +- Sources/.editorconfig | 9 + Sources/AngouriMath/Convenience/MathS.cs | 8 + Sources/AngouriMath/Core/Antlr/AngouriMath.g | 4 +- .../AngouriMath/Core/Antlr/AngouriMath.interp | 4 +- .../AngouriMath/Core/Antlr/AngouriMath.tokens | 60 +-- .../Core/Antlr/AngouriMathLexer.cs | 357 +++++++++--------- .../Core/Antlr/AngouriMathLexer.interp | 6 +- .../Core/Antlr/AngouriMathLexer.tokens | 60 +-- .../Core/Antlr/AngouriMathParser.cs | 72 ++-- Sources/AngouriMath/Core/Domains.Classes.cs | 8 + .../Entity.Continuous.LambertW.Classes.cs | 41 ++ .../Core/Entity/Continuous/Number/LambertW.cs | 167 ++++++++ .../Serialization/Entity.Serialization.cs | 1 + .../Transformations/Matching/MatchPattern.cs | 1 + .../Docs/Contributing/WritingARule.md | 2 +- Sources/AngouriMath/Docs/Usage/Syntax.md | 10 +- .../Functions/Continuous/Differentiation.cs | 12 + .../EquationSolver/InvertNode.Classes.cs | 8 + ...aluation.Continuous.Arithmetics.Classes.cs | 39 ++ .../Output/Latex/Latex.Arithmetics.Classes.cs | 9 + .../ToString/ToString.Arithmetics.Classes.cs | 9 + .../ToSympy/ToSympy.Arithmetics.Classes.cs | 7 + Sources/AngouriMath/Functions/Substitute.cs | 7 + .../Functions/TreeAnalyzer/Sort.Classes.cs | 5 + Sources/MCP/AngouriMath.Mcp/Resources.cs | 4 +- Sources/Tests/AotSmokeTest/Program.cs | 2 + Sources/Tests/UnitTests/Common/PublicApi.txt | 25 ++ .../UnitTests/Convenience/LambertWTest.cs | 154 ++++++++ .../MissingFunctionNamesRefusedTest.cs | 6 +- .../Transformations/RuleAuthoringGuideTest.cs | 2 +- 31 files changed, 825 insertions(+), 291 deletions(-) create mode 100644 Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.LambertW.Classes.cs create mode 100644 Sources/AngouriMath/Core/Entity/Continuous/Number/LambertW.cs create mode 100644 Sources/Tests/UnitTests/Convenience/LambertWTest.cs diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md index 8c375c080..65ec24164 100644 --- a/BREAKING-CHANGES.md +++ b/BREAKING-CHANGES.md @@ -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 @@ -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 diff --git a/Sources/.editorconfig b/Sources/.editorconfig index 7557d58d4..849786d9a 100644 --- a/Sources/.editorconfig +++ b/Sources/.editorconfig @@ -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 diff --git a/Sources/AngouriMath/Convenience/MathS.cs b/Sources/AngouriMath/Convenience/MathS.cs index 2457c98c8..f2dde916f 100644 --- a/Sources/AngouriMath/Convenience/MathS.cs +++ b/Sources/AngouriMath/Convenience/MathS.cs @@ -1631,6 +1631,14 @@ public static Entity VectorLength(Matrix v) [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Entity Digamma(Entity argument) => new Polygammaf(Integer.Zero, argument); + /// The principal branch of the Lambert W function, the solution w of w e^w = z + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity LambertW(Entity z) => new LambertWf(Integer.Zero, z); + + /// The branch of the Lambert W function + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity LambertW(Entity k, Entity z) => new LambertWf(k, z); + /// The upper incomplete gamma function, Gamma(a, z) = int_z^oo t^(a - 1) e^(-t) dt /// The parameter a, any complex number /// The lower limit z, any complex number; 0 only where Re a > 0 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g index 37b2e1b50..c74556c6d 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g @@ -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 */ @@ -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"); } diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp index ba6f01765..3b5c2757a 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp @@ -187,6 +187,8 @@ null 'erfi(' 'Ei(' 'li(' +'lambertw(' +'productlog(' 'polygamma(' 'digamma(' 'Si(' @@ -215,8 +217,6 @@ null 'zeta(' 'riemannzeta(' 'hurwitzzeta(' -'lambertw(' -'productlog(' 'heaviside(' 'unitstep(' 'isprime(' diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens index 280a47a99..33677c693 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens @@ -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 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs index a2075466a..e64b4d4fd 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs @@ -160,12 +160,12 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'multinomial('", "'catalannumber('", "'harmonicnumber('", "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", - "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", - "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", - "'cross('", "'laplacian('", "'forwarddifference('", "'jacobian('", "'hessian('", - "'resultant('", "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", - "'re('", "'real('", "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", - "'hurwitzzeta('", "'lambertw('", "'productlog('", "'heaviside('", "'unitstep('", + "'erfc('", "'erfi('", "'Ei('", "'li('", "'lambertw('", "'productlog('", + "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", + "'transpose('", "'dot('", "'cross('", "'laplacian('", "'forwarddifference('", + "'jacobian('", "'hessian('", "'resultant('", "'conjugate('", "'conj('", + "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", + "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'heaviside('", "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" @@ -353,24 +353,24 @@ static AngouriMathLexer() { 1,181,1,182,1,182,1,182,1,182,1,182,1,183,1,183,1,183,1,183,1,183,1,183, 1,184,1,184,1,184,1,184,1,184,1,184,1,185,1,185,1,185,1,185,1,186,1,186, 1,186,1,186,1,187,1,187,1,187,1,187,1,187,1,187,1,187,1,187,1,187,1,187, - 1,187,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,189,1,189, - 1,189,1,189,1,190,1,190,1,190,1,190,1,191,1,191,1,191,1,191,1,191,1,192, + 1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188, + 1,189,1,189,1,189,1,189,1,189,1,189,1,189,1,189,1,189,1,189,1,189,1,190, + 1,190,1,190,1,190,1,190,1,190,1,190,1,190,1,190,1,191,1,191,1,191,1,191, 1,192,1,192,1,192,1,192,1,193,1,193,1,193,1,193,1,193,1,194,1,194,1,194, - 1,194,1,194,1,194,1,194,1,194,1,194,1,194,1,194,1,195,1,195,1,195,1,195, - 1,195,1,196,1,196,1,196,1,196,1,196,1,196,1,196,1,197,1,197,1,197,1,197, - 1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,198,1,198,1,198,1,198,1,198, - 1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198, - 1,198,1,198,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199, - 1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,201,1,201,1,201, - 1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,202,1,202,1,202,1,202, + 1,194,1,194,1,195,1,195,1,195,1,195,1,195,1,196,1,196,1,196,1,196,1,196, + 1,196,1,196,1,196,1,196,1,196,1,196,1,197,1,197,1,197,1,197,1,197,1,198, + 1,198,1,198,1,198,1,198,1,198,1,198,1,199,1,199,1,199,1,199,1,199,1,199, + 1,199,1,199,1,199,1,199,1,199,1,200,1,200,1,200,1,200,1,200,1,200,1,200, + 1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200, + 1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,202,1,202, 1,202,1,202,1,202,1,202,1,202,1,202,1,202,1,203,1,203,1,203,1,203,1,203, - 1,203,1,204,1,204,1,204,1,204,1,204,1,205,1,205,1,205,1,205,1,206,1,206, - 1,206,1,206,1,207,1,207,1,207,1,207,1,208,1,208,1,208,1,208,1,208,1,208, + 1,203,1,203,1,203,1,203,1,203,1,203,1,204,1,204,1,204,1,204,1,204,1,204, + 1,204,1,204,1,204,1,204,1,204,1,205,1,205,1,205,1,205,1,205,1,205,1,206, + 1,206,1,206,1,206,1,206,1,207,1,207,1,207,1,207,1,208,1,208,1,208,1,208, 1,209,1,209,1,209,1,209,1,210,1,210,1,210,1,210,1,210,1,210,1,211,1,211, - 1,211,1,211,1,211,1,211,1,211,1,212,1,212,1,212,1,212,1,212,1,212,1,213, - 1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213, - 1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214, - 1,214,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,216, + 1,211,1,211,1,212,1,212,1,212,1,212,1,212,1,212,1,213,1,213,1,213,1,213, + 1,213,1,213,1,213,1,214,1,214,1,214,1,214,1,214,1,214,1,215,1,215,1,215, + 1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,216,1,216, 1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,217, 1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,218,1,218, 1,218,1,218,1,218,1,218,1,218,1,218,1,218,1,218,1,219,1,219,1,219,1,219, @@ -514,14 +514,14 @@ static AngouriMathLexer() { 0,0,349,1538,1,0,0,0,351,1551,1,0,0,0,353,1566,1,0,0,0,355,1582,1,0,0, 0,357,1600,1,0,0,0,359,1616,1,0,0,0,361,1633,1,0,0,0,363,1642,1,0,0,0, 365,1649,1,0,0,0,367,1654,1,0,0,0,369,1660,1,0,0,0,371,1666,1,0,0,0,373, - 1670,1,0,0,0,375,1674,1,0,0,0,377,1685,1,0,0,0,379,1694,1,0,0,0,381,1698, - 1,0,0,0,383,1702,1,0,0,0,385,1707,1,0,0,0,387,1712,1,0,0,0,389,1717,1, - 0,0,0,391,1728,1,0,0,0,393,1733,1,0,0,0,395,1740,1,0,0,0,397,1751,1,0, - 0,0,399,1770,1,0,0,0,401,1780,1,0,0,0,403,1789,1,0,0,0,405,1800,1,0,0, - 0,407,1811,1,0,0,0,409,1817,1,0,0,0,411,1822,1,0,0,0,413,1826,1,0,0,0, - 415,1830,1,0,0,0,417,1834,1,0,0,0,419,1840,1,0,0,0,421,1844,1,0,0,0,423, - 1850,1,0,0,0,425,1857,1,0,0,0,427,1863,1,0,0,0,429,1876,1,0,0,0,431,1889, - 1,0,0,0,433,1899,1,0,0,0,435,1911,1,0,0,0,437,1922,1,0,0,0,439,1932,1, + 1670,1,0,0,0,375,1674,1,0,0,0,377,1684,1,0,0,0,379,1696,1,0,0,0,381,1707, + 1,0,0,0,383,1716,1,0,0,0,385,1720,1,0,0,0,387,1724,1,0,0,0,389,1729,1, + 0,0,0,391,1734,1,0,0,0,393,1739,1,0,0,0,395,1750,1,0,0,0,397,1755,1,0, + 0,0,399,1762,1,0,0,0,401,1773,1,0,0,0,403,1792,1,0,0,0,405,1802,1,0,0, + 0,407,1811,1,0,0,0,409,1822,1,0,0,0,411,1833,1,0,0,0,413,1839,1,0,0,0, + 415,1844,1,0,0,0,417,1848,1,0,0,0,419,1852,1,0,0,0,421,1856,1,0,0,0,423, + 1862,1,0,0,0,425,1866,1,0,0,0,427,1872,1,0,0,0,429,1879,1,0,0,0,431,1885, + 1,0,0,0,433,1898,1,0,0,0,435,1911,1,0,0,0,437,1922,1,0,0,0,439,1932,1, 0,0,0,441,1941,1,0,0,0,443,1953,1,0,0,0,445,1970,1,0,0,0,447,1982,1,0, 