From 767737f46f6c3b3e2909492ea2db25043831c09b Mon Sep 17 00:00:00 2001 From: Rafael Vuijk Date: Thu, 29 Oct 2026 12:19:08 +0000 Subject: [PATCH] The harmonic numbers harmonicnumber(n) and harmonicnumber(n, m) were reserved by name in #2184 and are now Entity.HarmonicNumberf, built by MathS.HarmonicNumber. For a whole n >= 0 they are 1 + 1/2^m + ... + 1/n^m, summed exactly for a rational order: harmonicnumber(4) is 25/12 and harmonicnumber(4, 2) is 205/144. Elsewhere they are zeta(m) - zeta(m, n + 1), as Mathematica's HarmonicNumber is, which is evaluated numerically for a whole m >= 1 through the polygamma function: psi(n + 1) - psi(1) at m = 1, and (-1)^m / (m - 1)! (psi^(m - 1)(1) - psi^(m - 1)(n + 1)) above it. harmonicnumber(1/2) is 2 - 2 ln 2 and agrees with mpmath to 1e-25, as do H(5/2), H(-1/2) and H(1/2, 2). A negative integer n is a pole of the Hurwitz zeta function, and has no value but for a whole order m <= 0, where the harmonic number is a polynomial in n. What is not computed is left as the node. They print as harmonicnumber(n) and harmonicnumber(n, m), draw as \operatorname{H}_{n} and \operatorname{H}_{n}^{(m)}, and export to SymPy's harmonic. 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 | 3 + Sources/AngouriMath/Convenience/MathS.cs | 8 + Sources/AngouriMath/Core/Antlr/AngouriMath.g | 2 +- .../AngouriMath/Core/Antlr/AngouriMath.interp | 2 +- .../AngouriMath/Core/Antlr/AngouriMath.tokens | 80 ++-- .../Core/Antlr/AngouriMathLexer.cs | 443 +++++++++--------- .../Core/Antlr/AngouriMathLexer.interp | 4 +- .../Core/Antlr/AngouriMathLexer.tokens | 80 ++-- .../Core/Antlr/AngouriMathParser.cs | 98 ++-- Sources/AngouriMath/Core/Domains.Classes.cs | 8 + .../Entity.Continuous.Factorial.Classes.cs | 27 ++ .../Serialization/Entity.Serialization.cs | 1 + .../Transformations/Matching/MatchPattern.cs | 1 + .../Docs/Contributing/WritingARule.md | 2 +- Sources/AngouriMath/Docs/Usage/Syntax.md | 9 +- .../EquationSolver/InvertNode.Classes.cs | 8 + ...aluation.Continuous.Arithmetics.Classes.cs | 41 ++ .../Output/Latex/Latex.Arithmetics.Classes.cs | 7 + .../ToString/ToString.Arithmetics.Classes.cs | 9 + .../ToSympy/ToSympy.Arithmetics.Classes.cs | 6 + 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 | 24 + .../Convenience/HarmonicNumberTest.cs | 81 ++++ .../MissingFunctionNamesRefusedTest.cs | 5 +- .../Transformations/RuleAuthoringGuideTest.cs | 2 +- 29 files changed, 621 insertions(+), 365 deletions(-) create mode 100644 Sources/Tests/UnitTests/Convenience/HarmonicNumberTest.cs diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md index 5384e7496..9e004729b 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`, `productlog`, `harmonicnumber` and +is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog` and `forwarddifference`. Names that will not be functions, because what they mean differs between sources or is already written exactly, are refused with the spelling to use: `heaviside`, `unitstep`, `isprime`, `pochhammer`, `doublefactorial`, `factorial2`, `fractionalpart` and `quotient`. @@ -496,7 +496,7 @@ Each name without a bracket is still a variable, and short names such as `beta` | `"zeta(2)".ToEntity().Simplify()` | `2 * zeta` | throws `UnrecognizedFunctionParseException` | | `"isprime(7)".ToEntity()` | `isprime * 7` | throws `UnrecognizedFunctionParseException`: write `n in PP` | | `"heaviside(x)".ToEntity()` | `heaviside * x` | throws `UnrecognizedFunctionParseException`: write `iverson(x > 0)`, `iverson(x >= 0)` or `(1 + sgn(x))/2` | -| `"harmonicnumber(n, m)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` | +| `"hurwitzzeta(s, a)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` | ### The Möbius, divisor and prime-counting functions @@ -532,6 +532,19 @@ is ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). | `"hessian(x^3 y^2, [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `[[6 * x * y ^ 2, 6 * x ^ 2 * y], [6 * x ^ 2 * y, 2 * x ^ 3]]` | | `"jacobian(x y, {x, y})".ToEntity()` | throws `UnhandledParseException` | throws `InvalidArgumentParseException`: a set has no order for the columns | +### The harmonic numbers + +**Not silent: `harmonicnumber(n)` and `harmonicnumber(n, m)` are the harmonic numbers, where the one was a product and the +other a parse error.** They are `1 + 1/2^m + ... + 1/n^m` for a whole `n >= 0`, exact for a rational `m`, and +`ζ(m) - ζ(m, n + 1)` elsewhere, as Mathematica's `HarmonicNumber` is: `ψ(n + 1) - ψ(1)` for `m = 1`, evaluated numerically +through `digamma` and `polygamma` for a whole `m >= 1`. A negative integer `n` has no value but for a whole `m <= 0` +([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). + +| Input | Was (2.6.0) | Now | +|---|---|---| +| `"harmonicnumber(4)".ToEntity().Simplify()` | `4 * harmonicnumber` | `25/12` | +| `"harmonicnumber(n, 2)".ToEntity()` | throws `UnhandledParseException` | `harmonicnumber(n, 2)` | + ### 