0,0,449,1998,1,0,0,0,451,2008,1,0,0,0,453,2016,1,0,0,0,455,2027,1,0,0, 0,457,2034,1,0,0,0,459,2046,1,0,0,0,461,2052,1,0,0,0,463,2094,1,0,0,0, @@ -835,155 +835,156 @@ static AngouriMathLexer() { 1663,5,102,0,0,1663,1664,5,105,0,0,1664,1665,5,40,0,0,1665,370,1,0,0,0, 1666,1667,5,69,0,0,1667,1668,5,105,0,0,1668,1669,5,40,0,0,1669,372,1,0, 0,0,1670,1671,5,108,0,0,1671,1672,5,105,0,0,1672,1673,5,40,0,0,1673,374, - 1,0,0,0,1674,1675,5,112,0,0,1675,1676,5,111,0,0,1676,1677,5,108,0,0,1677, - 1678,5,121,0,0,1678,1679,5,103,0,0,1679,1680,5,97,0,0,1680,1681,5,109, - 0,0,1681,1682,5,109,0,0,1682,1683,5,97,0,0,1683,1684,5,40,0,0,1684,376, - 1,0,0,0,1685,1686,5,100,0,0,1686,1687,5,105,0,0,1687,1688,5,103,0,0,1688, - 1689,5,97,0,0,1689,1690,5,109,0,0,1690,1691,5,109,0,0,1691,1692,5,97,0, - 0,1692,1693,5,40,0,0,1693,378,1,0,0,0,1694,1695,5,83,0,0,1695,1696,5,105, - 0,0,1696,1697,5,40,0,0,1697,380,1,0,0,0,1698,1699,5,67,0,0,1699,1700,5, - 105,0,0,1700,1701,5,40,0,0,1701,382,1,0,0,0,1702,1703,5,83,0,0,1703,1704, - 5,104,0,0,1704,1705,5,105,0,0,1705,1706,5,40,0,0,1706,384,1,0,0,0,1707, - 1708,5,67,0,0,1708,1709,5,104,0,0,1709,1710,5,105,0,0,1710,1711,5,40,0, - 0,1711,386,1,0,0,0,1712,1713,5,100,0,0,1713,1714,5,101,0,0,1714,1715,5, - 116,0,0,1715,1716,5,40,0,0,1716,388,1,0,0,0,1717,1718,5,116,0,0,1718,1719, - 5,114,0,0,1719,1720,5,97,0,0,1720,1721,5,110,0,0,1721,1722,5,115,0,0,1722, - 1723,5,112,0,0,1723,1724,5,111,0,0,1724,1725,5,115,0,0,1725,1726,5,101, - 0,0,1726,1727,5,40,0,0,1727,390,1,0,0,0,1728,1729,5,100,0,0,1729,1730, - 5,111,0,0,1730,1731,5,116,0,0,1731,1732,5,40,0,0,1732,392,1,0,0,0,1733, - 1734,5,99,0,0,1734,1735,5,114,0,0,1735,1736,5,111,0,0,1736,1737,5,115, - 0,0,1737,1738,5,115,0,0,1738,1739,5,40,0,0,1739,394,1,0,0,0,1740,1741, - 5,108,0,0,1741,1742,5,97,0,0,1742,1743,5,112,0,0,1743,1744,5,108,0,0,1744, - 1745,5,97,0,0,1745,1746,5,99,0,0,1746,1747,5,105,0,0,1747,1748,5,97,0, - 0,1748,1749,5,110,0,0,1749,1750,5,40,0,0,1750,396,1,0,0,0,1751,1752,5, - 102,0,0,1752,1753,5,111,0,0,1753,1754,5,114,0,0,1754,1755,5,119,0,0,1755, - 1756,5,97,0,0,1756,1757,5,114,0,0,1757,1758,5,100,0,0,1758,1759,5,100, - 0,0,1759,1760,5,105,0,0,1760,1761,5,102,0,0,1761,1762,5,102,0,0,1762,1763, - 5,101,0,0,1763,1764,5,114,0,0,1764,1765,5,101,0,0,1765,1766,5,110,0,0, - 1766,1767,5,99,0,0,1767,1768,5,101,0,0,1768,1769,5,40,0,0,1769,398,1,0, - 0,0,1770,1771,5,106,0,0,1771,1772,5,97,0,0,1772,1773,5,99,0,0,1773,1774, - 5,111,0,0,1774,1775,5,98,0,0,1775,1776,5,105,0,0,1776,1777,5,97,0,0,1777, - 1778,5,110,0,0,1778,1779,5,40,0,0,1779,400,1,0,0,0,1780,1781,5,104,0,0, - 1781,1782,5,101,0,0,1782,1783,5,115,0,0,1783,1784,5,115,0,0,1784,1785, - 5,105,0,0,1785,1786,5,97,0,0,1786,1787,5,110,0,0,1787,1788,5,40,0,0,1788, - 402,1,0,0,0,1789,1790,5,114,0,0,1790,1791,5,101,0,0,1791,1792,5,115,0, - 0,1792,1793,5,117,0,0,1793,1794,5,108,0,0,1794,1795,5,116,0,0,1795,1796, - 5,97,0,0,1796,1797,5,110,0,0,1797,1798,5,116,0,0,1798,1799,5,40,0,0,1799, - 404,1,0,0,0,1800,1801,5,99,0,0,1801,1802,5,111,0,0,1802,1803,5,110,0,0, - 1803,1804,5,106,0,0,1804,1805,5,117,0,0,1805,1806,5,103,0,0,1806,1807, - 5,97,0,0,1807,1808,5,116,0,0,1808,1809,5,101,0,0,1809,1810,5,40,0,0,1810, - 406,1,0,0,0,1811,1812,5,99,0,0,1812,1813,5,111,0,0,1813,1814,5,110,0,0, - 1814,1815,5,106,0,0,1815,1816,5,40,0,0,1816,408,1,0,0,0,1817,1818,5,97, - 0,0,1818,1819,5,114,0,0,1819,1820,5,103,0,0,1820,1821,5,40,0,0,1821,410, - 1,0,0,0,1822,1823,5,82,0,0,1823,1824,5,101,0,0,1824,1825,5,40,0,0,1825, - 412,1,0,0,0,1826,1827,5,73,0,0,1827,1828,5,109,0,0,1828,1829,5,40,0,0, - 1829,414,1,0,0,0,1830,1831,5,114,0,0,1831,1832,5,101,0,0,1832,1833,5,40, - 0,0,1833,416,1,0,0,0,1834,1835,5,114,0,0,1835,1836,5,101,0,0,1836,1837, - 5,97,0,0,1837,1838,5,108,0,0,1838,1839,5,40,0,0,1839,418,1,0,0,0,1840, - 1841,5,105,0,0,1841,1842,5,109,0,0,1842,1843,5,40,0,0,1843,420,1,0,0,0, - 1844,1845,5,105,0,0,1845,1846,5,109,0,0,1846,1847,5,97,0,0,1847,1848,5, - 103,0,0,1848,1849,5,40,0,0,1849,422,1,0,0,0,1850,1851,5,116,0,0,1851,1852, - 5,114,0,0,1852,1853,5,117,0,0,1853,1854,5,110,0,0,1854,1855,5,99,0,0,1855, - 1856,5,40,0,0,1856,424,1,0,0,0,1857,1858,5,122,0,0,1858,1859,5,101,0,0, - 1859,1860,5,116,0,0,1860,1861,5,97,0,0,1861,1862,5,40,0,0,1862,426,1,0, - 0,0,1863,1864,5,114,0,0,1864,1865,5,105,0,0,1865,1866,5,101,0,0,1866,1867, - 5,109,0,0,1867,1868,5,97,0,0,1868,1869,5,110,0,0,1869,1870,5,110,0,0,1870, - 1871,5,122,0,0,1871,1872,5,101,0,0,1872,1873,5,116,0,0,1873,1874,5,97, - 0,0,1874,1875,5,40,0,0,1875,428,1,0,0,0,1876,1877,5,104,0,0,1877,1878, - 5,117,0,0,1878,1879,5,114,0,0,1879,1880,5,119,0,0,1880,1881,5,105,0,0, - 1881,1882,5,116,0,0,1882,1883,5,122,0,0,1883,1884,5,122,0,0,1884,1885, - 5,101,0,0,1885,1886,5,116,0,0,1886,1887,5,97,0,0,1887,1888,5,40,0,0,1888, - 430,1,0,0,0,1889,1890,5,108,0,0,1890,1891,5,97,0,0,1891,1892,5,109,0,0, - 1892,1893,5,98,0,0,1893,1894,5,101,0,0,1894,1895,5,114,0,0,1895,1896,5, - 116,0,0,1896,1897,5,119,0,0,1897,1898,5,40,0,0,1898,432,1,0,0,0,1899,1900, - 5,112,0,0,1900,1901,5,114,0,0,1901,1902,5,111,0,0,1902,1903,5,100,0,0, - 1903,1904,5,117,0,0,1904,1905,5,99,0,0,1905,1906,5,116,0,0,1906,1907,5, - 108,0,0,1907,1908,5,111,0,0,1908,1909,5,103,0,0,1909,1910,5,40,0,0,1910, - 434,1,0,0,0,1911,1912,5,104,0,0,1912,1913,5,101,0,0,1913,1914,5,97,0,0, - 1914,1915,5,118,0,0,1915,1916,5,105,0,0,1916,1917,5,115,0,0,1917,1918, - 5,105,0,0,1918,1919,5,100,0,0,1919,1920,5,101,0,0,1920,1921,5,40,0,0,1921, - 436,1,0,0,0,1922,1923,5,117,0,0,1923,1924,5,110,0,0,1924,1925,5,105,0, - 0,1925,1926,5,116,0,0,1926,1927,5,115,0,0,1927,1928,5,116,0,0,1928,1929, - 5,101,0,0,1929,1930,5,112,0,0,1930,1931,5,40,0,0,1931,438,1,0,0,0,1932, - 1933,5,105,0,0,1933,1934,5,115,0,0,1934,1935,5,112,0,0,1935,1936,5,114, - 0,0,1936,1937,5,105,0,0,1937,1938,5,109,0,0,1938,1939,5,101,0,0,1939,1940, - 5,40,0,0,1940,440,1,0,0,0,1941,1942,5,112,0,0,1942,1943,5,111,0,0,1943, - 1944,5,99,0,0,1944,1945,5,104,0,0,1945,1946,5,104,0,0,1946,1947,5,97,0, - 0,1947,1948,5,109,0,0,1948,1949,5,109,0,0,1949,1950,5,101,0,0,1950,1951, - 5,114,0,0,1951,1952,5,40,0,0,1952,442,1,0,0,0,1953,1954,5,100,0,0,1954, - 1955,5,111,0,0,1955,1956,5,117,0,0,1956,1957,5,98,0,0,1957,1958,5,108, - 0,0,1958,1959,5,101,0,0,1959,1960,5,102,0,0,1960,1961,5,97,0,0,1961,1962, - 5,99,0,0,1962,1963,5,116,0,0,1963,1964,5,111,0,0,1964,1965,5,114,0,0,1965, - 1966,5,105,0,0,1966,1967,5,97,0,0,1967,1968,5,108,0,0,1968,1969,5,40,0, - 0,1969,444,1,0,0,0,1970,1971,5,102,0,0,1971,1972,5,97,0,0,1972,1973,5, - 99,0,0,1973,1974,5,116,0,0,1974,1975,5,111,0,0,1975,1976,5,114,0,0,1976, - 1977,5,105,0,0,1977,1978,5,97,0,0,1978,1979,5,108,0,0,1979,1980,5,50,0, - 0,1980,1981,5,40,0,0,1981,446,1,0,0,0,1982,1983,5,102,0,0,1983,1984,5, - 114,0,0,1984,1985,5,97,0,0,1985,1986,5,99,0,0,1986,1987,5,116,0,0,1987, - 1988,5,105,0,0,1988,1989,5,111,0,0,1989,1990,5,110,0,0,1990,1991,5,97, - 0,0,1991,1992,5,108,0,0,1992,1993,5,112,0,0,1993,1994,5,97,0,0,1994,1995, - 5,114,0,0,1995,1996,5,116,0,0,1996,1997,5,40,0,0,1997,448,1,0,0,0,1998, - 1999,5,113,0,0,1999,2000,5,117,0,0,2000,2001,5,111,0,0,2001,2002,5,116, - 0,0,2002,2003,5,105,0,0,2003,2004,5,101,0,0,2004,2005,5,110,0,0,2005,2006, - 5,116,0,0,2006,2007,5,40,0,0,2007,450,1,0,0,0,2008,2009,5,100,0,0,2009, - 2010,5,111,0,0,2010,2011,5,109,0,0,2011,2012,5,97,0,0,2012,2013,5,105, - 0,0,2013,2014,5,110,0,0,2014,2015,5,40,0,0,2015,452,1,0,0,0,2016,2017, - 5,112,0,0,2017,2018,5,105,0,0,2018,2019,5,101,0,0,2019,2020,5,99,0,0,2020, - 2021,5,101,0,0,2021,2022,5,119,0,0,2022,2023,5,105,0,0,2023,2024,5,115, - 0,0,2024,2025,5,101,0,0,2025,2026,5,40,0,0,2026,454,1,0,0,0,2027,2028, - 5,97,0,0,2028,2029,5,112,0,0,2029,2030,5,112,0,0,2030,2031,5,108,0,0,2031, - 2032,5,121,0,0,2032,2033,5,40,0,0,2033,456,1,0,0,0,2034,2035,5,108,0,0, - 2035,2036,5,97,0,0,2036,2037,5,109,0,0,2037,2038,5,98,0,0,2038,2039,5, - 100,0,0,2039,2040,5,97,0,0,2040,2041,5,40,0,0,2041,458,1,0,0,0,2042,2044, - 5,13,0,0,2043,2042,1,0,0,0,2043,2044,1,0,0,0,2044,2045,1,0,0,0,2045,2047, - 5,10,0,0,2046,2043,1,0,0,0,2047,2048,1,0,0,0,2048,2046,1,0,0,0,2048,2049, - 1,0,0,0,2049,2050,1,0,0,0,2050,2051,6,229,0,0,2051,460,1,0,0,0,2052,2054, - 7,0,0,0,2053,2055,7,1,0,0,2054,2053,1,0,0,0,2054,2055,1,0,0,0,2055,2057, - 1,0,0,0,2056,2058,2,48,57,0,2057,2056,1,0,0,0,2058,2059,1,0,0,0,2059,2057, - 1,0,0,0,2059,2060,1,0,0,0,2060,462,1,0,0,0,2061,2063,2,48,57,0,2062,2061, - 1,0,0,0,2063,2064,1,0,0,0,2064,2062,1,0,0,0,2064,2065,1,0,0,0,2065,2066, - 1,0,0,0,2066,2070,5,46,0,0,2067,2069,2,48,57,0,2068,2067,1,0,0,0,2069, - 2072,1,0,0,0,2070,2068,1,0,0,0,2070,2071,1,0,0,0,2071,2074,1,0,0,0,2072, - 2070,1,0,0,0,2073,2075,3,461,230,0,2074,2073,1,0,0,0,2074,2075,1,0,0,0, - 2075,2077,1,0,0,0,2076,2078,5,105,0,0,2077,2076,1,0,0,0,2077,2078,1,0, - 0,0,2078,2095,1,0,0,0,2079,2081,5,46,0,0,2080,2079,1,0,0,0,2080,2081,1, - 0,0,0,2081,2083,1,0,0,0,2082,2084,2,48,57,0,2083,2082,1,0,0,0,2084,2085, - 1,0,0,0,2085,2083,1,0,0,0,2085,2086,1,0,0,0,2086,2088,1,0,0,0,2087,2089, - 3,461,230,0,2088,2087,1,0,0,0,2088,2089,1,0,0,0,2089,2091,1,0,0,0,2090, - 2092,5,105,0,0,2091,2090,1,0,0,0,2091,2092,1,0,0,0,2092,2095,1,0,0,0,2093, - 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1936,5,114,0,0,1936,1937,5,105,0,0,1937,1938,5,109,0,0,1938,1939,5,101, + 0,0,1939,1940,5,40,0,0,1940,440,1,0,0,0,1941,1942,5,112,0,0,1942,1943, + 5,111,0,0,1943,1944,5,99,0,0,1944,1945,5,104,0,0,1945,1946,5,104,0,0,1946, + 1947,5,97,0,0,1947,1948,5,109,0,0,1948,1949,5,109,0,0,1949,1950,5,101, + 0,0,1950,1951,5,114,0,0,1951,1952,5,40,0,0,1952,442,1,0,0,0,1953,1954, + 5,100,0,0,1954,1955,5,111,0,0,1955,1956,5,117,0,0,1956,1957,5,98,0,0,1957, + 1958,5,108,0,0,1958,1959,5,101,0,0,1959,1960,5,102,0,0,1960,1961,5,97, + 0,0,1961,1962,5,99,0,0,1962,1963,5,116,0,0,1963,1964,5,111,0,0,1964,1965, + 5,114,0,0,1965,1966,5,105,0,0,1966,1967,5,97,0,0,1967,1968,5,108,0,0,1968, + 1969,5,40,0,0,1969,444,1,0,0,0,1970,1971,5,102,0,0,1971,1972,5,97,0,0, + 1972,1973,5,99,0,0,1973,1974,5,116,0,0,1974,1975,5,111,0,0,1975,1976,5, + 114,0,0,1976,1977,5,105,0,0,1977,1978,5,97,0,0,1978,1979,5,108,0,0,1979, + 1980,5,50,0,0,1980,1981,5,40,0,0,1981,446,1,0,0,0,1982,1983,5,102,0,0, + 1983,1984,5,114,0,0,1984,1985,5,97,0,0,1985,1986,5,99,0,0,1986,1987,5, + 116,0,0,1987,1988,5,105,0,0,1988,1989,5,111,0,0,1989,1990,5,110,0,0,1990, + 1991,5,97,0,0,1991,1992,5,108,0,0,1992,1993,5,112,0,0,1993,1994,5,97,0, + 0,1994,1995,5,114,0,0,1995,1996,5,116,0,0,1996,1997,5,40,0,0,1997,448, + 1,0,0,0,1998,1999,5,113,0,0,1999,2000,5,117,0,0,2000,2001,5,111,0,0,2001, + 2002,5,116,0,0,2002,2003,5,105,0,0,2003,2004,5,101,0,0,2004,2005,5,110, + 0,0,2005,2006,5,116,0,0,2006,2007,5,40,0,0,2007,450,1,0,0,0,2008,2009, + 5,100,0,0,2009,2010,5,111,0,0,2010,2011,5,109,0,0,2011,2012,5,97,0,0,2012, + 2013,5,105,0,0,2013,2014,5,110,0,0,2014,2015,5,40,0,0,2015,452,1,0,0,0, + 2016,2017,5,112,0,0,2017,2018,5,105,0,0,2018,2019,5,101,0,0,2019,2020, + 5,99,0,0,2020,2021,5,101,0,0,2021,2022,5,119,0,0,2022,2023,5,105,0,0,2023, + 2024,5,115,0,0,2024,2025,5,101,0,0,2025,2026,5,40,0,0,2026,454,1,0,0,0, + 2027,2028,5,97,0,0,2028,2029,5,112,0,0,2029,2030,5,112,0,0,2030,2031,5, + 108,0,0,2031,2032,5,121,0,0,2032,2033,5,40,0,0,2033,456,1,0,0,0,2034,2035, + 5,108,0,0,2035,2036,5,97,0,0,2036,2037,5,109,0,0,2037,2038,5,98,0,0,2038, + 2039,5,100,0,0,2039,2040,5,97,0,0,2040,2041,5,40,0,0,2041,458,1,0,0,0, + 2042,2044,5,13,0,0,2043,2042,1,0,0,0,2043,2044,1,0,0,0,2044,2045,1,0,0, + 0,2045,2047,5,10,0,0,2046,2043,1,0,0,0,2047,2048,1,0,0,0,2048,2046,1,0, + 0,0,2048,2049,1,0,0,0,2049,2050,1,0,0,0,2050,2051,6,229,0,0,2051,460,1, + 0,0,0,2052,2054,7,0,0,0,2053,2055,7,1,0,0,2054,2053,1,0,0,0,2054,2055, + 1,0,0,0,2055,2057,1,0,0,0,2056,2058,2,48,57,0,2057,2056,1,0,0,0,2058,2059, + 1,0,0,0,2059,2057,1,0,0,0,2059,2060,1,0,0,0,2060,462,1,0,0,0,2061,2063, + 2,48,57,0,2062,2061,1,0,0,0,2063,2064,1,0,0,0,2064,2062,1,0,0,0,2064,2065, + 1,0,0,0,2065,2066,1,0,0,0,2066,2070,5,46,0,0,2067,2069,2,48,57,0,2068, + 2067,1,0,0,0,2069,2072,1,0,0,0,2070,2068,1,0,0,0,2070,2071,1,0,0,0,2071, + 2074,1,0,0,0,2072,2070,1,0,0,0,2073,2075,3,461,230,0,2074,2073,1,0,0,0, + 2074,2075,1,0,0,0,2075,2077,1,0,0,0,2076,2078,5,105,0,0,2077,2076,1,0, + 0,0,2077,2078,1,0,0,0,2078,2095,1,0,0,0,2079,2081,5,46,0,0,2080,2079,1, + 0,0,0,2080,2081,1,0,0,0,2081,2083,1,0,0,0,2082,2084,2,48,57,0,2083,2082, + 1,0,0,0,2084,2085,1,0,0,0,2085,2083,1,0,0,0,2085,2086,1,0,0,0,2086,2088, + 1,0,0,0,2087,2089,3,461,230,0,2088,2087,1,0,0,0,2088,2089,1,0,0,0,2089, + 2091,1,0,0,0,2090,2092,5,105,0,0,2091,2090,1,0,0,0,2091,2092,1,0,0,0,2092, + 2095,1,0,0,0,2093,2095,5,105,0,0,2094,2062,1,0,0,0,2094,2080,1,0,0,0,2094, + 2093,1,0,0,0,2095,464,1,0,0,0,2096,2097,5,67,0,0,2097,2115,5,67,0,0,2098, + 2099,5,82,0,0,2099,2115,5,82,0,0,2100,2101,5,81,0,0,2101,2115,5,81,0,0, + 2102,2103,5,90,0,0,2103,2115,5,90,0,0,2104,2105,5,66,0,0,2105,2115,5,66, + 0,0,2106,2107,5,90,0,0,2107,2108,5,90,0,0,2108,2115,5,42,0,0,2109,2110, + 5,90,0,0,2110,2111,5,90,0,0,2111,2115,5,43,0,0,2112,2113,5,80,0,0,2113, + 2115,5,80,0,0,2114,2096,1,0,0,0,2114,2098,1,0,0,0,2114,2100,1,0,0,0,2114, + 2102,1,0,0,0,2114,2104,1,0,0,0,2114,2106,1,0,0,0,2114,2109,1,0,0,0,2114, + 2112,1,0,0,0,2115,466,1,0,0,0,2116,2117,5,116,0,0,2117,2118,5,114,0,0, + 2118,2119,5,117,0,0,2119,2135,5,101,0,0,2120,2121,5,84,0,0,2121,2122,5, + 114,0,0,2122,2123,5,117,0,0,2123,2135,5,101,0,0,2124,2125,5,102,0,0,2125, + 2126,5,97,0,0,2126,2127,5,108,0,0,2127,2128,5,115,0,0,2128,2135,5,101, + 0,0,2129,2130,5,70,0,0,2130,2131,5,97,0,0,2131,2132,5,108,0,0,2132,2133, + 5,115,0,0,2133,2135,5,101,0,0,2134,2116,1,0,0,0,2134,2120,1,0,0,0,2134, + 2124,1,0,0,0,2134,2129,1,0,0,0,2135,468,1,0,0,0,2136,2137,5,78,0,0,2137, + 2138,5,97,0,0,2138,2139,5,78,0,0,2139,470,1,0,0,0,2140,2142,7,2,0,0,2141, + 2140,1,0,0,0,2142,2143,1,0,0,0,2143,2141,1,0,0,0,2143,2144,1,0,0,0,2144, + 2153,1,0,0,0,2145,2147,5,95,0,0,2146,2148,7,3,0,0,2147,2146,1,0,0,0,2148, + 2149,1,0,0,0,2149,2147,1,0,0,0,2149,2150,1,0,0,0,2150,2152,1,0,0,0,2151, + 2145,1,0,0,0,2152,2155,1,0,0,0,2153,2151,1,0,0,0,2153,2154,1,0,0,0,2154, + 472,1,0,0,0,2155,2153,1,0,0,0,2156,2157,5,47,0,0,2157,2158,5,47,0,0,2158, + 2162,1,0,0,0,2159,2161,8,4,0,0,2160,2159,1,0,0,0,2161,2164,1,0,0,0,2162, + 2160,1,0,0,0,2162,2163,1,0,0,0,2163,2169,1,0,0,0,2164,2162,1,0,0,0,2165, + 2167,5,13,0,0,2166,2165,1,0,0,0,2166,2167,1,0,0,0,2167,2168,1,0,0,0,2168, + 2170,5,10,0,0,2169,2166,1,0,0,0,2169,2170,1,0,0,0,2170,2183,1,0,0,0,2171, + 2172,5,47,0,0,2172,2173,5,42,0,0,2173,2177,1,0,0,0,2174,2176,9,0,0,0,2175, + 2174,1,0,0,0,2176,2179,1,0,0,0,2177,2178,1,0,0,0,2177,2175,1,0,0,0,2178, + 2180,1,0,0,0,2179,2177,1,0,0,0,2180,2181,5,42,0,0,2181,2183,5,47,0,0,2182, + 2156,1,0,0,0,2182,2171,1,0,0,0,2183,2184,1,0,0,0,2184,2185,6,236,0,0,2185, + 474,1,0,0,0,2186,2188,7,5,0,0,2187,2186,1,0,0,0,2188,2189,1,0,0,0,2189, + 2187,1,0,0,0,2189,2190,1,0,0,0,2190,2191,1,0,0,0,2191,2192,6,237,0,0,2192, + 476,1,0,0,0,25,0,2043,2048,2054,2059,2064,2070,2074,2077,2080,2085,2088, + 2091,2094,2114,2134,2143,2149,2153,2162,2166,2169,2177,2182,2189,1,6,0, + 0 }; public static readonly ATN _ATN = diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp index 70684accf..9f8eccd7d 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp @@ -187,6 +187,8 @@ null 'erfi(' 'Ei(' 'li(' +'lambertw(' +'productlog(' 'polygamma(' 'digamma(' 'Si(' @@ -215,8 +217,6 @@ null 'zeta(' 'riemannzeta(' 'hurwitzzeta(' -'lambertw(' -'productlog(' 'heaviside(' 'unitstep(' 'isprime(' @@ -726,4 +726,4 @@ mode names: DEFAULT_MODE atn: -[4, 0, 237, 2193, 6, -1, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 2, 6, 7, 6, 2, 7, 7, 7, 2, 8, 7, 8, 2, 9, 7, 9, 2, 10, 7, 10, 2, 11, 7, 11, 2, 12, 7, 12, 2, 13, 7, 13, 2, 14, 7, 14, 2, 15, 7, 15, 2, 16, 7, 16, 2, 17, 7, 17, 2, 18, 7, 18, 2, 19, 7, 19, 2, 20, 7, 20, 2, 21, 7, 21, 2, 22, 7, 22, 2, 23, 7, 23, 2, 24, 7, 24, 2, 25, 7, 25, 2, 26, 7, 26, 2, 27, 7, 27, 2, 28, 7, 28, 2, 29, 7, 29, 2, 30, 7, 30, 2, 31, 7, 31, 2, 32, 7, 32, 2, 33, 7, 33, 2, 34, 7, 34, 2, 35, 7, 35, 2, 36, 7, 36, 2, 37, 7, 37, 2, 38, 7, 38, 2, 39, 7, 39, 2, 40, 7, 40, 2, 41, 7, 41, 2, 42, 7, 42, 2, 43, 7, 43, 2, 44, 7, 44, 2, 45, 7, 45, 2, 46, 7, 46, 2, 47, 7, 47, 2, 48, 7, 48, 2, 49, 7, 49, 2, 50, 7, 50, 2, 51, 7, 51, 2, 52, 7, 52, 2, 53, 7, 53, 2, 54, 7, 54, 2, 55, 7, 55, 2, 56, 7, 56, 2, 57, 7, 57, 2, 58, 7, 58, 2, 59, 7, 59, 2, 60, 7, 60, 2, 61, 7, 61, 2, 62, 7, 62, 2, 63, 7, 63, 2, 64, 7, 64, 2, 65, 7, 65, 2, 66, 7, 66, 2, 67, 7, 67, 2, 68, 7, 68, 2, 69, 7, 69, 2, 70, 7, 70, 2, 71, 7, 71, 2, 72, 7, 72, 2, 73, 7, 73, 2, 74, 7, 74, 2, 75, 7, 75, 2, 76, 7, 76, 2, 77, 7, 77, 2, 78, 7, 78, 2, 79, 7, 79, 2, 80, 7, 80, 2, 81, 7, 81, 2, 82, 7, 82, 2, 83, 7, 83, 2, 84, 7, 84, 2, 85, 7, 85, 2, 86, 7, 86, 2, 87, 7, 87, 2, 88, 7, 88, 2, 89, 7, 89, 2, 90, 7, 90, 2, 91, 7, 91, 2, 92, 7, 92, 2, 93, 7, 93, 2, 94, 7, 94, 2, 95, 7, 95, 2, 96, 7, 96, 2, 97, 7, 97, 2, 98, 7, 98, 2, 99, 7, 99, 2, 100, 7, 100, 2, 101, 7, 101, 2, 102, 7, 102, 2, 103, 7, 103, 2, 104, 7, 104, 2, 105, 7, 105, 2, 106, 7, 106, 2, 107, 7, 107, 2, 108, 7, 108, 2, 109, 7, 109, 2, 110, 7, 110, 2, 111, 7, 111, 2, 112, 7, 112, 2, 113, 7, 113, 2, 114, 7, 114, 2, 115, 7, 115, 2, 116, 7, 116, 2, 117, 7, 117, 2, 118, 7, 118, 2, 119, 7, 119, 2, 120, 7, 120, 2, 121, 7, 121, 2, 122, 7, 122, 2, 123, 7, 123, 2, 124, 7, 124, 2, 125, 7, 125, 2, 126, 7, 126, 2, 127, 7, 127, 2, 128, 7, 128, 2, 129, 7, 129, 2, 130, 7, 130, 2, 131, 7, 131, 2, 132, 7, 132, 2, 133, 7, 133, 2, 134, 7, 134, 2, 135, 7, 135, 2, 136, 7, 136, 2, 137, 7, 137, 2, 138, 7, 138, 2, 139, 7, 139, 2, 140, 7, 140, 2, 141, 7, 141, 2, 142, 7, 142, 2, 143, 7, 143, 2, 144, 7, 144, 2, 145, 7, 145, 2, 146, 7, 146, 2, 147, 7, 147, 2, 148, 7, 148, 2, 149, 7, 149, 2, 150, 7, 150, 2, 151, 7, 151, 2, 152, 7, 152, 2, 153, 7, 153, 2, 154, 7, 154, 2, 155, 7, 155, 2, 156, 7, 156, 2, 157, 7, 157, 2, 158, 7, 158, 2, 159, 7, 159, 2, 160, 7, 160, 2, 161, 7, 161, 2, 162, 7, 162, 2, 163, 7, 163, 2, 164, 7, 164, 2, 165, 7, 165, 2, 166, 7, 166, 2, 167, 7, 167, 2, 168, 7, 168, 2, 169, 7, 169, 2, 170, 7, 170, 2, 171, 7, 171, 2, 172, 7, 172, 2, 173, 7, 173, 2, 174, 7, 174, 2, 175, 7, 175, 2, 176, 7, 176, 2, 177, 7, 177, 2, 178, 7, 178, 2, 179, 7, 179, 2, 180, 7, 180, 2, 181, 7, 181, 2, 182, 7, 182, 2, 183, 7, 183, 2, 184, 7, 184, 2, 185, 7, 185, 2, 186, 7, 186, 2, 187, 7, 187, 2, 188, 7, 188, 2, 189, 7, 189, 2, 190, 7, 190, 2, 191, 7, 191, 2, 192, 7, 192, 2, 193, 7, 193, 2, 194, 7, 194, 2, 195, 7, 195, 2, 196, 7, 196, 2, 197, 7, 197, 2, 198, 7, 198, 2, 199, 7, 199, 2, 200, 7, 200, 2, 201, 7, 201, 2, 202, 7, 202, 2, 203, 7, 203, 2, 204, 7, 204, 2, 205, 7, 205, 2, 206, 7, 206, 2, 207, 7, 207, 2, 208, 7, 208, 2, 209, 7, 209, 2, 210, 7, 210, 2, 211, 7, 211, 2, 212, 7, 212, 2, 213, 7, 213, 2, 214, 7, 214, 2, 215, 7, 215, 2, 216, 7, 216, 2, 217, 7, 217, 2, 218, 7, 218, 2, 219, 7, 219, 2, 220, 7, 220, 2, 221, 7, 221, 2, 222, 7, 222, 2, 223, 7, 223, 2, 224, 7, 224, 2, 225, 7, 225, 2, 226, 7, 226, 2, 227, 7, 227, 2, 228, 7, 228, 2, 229, 7, 229, 2, 230, 7, 230, 2, 231, 7, 231, 2, 232, 7, 232, 2, 233, 7, 233, 2, 234, 7, 234, 2, 235, 7, 235, 2, 236, 7, 236, 2, 237, 7, 237, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, 1, 7, 1, 7, 1, 8, 1, 8, 1, 9, 1, 9, 1, 10, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 12, 1, 12, 1, 12, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 14, 1, 14, 1, 14, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 16, 1, 16, 1, 17, 1, 17, 1, 17, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 19, 1, 19, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 21, 1, 21, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 23, 1, 23, 1, 24, 1, 24, 1, 24, 1, 25, 1, 25, 1, 25, 1, 26, 1, 26, 1, 27, 1, 27, 1, 28, 1, 28, 1, 29, 1, 29, 1, 29, 1, 30, 1, 30, 1, 31, 1, 31, 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25, 0, 2043, 2048, 2054, 2059, 2064, 2070, 2074, 2077, 2080, 2085, 2088, 2091, 2094, 2114, 2134, 2143, 2149, 2153, 2162, 2166, 2169, 2177, 2182, 2189, 1, 6, 0, 0] \ No newline at end of file diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens index 280a47a99..33677c693 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens @@ -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 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs index cc5be1a82..06df1e7e8 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs @@ -132,12 +132,12 @@ public const int "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'multinomial('", "'catalannumber('", "'harmonicnumber('", "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", - "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", - "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", - "'cross('", "'laplacian('", "'forwarddifference('", "'jacobian('", "'hessian('", - "'resultant('", "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", - "'re('", "'real('", "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", - "'hurwitzzeta('", "'lambertw('", "'productlog('", "'heaviside('", "'unitstep('", + "'erfc('", "'erfi('", "'Ei('", "'li('", "'lambertw('", "'productlog('", + "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", + "'transpose('", "'dot('", "'cross('", "'laplacian('", "'forwarddifference('", + "'jacobian('", "'hessian('", "'resultant('", "'conjugate('", "'conj('", + "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", + "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'heaviside('", "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" @@ -5270,7 +5270,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1154; Match(T__32); - Assert("polygamma", 2, _localctx.args.list.Count); _localctx.value = MathS.Polygamma(_localctx.args.list[0], _localctx.args.list[1]); + if (Assert("lambertw", (2, 1), _localctx.args.list.Count)) _localctx.value = MathS.LambertW(_localctx.args.list[0], _localctx.args.list[1]); else _localctx.value = MathS.LambertW(_localctx.args.list[0]); } break; case 146: @@ -5282,7 +5282,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1159; Match(T__32); - Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_localctx.args.list[0]); + if (Assert("productlog", (2, 1), _localctx.args.list.Count)) _localctx.value = MathS.LambertW(_localctx.args.list[0], _localctx.args.list[1]); else _localctx.value = MathS.LambertW(_localctx.args.list[0]); } break; case 147: @@ -5294,7 +5294,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1164; Match(T__32); - Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); + Assert("polygamma", 2, _localctx.args.list.Count); _localctx.value = MathS.Polygamma(_localctx.args.list[0], _localctx.args.list[1]); } break; case 148: @@ -5306,7 +5306,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1169; Match(T__32); - Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); + Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_localctx.args.list[0]); } break; case 149: @@ -5318,7 +5318,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1174; Match(T__32); - Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); + Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); } break; case 150: @@ -5330,7 +5330,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1179; Match(T__32); - Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); + Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); } break; case 151: @@ -5342,7 +5342,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1184; Match(T__32); - Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_localctx.args.list[0]); + Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); } break; case 152: @@ -5354,7 +5354,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1189; Match(T__32); - Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); + Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); } break; case 153: @@ -5366,7 +5366,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1194; Match(T__32); - Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_localctx.args.list[0], _localctx.args.list[1]); + Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_localctx.args.list[0]); } break; case 154: @@ -5378,7 +5378,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1199; Match(T__32); - Assert("cross", (1, 2), _localctx.args.list.Count); _localctx.value = ParsingHelpers.Cross(_localctx.args.list); + Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); } break; case 155: @@ -5390,7 +5390,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1204; Match(T__32); - Assert("laplacian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Laplacian(_localctx.args.list[0], _localctx.args.list[1]); + Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_localctx.args.list[0], _localctx.args.list[1]); } break; case 156: @@ -5402,7 +5402,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1209; Match(T__32); - Assert("forwarddifference", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.ForwardDifference(_localctx.args.list[0], _localctx.args.list[1]); + Assert("cross", (1, 2), _localctx.args.list.Count); _localctx.value = ParsingHelpers.Cross(_localctx.args.list); } break; case 157: @@ -5414,7 +5414,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1214; Match(T__32); - Assert("jacobian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Jacobian(_localctx.args.list[0], _localctx.args.list[1]); + Assert("laplacian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Laplacian(_localctx.args.list[0], _localctx.args.list[1]); } break; case 158: @@ -5426,7 +5426,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1219; Match(T__32); - Assert("hessian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Hessian(_localctx.args.list[0], _localctx.args.list[1]); + Assert("forwarddifference", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.ForwardDifference(_localctx.args.list[0], _localctx.args.list[1]); } break; case 159: @@ -5438,7 +5438,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1224; Match(T__32); - Assert("resultant", 3, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Resultant(_localctx.args.list[0], _localctx.args.list[1], _localctx.args.list[2]); + Assert("jacobian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Jacobian(_localctx.args.list[0], _localctx.args.list[1]); } break; case 160: @@ -5450,7 +5450,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1229; Match(T__32); - Assert("conjugate", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); + Assert("hessian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Hessian(_localctx.args.list[0], _localctx.args.list[1]); } break; case 161: @@ -5462,7 +5462,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1234; Match(T__32); - Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); + Assert("resultant", 3, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Resultant(_localctx.args.list[0], _localctx.args.list[1], _localctx.args.list[2]); } break; case 162: @@ -5474,7 +5474,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1239; Match(T__32); - Assert("arg", 1, _localctx.args.list.Count); _localctx.value = MathS.Arg(_localctx.args.list[0]); + Assert("conjugate", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 163: @@ -5486,7 +5486,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1244; Match(T__32); - Assert("Re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 164: @@ -5498,7 +5498,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1249; Match(T__32); - Assert("Im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); + Assert("arg", 1, _localctx.args.list.Count); _localctx.value = MathS.Arg(_localctx.args.list[0]); } break; case 165: @@ -5510,7 +5510,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1254; Match(T__32); - Assert("re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("Re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 166: @@ -5522,7 +5522,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1259; Match(T__32); - Assert("real", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("Im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 167: @@ -5534,7 +5534,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1264; Match(T__32); - Assert("im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); + Assert("re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 168: @@ -5546,7 +5546,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1269; Match(T__32); - Assert("imag", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); + Assert("real", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 169: @@ -5558,7 +5558,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1274; Match(T__32); - _localctx.value = NotImplementedFunction("trunc", "rounding functions"); + Assert("im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 170: @@ -5570,7 +5570,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1279; Match(T__32); - _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); + Assert("imag", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 171: @@ -5582,7 +5582,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1284; Match(T__32); - _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); + _localctx.value = NotImplementedFunction("trunc", "rounding functions"); } break; case 172: @@ -5594,7 +5594,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1289; Match(T__32); - _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); + _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); } break; case 173: @@ -5606,7 +5606,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1294; Match(T__32); - _localctx.value = NotImplementedFunction("lambertw", "Lambert W function yet"); + _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); } break; case 174: @@ -5618,7 +5618,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1299; Match(T__32); - _localctx.value = NotImplementedFunction("productlog", "Lambert W function yet"); + _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); } break; case 175: diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs index 988920208..1ad83b90b 100644 --- a/Sources/AngouriMath/Core/Domains.Classes.cs +++ b/Sources/AngouriMath/Core/Domains.Classes.cs @@ -435,6 +435,14 @@ partial record Lif internal override Domain DefaultCodomain => Domain.Complex; } + partial record LambertWf + { + /// + public override Domain Codomain { get; protected init; } = Domain.Complex; + /// + internal override Domain DefaultCodomain => Domain.Complex; + } + partial record Polygammaf { /// diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.LambertW.Classes.cs b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.LambertW.Classes.cs new file mode 100644 index 000000000..436a7178e --- /dev/null +++ b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.LambertW.Classes.cs @@ -0,0 +1,41 @@ +// +// Copyright (c) 2019-2026 Angouri. +// AngouriMath is licensed under MIT. +// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md. +// Website: https://am.angouri.org. +// + +using System; + +namespace AngouriMath +{ + partial record Entity + { + /// + /// The Lambert W function W_k(z), the solution w of w e^w = z on the branch + /// k, a whole number: lambertw(z) is the principal branch and lambertw(k, z) + /// the branch k, as Mathematica's ProductLog is. + /// + /// + /// The branches are those of Corless, Gonnet, Hare, Jeffrey and Knuth (1996): W_0 is real + /// on [-1/e, +oo) and W_(-1) on [-1/e, 0), and both are -1 at -1/e. + /// https://github.com/asc-community/AngouriMath/issues/2182 + /// + public sealed partial record LambertWf(Entity Branch, Entity Argument) : Function, IBinaryNode + { + internal LambertWf New(Entity branch, Entity argument) => + ReferenceEquals(Branch, branch) && ReferenceEquals(Argument, argument) ? this : new(branch, argument) { Codomain = Codomain }; + + /// + public Entity NodeFirstChild => Branch; + + /// + public Entity NodeSecondChild => Argument; + + /// + public override Entity Replace(Func func) => func(New(Branch.Replace(func), Argument.Replace(func))); + /// + protected override Entity[] InitDirectChildren() => new[] { Branch, Argument }; + } + } +} diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Number/LambertW.cs b/Sources/AngouriMath/Core/Entity/Continuous/Number/LambertW.cs new file mode 100644 index 000000000..3e01c4bff --- /dev/null +++ b/Sources/AngouriMath/Core/Entity/Continuous/Number/LambertW.cs @@ -0,0 +1,167 @@ +// +// Copyright (c) 2019-2026 Angouri. +// AngouriMath is licensed under MIT. +// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md. +// Website: https://am.angouri.org. +// + +using System; +using PeterO.Numbers; +using AngouriMath.Functions; +using NumericsComplex = System.Numerics.Complex; + +namespace AngouriMath +{ + partial record Entity + { + partial record Number + { + /// + /// The branch of the Lambert W function at , + /// the solution w of w e^w = z on that branch, at the working precision; or + /// where it is not computed. + /// + /// + /// + /// The branches are those of Corless, Gonnet, Hare, Jeffrey and Knuth, "On the Lambert W + /// function" (1996), as Mathematica's ProductLog and mpmath's lambertw have + /// them: the principal branch W_0 is real on [-1/e, +oo), W_(-1) is real + /// on [-1/e, 0), and a value on a branch cut is the one approached from above. + /// + /// + /// The branch is found in double precision, where it is cheap: from the series in + /// p = sqrt(2 (e z + 1)) about the branch point -1/e, from ln(1 + z) elsewhere on + /// the principal branch short of |z| = 3, and from ln z + 2 pi i k - ln(ln z + 2 pi i k) otherwise, + /// each then taken to a root by Halley's iteration. That root is refined by the same iteration + /// at the working precision, which triples the digits with each step and does not leave the + /// branch. Near the branch point, where double precision cannot resolve z + 1/e, the + /// series is evaluated at the working precision instead, and refined from there. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + /// + internal static Complex? LambertW(EInteger branch, Complex z) + { + var context = MathS.Settings.DecimalPrecisionContext.Value; + var (re, im) = (z.RealPart.EDecimal, z.ImaginaryPart.EDecimal); + if (re.IsNaN() || im.IsNaN()) + return Real.NaN; + if (!re.IsFinite || !im.IsFinite || !branch.CanFitInInt32()) + return null; + var k = branch.ToInt32Checked(); + if (re.IsZero && im.IsZero) + return k == 0 ? Integer.Zero : Real.NegativeInfinity; + var work = Working(context, 16); + var precision = work.Precision.ToInt32Checked(); + + // Real where the branch is real: W_0 on [-1/e, +oo) and W_(-1) on [-1/e, 0). + var e = EDecimal.One.Exponential(work); + var nearTheBranchPoint = e.Multiply(re, work).Add(EDecimal.One, work); + var isReal = im.IsZero && (k == 0 && nearTheBranchPoint.Sign >= 0 || k == -1 && nearTheBranchPoint.Sign >= 0 && re.Sign < 0); + + (EDecimal Re, EDecimal Im) w; + var distance = Magnitude((nearTheBranchPoint, e.Multiply(im, work))); + // The two branches that meet at -1/e: W_0 from either side, W_(-1) from above and on the + // axis, W_1 from below. + var meetsTheBranchPoint = k == 0 || k == -1 && im.Sign >= 0 || k == 1 && im.Sign < 0; + if (meetsTheBranchPoint && distance.CompareTo(EDecimal.FromString("0.25")) < 0) + { + // p = sqrt(2 (e z + 1)), principal, and w = -1 + p - p^2/3 + 11 p^3/72 on W_0, -p on + // the other branch. At the working precision, since e z + 1 cancels. + (EDecimal Re, EDecimal Im) twice = (nearTheBranchPoint.Multiply(EDecimal.FromInt32(2), work), e.Multiply(im, work).Multiply(EDecimal.FromInt32(2), work)); + var p = Sqrt(twice, work); + if (k != 0) + p = (p.Re.Negate(), p.Im.Negate()); + var p2 = Multiply(p, p, work); + var p3 = Multiply(p2, p, work); + w = (EDecimal.One.Negate().Add(p.Re, work).Subtract(p2.Re.Divide(EDecimal.FromInt32(3), work), work).Add(p3.Re.Multiply(EDecimal.FromInt32(11), work).Divide(EDecimal.FromInt32(72), work), work), + p.Im.Subtract(p2.Im.Divide(EDecimal.FromInt32(3), work), work).Add(p3.Im.Multiply(EDecimal.FromInt32(11), work).Divide(EDecimal.FromInt32(72), work), work)); + } + else + { + var start = InDoublePrecision(k, new NumericsComplex(re.ToDouble(), im.ToDouble())); + if (double.IsNaN(start.Real) || double.IsNaN(start.Imaginary) || double.IsInfinity(start.Real) || double.IsInfinity(start.Imaginary)) + return null; + w = (EDecimal.FromDouble(start.Real), EDecimal.FromDouble(start.Imaginary)); + } + if (isReal) + w = (w.Re, EDecimal.Zero); + + var tolerance = EDecimal.Create(EInteger.One, EInteger.FromInt32(-precision + 4)); + for (var step = 0; step < 64; step++) + { + // Halley: w - f / (e^w (w + 1) - (w + 2) f / (2 w + 2)), with f = w e^w - z. + var ew = Exp(w, work); + var wew = Multiply(w, ew, work); + (EDecimal Re, EDecimal Im) f = (wew.Re.Subtract(re, work), wew.Im.Subtract(im, work)); + (EDecimal Re, EDecimal Im) wPlusOne = (w.Re.Add(EDecimal.One, work), w.Im); + if (wPlusOne.Re.IsZero && wPlusOne.Im.IsZero) + break; + var correction = Divide(Multiply((w.Re.Add(EDecimal.FromInt32(2), work), w.Im), f, work), + (wPlusOne.Re.Multiply(EDecimal.FromInt32(2), work), wPlusOne.Im.Multiply(EDecimal.FromInt32(2), work)), work); + var slope = Multiply(ew, wPlusOne, work); + var change = Divide(f, (slope.Re.Subtract(correction.Re, work), slope.Im.Subtract(correction.Im, work)), work); + w = (w.Re.Subtract(change.Re, work), isReal ? EDecimal.Zero : w.Im.Subtract(change.Im, work)); + if (Magnitude(change).CompareTo(tolerance.Multiply(EDecimal.Max(Magnitude(w), EDecimal.One), work)) <= 0) + break; + } + return Complex.Create(w.Re.RoundToPrecision(context), w.Im.RoundToPrecision(context)); + } + + /// + /// W_k(z) in double precision, from a start on the branch and Halley's iteration: the + /// branch is chosen here, and the working precision only refines the root. + /// + internal static NumericsComplex InDoublePrecision(int k, NumericsComplex z) + { + NumericsComplex w; + var p = NumericsComplex.Sqrt(2 * (Math.E * z + 1)); + // The series about the branch point, within 1/e of it, on the principal branch; ln(1 + z) + // short of the asymptotic reach, which W_0 is close to there and the asymptotic start is + // not: from that one, 0.5i went to another branch. Between -1 and -1/e on the axis + // ln(1 + z) is real where W_0 is not, and only the series reaches the root. + if (k == 0 && NumericsComplex.Abs(Math.E * z + 1) < 1) + w = -1 + p - p * p / 3 + 11 * p * p * p / 72; + else if (k == 0 && NumericsComplex.Abs(z) < 3) + w = NumericsComplex.Log(1 + z); + else + { + var l1 = NumericsComplex.Log(z) + new NumericsComplex(0, 2 * Math.PI * k); + var l2 = NumericsComplex.Log(l1); + w = l1 - l2 + l2 / l1; + } + for (var step = 0; step < 64; step++) + { + var ew = NumericsComplex.Exp(w); + var f = w * ew - z; + var change = f / (ew * (w + 1) - (w + 2) * f / (2 * w + 2)); + w -= change; + if (NumericsComplex.Abs(change) <= 1e-15 * Math.Max(NumericsComplex.Abs(w), 1)) + break; + } + return w; + } + + private static (EDecimal Re, EDecimal Im) Exp((EDecimal Re, EDecimal Im) w, EContext work) + { + var modulus = w.Re.Exponential(work); + return (modulus.Multiply(w.Im.Cos(work), work), modulus.Multiply(w.Im.Sin(work), work)); + } + + private static (EDecimal Re, EDecimal Im) Divide((EDecimal Re, EDecimal Im) a, (EDecimal Re, EDecimal Im) b, EContext work) + { + var norm = b.Re.Multiply(b.Re, work).Add(b.Im.Multiply(b.Im, work), work); + return (a.Re.Multiply(b.Re, work).Add(a.Im.Multiply(b.Im, work), work).Divide(norm, work), + a.Im.Multiply(b.Re, work).Subtract(a.Re.Multiply(b.Im, work), work).Divide(norm, work)); + } + + /// The principal square root, with its cut on the negative axis, approached from above. + private static (EDecimal Re, EDecimal Im) Sqrt((EDecimal Re, EDecimal Im) z, EContext work) + { + var modulus = z.Re.Multiply(z.Re, work).Add(z.Im.Multiply(z.Im, work), work).SqrtByIntegerRoot(work); + var re = modulus.Add(z.Re, work).Divide(EDecimal.FromInt32(2), work).SqrtByIntegerRoot(work); + var im = modulus.Subtract(z.Re, work).Divide(EDecimal.FromInt32(2), work).SqrtByIntegerRoot(work); + return (re, z.Im.Sign < 0 ? im.Negate() : im); + } + } + } +} diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs index b1c0563ea..b67031b9d 100644 --- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs +++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs @@ -141,6 +141,7 @@ [EntityJsonConverter] partial record SpecialSet [EntityJsonConverter] partial record Eif; [EntityJsonConverter] partial record Lif; [EntityJsonConverter] partial record Polygammaf; + [EntityJsonConverter] partial record LambertWf; [EntityJsonConverter] partial record IncompleteGammaf; [EntityJsonConverter] partial record Sif; [EntityJsonConverter] partial record Cif; diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs index 290797cec..13643d6a8 100644 --- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs +++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs @@ -484,6 +484,7 @@ internal abstract bool ETryBuild( [typeof(Entity.Eif)] = (1, static c => new Entity.Eif(c[0])), [typeof(Entity.Lif)] = (1, static c => new Entity.Lif(c[0])), [typeof(Entity.Polygammaf)] = (2, static c => new Entity.Polygammaf(c[0], c[1])), + [typeof(Entity.LambertWf)] = (2, static c => new Entity.LambertWf(c[0], c[1])), [typeof(Entity.IncompleteGammaf)] = (2, static c => new Entity.IncompleteGammaf(c[0], c[1])), [typeof(Entity.Sif)] = (1, static c => new Entity.Sif(c[0])), [typeof(Entity.Cif)] = (1, static c => new Entity.Cif(c[0])), diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md index 14410ac05..4c5f9597d 100644 --- a/Sources/AngouriMath/Docs/Contributing/WritingARule.md +++ b/Sources/AngouriMath/Docs/Contributing/WritingARule.md @@ -110,7 +110,7 @@ itself, and needs no `when:` to say so. It is also strictly more specific than ` the ordering knows about — see below. **Matchable is not the same as buildable.** A pattern can be *matched* against any node type, but a -pattern used as a **replacement** must be one the library can construct: there are **77** such types. +pattern used as a **replacement** must be one the library can construct: there are **78** such types. Two families are deliberately absent, and neither is an oversight: - **binders** — `Lambda`, `Set.ConditionalSet`. They bind a variable, and `DirectChildren` renames it diff --git a/Sources/AngouriMath/Docs/Usage/Syntax.md b/Sources/AngouriMath/Docs/Usage/Syntax.md index 39e8f63ff..6a73f625e 100644 --- a/Sources/AngouriMath/Docs/Usage/Syntax.md +++ b/Sources/AngouriMath/Docs/Usage/Syntax.md @@ -405,6 +405,14 @@ differentiated from its definition: the derivative of `Si(x)` is `sin(x) / x`, o `cos(x) / x`, and of `Shi(x)` and `Chi(x)` it is `sinh(x) / x` and `cosh(x) / x`. `Ci` and `Chi` are undefined at `0`; `Si(+oo)` is `pi / 2` and `Ci(+oo)` is `0`. +**Lambert W function** — `lambertw(z)` and `lambertw(k, z)`, also `productlog`, the solution `w` of +`w e^w = z`, on the principal branch and on the branch `k`, drawn `\operatorname{W}_{k}`. 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)`, and below `-1/e` the two are conjugates. +`lambertw(e)` is `1`, `lambertw(-1/e)` is `-1`, a `c e^c` for a real `c` the branch takes is `c`, and +anything else numeric is evaluated: `lambertw(1)` is `0.5671432904…`, the omega constant +([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). + **Polygamma functions** — `polygamma(n, z)` `digamma(z)`. The polygamma function `psi^(n)(z)`, the `(n + 1)`-th derivative of `ln Gamma(z)` for a whole `n >= 0`, and the digamma function `psi(z) = Gamma'(z)/Gamma(z)`, which is `polygamma(0, z)` and prints as `digamma(z)`. Each is evaluated @@ -538,7 +546,7 @@ of them: `ZZ unite QQ` is `QQ`, `BB intersect ZZ` is `{}`, `ZZ* \ ZZ+` is `{ 0 } `{ x in QQ : not x in ZZ }`. The tokens take the sign: `ZZ*2` no longer reads as `ZZ * 2`. **Refused by name** — `trunc`, and the long names of functions to come: `zeta` `riemannzeta` -`hurwitzzeta` `lambertw` `productlog`. Each is what some other +`hurwitzzeta`. Each is what some other system calls a function, so a caller reaches for it, and left alone it would be read as a product under the rule above and answer silently and wrongly, `zeta(2)` as `2 * zeta`; it raises a parse error naming the function instead. What each will mean is fixed in diff --git a/Sources/AngouriMath/Functions/Continuous/Differentiation.cs b/Sources/AngouriMath/Functions/Continuous/Differentiation.cs index e929ce184..c150157ae 100644 --- a/Sources/AngouriMath/Functions/Continuous/Differentiation.cs +++ b/Sources/AngouriMath/Functions/Continuous/Differentiation.cs @@ -327,6 +327,18 @@ protected override Entity InnerDifferentiate(Variable variable) => Argument.DerivativeOver(variable) / MathS.Ln(Argument); } + partial record LambertWf + { + // W'(u) = e^(-W(u)) / (1 + W(u)) u', the same as W(u) / (u (1 + W(u))) u' and 1 at u = 0 on the + // principal branch, where that one is 0/0. A branch that varies has no derivative in it. + // https://github.com/asc-community/AngouriMath/issues/2182 + /// + protected override Entity InnerDifferentiate(Variable variable) => + Branch.ContainsNode(variable) + ? base.InnerDifferentiate(variable) + : MathS.Pow(MathS.e, -this) / (1 + this) * Argument.DerivativeOver(variable); + } + partial record Polygammaf { // psi^(n)(a)' = psi^(n + 1)(a) a'. The order is whole, so an order that varies has no derivative diff --git a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs index ff6406412..1a296e8c4 100644 --- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs +++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs @@ -324,6 +324,14 @@ partial record Lif // The polygamma functions have no inverse among the library's nodes. // https://github.com/asc-community/AngouriMath/issues/171 + partial record LambertWf + { + // W_k(f) = v is f = v e^v, where v is a value of that branch; which values a branch takes is + // not decided here, so it is left unsolved rather than answered wrongly. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + partial record Polygammaf { private protected override IEnumerable? InvertNode(Entity value, Entity x) => diff --git a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs index b5399996b..02b5e7715 100644 --- a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs @@ -740,6 +740,45 @@ private static Entity Numerically(Complex n, int m) private const int LargestOrder = 64; } + public partial record LambertWf + { + // Every whole branch, and every z but 0 off the principal branch, where W_k(z) goes to -oo as ln z does. + private protected override Entity IntrinsicCondition => + Branch.In(MathS.Sets.Z) & (Branch.Equalizes(Integer.Zero) | !Argument.Equalizes(Integer.Zero)); + + /// + protected override Entity InnerSimplify(bool isExact) => + ExpandOnTwoArguments(Branch, Argument, + (k, z) => (k, z) switch + { + (Integer { IsZero: true }, Integer { IsZero: true }) => Integer.Zero, + (Integer, Integer { IsZero: true }) => Real.NegativeInfinity, + // c e^c on the branch whose real values c is among: W_0 for c >= -1, W_(-1) for c <= -1, + // so -1/e is -1 on both and e is 1. + (Integer { EInteger: var branch }, _) when TheExponentOfAProductWithItsExponential(z) is { } c + && (branch.IsZero && c.EDecimal.CompareTo(PeterO.Numbers.EDecimal.FromInt32(-1)) >= 0 + || branch.Equals(PeterO.Numbers.EInteger.FromInt32(-1)) && c.EDecimal.CompareTo(PeterO.Numbers.EDecimal.FromInt32(-1)) <= 0) + => c, + (Integer { EInteger: var branch }, Complex value) when !isExact => Number.LambertW(branch, value), + (Number, Number) when k is not Integer => MathS.NaN, + _ => null + }, + (@this, k, z) => ((LambertWf)@this).New(k, z), isExact); + + // c where z is c e^c for a real number c, as -e^(-1), 2 e^2 and e are written. + private static Real? TheExponentOfAProductWithItsExponential(Entity z) + => z switch + { + Variable { Name: "e" } => Integer.One, + Powf(Variable { Name: "e" }, Real exponent) when exponent == Integer.One => exponent, + Mulf(Real c, Powf(Variable { Name: "e" }, Real exponent)) when c == exponent => c, + Mulf(Powf(Variable { Name: "e" }, Real exponent), Real c) when c == exponent => c, + Divf(Real c, Variable { Name: "e" }) when c == Integer.MinusOne => c, + Divf(Real c, Powf(Variable { Name: "e" }, Real exponent)) when c == -exponent => c, + _ => null + }; + } + public partial record Ref { // Defined everywhere on the complex plane. diff --git a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs index e460ffd55..9955a1b87 100644 --- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs @@ -255,6 +255,15 @@ private protected override string LatexizeNode() => $@"\operatorname{{li}}\left({Argument.Latexize()}\right)"; } + partial record LambertWf + { + /// + private protected override string LatexizeNode() + => Branch == Integer.Zero + ? $@"\operatorname{{W}}\left({Argument.Latexize()}\right)" + : $@"\operatorname{{W}}_{{{Branch.Latexize()}}}\left({Argument.Latexize()}\right)"; + } + partial record Polygammaf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs index f28fc478d..de663adce 100644 --- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs @@ -277,6 +277,15 @@ public partial record Lif public override string ToString() => Stringize(); } + partial record LambertWf + { + /// + private protected override string StringizeNode() + => Branch == Integer.Zero ? $"lambertw({Argument.Stringize()})" : $"lambertw({Branch.Stringize()}, {Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + public partial record Polygammaf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs index cba300dfb..b18e1d202 100644 --- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs @@ -150,6 +150,13 @@ internal override string ToSymPy() => $@"sympy.li({Argument.ToSymPy()})"; } + public partial record LambertWf + { + // SymPy's LambertW takes the argument first and the branch second. + internal override string ToSymPy() + => Branch == Integer.Zero ? $"sympy.LambertW({Argument.ToSymPy()})" : $"sympy.LambertW({Argument.ToSymPy()}, {Branch.ToSymPy()})"; + } + public partial record Polygammaf { internal override string ToSymPy() diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs index 9b50e4930..29655c4bb 100644 --- a/Sources/AngouriMath/Functions/Substitute.cs +++ b/Sources/AngouriMath/Functions/Substitute.cs @@ -279,6 +279,13 @@ public override Entity Substitute(Entity x, Entity value) => this == x ? value : New(Argument.Substitute(x, value)); } + partial record LambertWf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Branch.Substitute(x, value), Argument.Substitute(x, value)); + } + partial record Polygammaf { /// diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs index f2fcc9b57..611b40e60 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs @@ -329,6 +329,11 @@ private protected override string SortHashName(SortLevel level) => Choice(level, "ei_", "li_", "li_"); } + public partial record LambertWf + { + private protected override string SortHashName(SortLevel level) => "lambertwf_"; + } + public partial record Polygammaf { private protected override string SortHashName(SortLevel level) diff --git a/Sources/MCP/AngouriMath.Mcp/Resources.cs b/Sources/MCP/AngouriMath.Mcp/Resources.cs index f0d1b5bf5..50074fd67 100644 --- a/Sources/MCP/AngouriMath.Mcp/Resources.cs +++ b/Sources/MCP/AngouriMath.Mcp/Resources.cs @@ -102,7 +102,7 @@ that every response returns. `catalannumber(n)`, the Catalan numbers, `harmonicnumber(n)` and `harmonicnumber(n, m)`, and `mobius divisorsigma primenu primeomega primepi` (`moebiusmu` is `mobius`): `divisorsigma(k, n)` sums the `k`-th powers of the divisors of `n` - - special functions: `erf erfc erfi Ei li Si Ci Shi Chi`, `digamma(z)` and `polygamma(n, z)`, and `gamma(a, z)`, the + - special functions: `erf erfc erfi Ei li Si Ci Shi Chi`, `digamma(z)` and `polygamma(n, z)`, `lambertw(z)` and `lambertw(k, z)` (also `productlog`), and `gamma(a, z)`, the upper incomplete gamma function - sets: `card powerset union intersection complement image preimage domain aleph iverson` @@ -121,7 +121,7 @@ apply lambda` | You might write | Reality | |---|---| | `arcsinh(x)` | **refused.** The inverse hyperbolics are area functions: write `arsinh`, `asinh` or `arsh` | - | `trunc`, `zeta`, `lambertw` and other long names of functions to come | refused by name — not yet in the library | + | `trunc`, `zeta` and other long names of functions to come | refused by name — not yet in the library | | `heaviside`, `unitstep`, `isprime`, `fractionalpart`, `quotient`, `pochhammer` | refused, with what to write: `iverson(x > 0)`, `iverson(x >= 0)` or `(1 + sgn(x))/2`; `n in PP`; `x mod 1`; `floor(a / b)` | | `elementin(x, A)`, `setsubtraction(A, B)`, `impl(a, b)` | **silently become products.** Use the infix `x in A`, `A \ B`, `a -> b` | | `union(A, B)`, `intersection(A, B)` | refused: both are indexed, `union(A_i, i in I)`. For two sets write `A \/ B` and `A /\ B` | diff --git a/Sources/Tests/AotSmokeTest/Program.cs b/Sources/Tests/AotSmokeTest/Program.cs index 928e79c96..7da7a29ec 100644 --- a/Sources/Tests/AotSmokeTest/Program.cs +++ b/Sources/Tests/AotSmokeTest/Program.cs @@ -140,6 +140,8 @@ private static void Parsing() CheckClose("multinomial(x, 3, 4) at x = 2", At(multinomial, "x", 2), 1260); var catalan = MathS.FromString("catalannumber(x)"); CheckClose("catalannumber at x = 5", At(catalan, "x", 5), 42); + var lambertW = MathS.FromString("lambertw(x)"); + CheckClose("lambertw at x = 1", At(lambertW, "x", 1), 0.56714329040978387); var harmonic = MathS.FromString("harmonicnumber(x, 2)"); CheckClose("harmonicnumber(x, 2) at x = 4", At(harmonic, "x", 4), 205.0 / 144); var difference = MathS.FromString("forwarddifference(x^3, x)"); diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt index 3d6457d02..3e257f43f 100644 --- a/Sources/Tests/UnitTests/Common/PublicApi.txt +++ b/Sources/Tests/UnitTests/Common/PublicApi.txt @@ -1451,6 +1451,28 @@ AngouriMath.Entity+Lambda.ToString() : System.String AngouriMath.Entity+Lambda.ctor(AngouriMath.Entity+Variable, AngouriMath.Entity) AngouriMath.Entity+Lambda.op_Equality(AngouriMath.Entity+Lambda, AngouriMath.Entity+Lambda) : System.Boolean AngouriMath.Entity+Lambda.op_Inequality(AngouriMath.Entity+Lambda, AngouriMath.Entity+Lambda) : System.Boolean +AngouriMath.Entity+LambertWf.$() : AngouriMath.Entity+LambertWf +AngouriMath.Entity+LambertWf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+LambertWf.Branch { } : AngouriMath.Entity +AngouriMath.Entity+LambertWf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+LambertWf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void +AngouriMath.Entity+LambertWf.EqualityContract { } : System.Type +AngouriMath.Entity+LambertWf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+LambertWf.Equals(AngouriMath.Entity+LambertWf) : System.Boolean +AngouriMath.Entity+LambertWf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+LambertWf.GetHashCode() : System.Int32 +AngouriMath.Entity+LambertWf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+LambertWf.InnerDifferentiate(AngouriMath.Entity+Variable) : AngouriMath.Entity +AngouriMath.Entity+LambertWf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+LambertWf.NodeFirstChild { } : AngouriMath.Entity +AngouriMath.Entity+LambertWf.NodeSecondChild { } : AngouriMath.Entity +AngouriMath.Entity+LambertWf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+LambertWf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+LambertWf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+LambertWf.ToString() : System.String +AngouriMath.Entity+LambertWf.ctor(AngouriMath.Entity, AngouriMath.Entity) +AngouriMath.Entity+LambertWf.op_Equality(AngouriMath.Entity+LambertWf, AngouriMath.Entity+LambertWf) : System.Boolean +AngouriMath.Entity+LambertWf.op_Inequality(AngouriMath.Entity+LambertWf, AngouriMath.Entity+LambertWf) : System.Boolean AngouriMath.Entity+Lcmf.$() : AngouriMath.Entity+Lcmf AngouriMath.Entity+Lcmf.Codomain { } : AngouriMath.Core.Domain AngouriMath.Entity+Lcmf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void @@ -3554,6 +3576,8 @@ AngouriMath.MathS.Interval(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath AngouriMath.MathS.Interval(AngouriMath.Entity, System.Boolean, AngouriMath.Entity, System.Boolean) : AngouriMath.Entity+Set+Interval AngouriMath.MathS.Iverson(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Lambda(AngouriMath.Entity+Variable, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.LambertW(AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.LambertW(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Latex(AngouriMath.Core.ILatexizeable) : System.String AngouriMath.MathS.Lcm(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.LessOrEqualThan(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity @@ -3744,6 +3768,7 @@ class AngouriMath.Entity+IncompleteGammaf class AngouriMath.Entity+Integralf class AngouriMath.Entity+Iversonf class AngouriMath.Entity+Lambda +class AngouriMath.Entity+LambertWf class AngouriMath.Entity+Lcmf class AngouriMath.Entity+LessOrEqualf class AngouriMath.Entity+Lessf diff --git a/Sources/Tests/UnitTests/Convenience/LambertWTest.cs b/Sources/Tests/UnitTests/Convenience/LambertWTest.cs new file mode 100644 index 000000000..cd4c2acd4 --- /dev/null +++ b/Sources/Tests/UnitTests/Convenience/LambertWTest.cs @@ -0,0 +1,154 @@ +// +// Copyright (c) 2019-2026 Angouri. +// AngouriMath is licensed under MIT. +// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md. +// Website: https://am.angouri.org. +// + +using AngouriMath; +using AngouriMath.Extensions; +using PeterO.Numbers; +using Xunit; +using static AngouriMath.Entity; + +namespace AngouriMath.Tests.Convenience +{ + /// + /// The Lambert W function, the solution w of w e^w = z on each branch, with the branches of + /// Corless et al. (1996) that Mathematica's ProductLog and mpmath's lambertw have. The name was + /// refused. #2182 + /// + [Trait("Area", "Convenience")] + public sealed class LambertWTest + { + /// + /// mpmath's lambertw at 60 digits, at the decimals written: on the real axis where each branch is real, across the cut + /// below -1/e where W_0 and W_(-1) are conjugates, about the branch point from above and below, + /// and far out. + /// + public static readonly TheoryData Points = new() + { + { 0, "1", "0", "0.56714329040978387299996866221035555", "0.0" }, + { 0, "2.5", "0", "0.95858635672870291216986678133245214", "0.0" }, + { 0, "10", "0", "1.7455280027406993830743012648753899", "0.0" }, + { 0, "1000000", "0", "11.383358086140052622000156781585004", "0.0" }, + { 0, "0.1", "0", "0.091276527160862264299895721423179569", "0.0" }, + { 0, "-0.1", "0", "-0.11183255915896296483356945682026584", "0.0" }, + { 0, "-0.3", "0", "-0.48940222718021496903623125199629337", "0.0" }, + { 0, "-0.36", "0", "-0.80608431597081777828552136162099200", "0.0" }, + { 0, "-0.5", "0", "-0.79402363234468936796301532190058981", "0.77011175051037910968131307740502893" }, + { 0, "-2", "0", "0.17281600283999997574575914578045636", "1.6736864137408426771888017779670810" }, + { 0, "-10", "0", "1.3699809685212708156194228571987809", "2.1401945270747131960165362216531737" }, + { 0, "1", "1", "0.65696606923043640587393518961502951", "0.32545033941341502998928195138862240" }, + { 0, "-1", "2", "0.62712187862672106128482581800205043", "1.0164525226857943480329954988558366" }, + { 0, "-3", "-4", "1.0750730665692549275718182498895184", "-1.3251023817343588822606049852999208" }, + { 0, "0", "0.5", "0.16259964821886692670376696666293535", "0.39262857399163941534774301910986139" }, + { 0, "0", "100", "3.3372744790013778465375635510033457", "1.2202535275983894290305770906784596" }, + { 0, "-0.36", "0.01", "-0.77692593162589352548613077434798300", "0.099106539538801071982698823506270403" }, + { 0, "-0.36", "-0.01", "-0.77692593162589352548613077434798300", "-0.099106539538801071982698823506270403" }, + { 0, "-0.367", "0", "-0.93239918474792848371646619087935721", "0.0" }, + { 0, "0.5", "0.5", "0.40431612353121278901924224143642299", "0.24343775688425395570266928474288716" }, + { 0, "-0.2", "0.3", "-0.079775717127478451154646095753164503", "0.38226147065890346680498485830193446" }, + { 0, "2", "-1.5", "0.93210073009396256291394339557696040", "-0.31632723076474133978590653951403091" }, + { -1, "-0.1", "0", "-3.5771520639572972184093919635119949", "0.0" }, + { -1, "-0.3", "0", "-1.7813370234216276119741702815127453", "0.0" }, + { -1, "-0.36", "0", "-1.2227701339785059531429380734238623", "0.0" }, + { -1, "-0.5", "0", "-0.79402363234468936796301532190058981", "-0.77011175051037910968131307740502893" }, + { -1, "-2", "0", "0.17281600283999997574575914578045636", "-1.6736864137408426771888017779670810" }, + { -1, "1", "0", "-1.5339133197935745079197410820727338", "-4.3751851530618983854709065648525843" }, + { -1, "1", "1", "-0.98696957322127523414822457230314696", "-3.6638570032847919874683044706668667" }, + { -1, "-1", "-1", "-1.6027125327569588280097149491309221", "-6.8383680385915972761916759143574442" }, + { -1, "-0.36", "0.01", "-1.2514376073860293427616444184098277", "-0.13609907407909009200297557730125840" }, + { -1, "-0.36", "-0.01", "-3.1073988682641031993153486904823598", "-7.4300990216044500554595691973401438" }, + { -1, "-0.00001", "0", "-14.163600815810183009109556303610900", "0.0" }, + { 1, "1", "0", "-1.5339133197935745079197410820727338", "4.3751851530618983854709065648525843" }, + { 1, "-1", "0", "-2.0622777295982838849784867200080460", "7.5886311784725126225689239541075844" }, + { 1, "-0.36", "-0.01", "-1.2514376073860293427616444184098277", "0.13609907407909009200297557730125840" }, + { 1, "-0.36", "0.01", "-3.1073988682641031993153486904823598", "7.4300990216044500554595691973401438" }, + { 1, "1", "1", "-1.3428489407008043011797745967257447", "5.2472493742914012056555318165948516" }, + { 1, "-2", "0", "-1.3607494244085734046050529099678950", "7.6785890798165936510026544586454389" }, + { 2, "1", "0", "-2.4015851048680028841741397746840765", "10.776299516115070898497103346391148" }, + { 2, "-1", "1", "-2.2466670775452915909711722757930199", "13.182968560741182863737480091832091" }, + { 2, "10", "0", "-0.094164747214147723021593974923742271", "10.987003940068022849033192477402823" }, + { -2, "1", "0", "-2.4015851048680028841741397746840765", "-10.776299516115070898497103346391148" }, + { -2, "-1", "1", "-1.8074833801113711199505175939657967", "-8.4281211380731151670788198279353834" }, + { -2, "10", "0", "-0.094164747214147723021593974923742271", "-10.987003940068022849033192477402823" }, + }; + + [Theory] + [MemberData(nameof(Points))] + public void ItAgreesWithMpmath(int branch, string re, string im, string expectedRe, string expectedIm) + { + var z = Number.Complex.Create(EDecimal.FromString(re), EDecimal.FromString(im)); + var w = Assert.IsAssignableFrom(MathS.LambertW(branch, z).EvalNumerical()); + var expected = Number.Complex.Create(EDecimal.FromString(expectedRe), EDecimal.FromString(expectedIm)); + var error = ((Number.Complex)(w - expected).EvalNumerical()).Abs().EDecimal; + var scale = EDecimal.Max(expected.Abs().EDecimal, EDecimal.One); + Assert.True(error.CompareTo(scale.Multiply(EDecimal.FromString("1e-25"))) < 0, $"W_{branch}({re} + {im}i) = {w.Stringize()}, expected {expected.Stringize()}"); + } + + [Theory] + [InlineData("lambertw(0)", "0")] + [InlineData("lambertw(e)", "1")] + [InlineData("lambertw(-1/e)", "-1")] + [InlineData("lambertw(-1, -1/e)", "-1")] + [InlineData("lambertw(2 e^2)", "2")] + [InlineData("lambertw(-1, -2 e^(-2))", "-2")] + [InlineData("productlog(e)", "1")] + public void ItIsExactWhereZIsANumberTimesItsExponential(string written, string expected) + => Assert.Equal(expected.ToEntity().InnerSimplified, written.ToEntity().InnerSimplified); + + /// Off the principal branch W_k(z) goes to -oo as z goes to 0, as ln z does. + [Fact] + public void OffThePrincipalBranchZeroIsMinusInfinity() + => Assert.Equal(Number.Real.NegativeInfinity, "lambertw(1, 0)".ToEntity().InnerSimplified); + + /// The branch is a whole number. + [Fact] + public void ABranchThatIsNotWholeHasNoValue() + => Assert.Equal(MathS.NaN, "lambertw(1/2, 1)".ToEntity().InnerSimplified); + + /// W(z) e^(W(z)) = z. + [Theory] + [InlineData(0, "3.5", "0")] + [InlineData(0, "-2", "1")] + [InlineData(-1, "-0.2", "0")] + [InlineData(3, "5", "-7")] + public void ItSolvesWTimesItsExponentialEqualsZ(int branch, string re, string im) + { + var z = Number.Complex.Create(EDecimal.FromString(re), EDecimal.FromString(im)); + var w = MathS.LambertW(branch, z); + var residual = ((Number.Complex)(w * MathS.Pow(MathS.e, w) - z).EvalNumerical()).Abs().EDecimal; + Assert.True(residual.CompareTo(EDecimal.FromString("1e-25")) < 0, residual.ToString()); + } + + /// W'(z) = W(z) / (z (1 + W(z))), and 1 at 0. + [Fact] + public void ItsDerivativeIsWOverZOnePlusW() + { + var derivative = MathS.LambertW("x").Differentiate("x"); + var atOne = ((Number.Real)derivative.Substitute("x", 1).EvalNumerical()).EDecimal; + var w = ((Number.Real)MathS.LambertW(1).EvalNumerical()).EDecimal; + var expected = w.Divide(w.Add(EDecimal.One), EContext.ForPrecision(40)); + Assert.True(atOne.Subtract(expected).Abs().CompareTo(EDecimal.FromString("1e-25")) < 0, atOne.ToString()); + Assert.Equal(Number.Integer.One, derivative.Substitute("x", 0).Evaled); + } + + [Fact] + public void ASymbolKeepsTheNode() + => Assert.IsType("lambertw(x)".ToEntity().InnerSimplified); + + [Theory] + [InlineData("lambertw(z)", "lambertw(z)", @"\operatorname{W}\left(z\right)", "sympy.LambertW(z)")] + [InlineData("lambertw(-1, z)", "lambertw(-1, z)", @"\operatorname{W}_{-1}\left(z\right)", "sympy.LambertW(z, -1)")] + [InlineData("productlog(1, z + 1)", "lambertw(1, z + 1)", @"\operatorname{W}_{1}\left(z+1\right)", "sympy.LambertW(z + 1, 1)")] + public void ItIsWrittenAsW(string written, string stringized, string latex, string sympy) + { + var parsed = written.ToEntity(); + Assert.Equal(stringized, parsed.Stringize()); + Assert.Equal(parsed, parsed.Stringize().ToEntity()); + Assert.Equal(latex, parsed.Latexize()); + Assert.Equal(sympy, parsed.ToSymPy()); + } + } +} diff --git a/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs b/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs index b9558cd56..4001cbdf0 100644 --- a/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs +++ b/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs @@ -38,16 +38,14 @@ public sealed class MissingFunctionNamesRefusedTest // https://github.com/asc-community/AngouriMath/issues/2182. zeta(s) was zeta * s. mobius, // moebiusmu, divisorsigma, primenu, primeomega and primepi, laplacian, jacobian and hessian, // fallingfactorial, factorialpower and risingfactorial, multinomial, catalannumber, - // harmonicnumber and forwarddifference were among them until they were implemented, in the - // same issue. + // harmonicnumber, forwarddifference, and lambertw and productlog, were among them until they + // were implemented, in the same issue. [Theory] [InlineData("trunc(x)")] [InlineData("zeta(s)")] [InlineData("zeta(s, a)")] [InlineData("riemannzeta(s)")] [InlineData("hurwitzzeta(s, a)")] - [InlineData("lambertw(x)")] - [InlineData("productlog(x)")] [InlineData("heaviside(x)")] [InlineData("unitstep(x)")] [InlineData("isprime(n)")] diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs index 2fe9072cc..2ba4a3320 100644 --- a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs +++ b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs @@ -79,7 +79,7 @@ public void TheIdentityIsNotTheName() [Fact] public void ThePatternLanguage() - => Stated(77, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); + => Stated(78, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); [Fact] public void ReplacementAPatternOrCode()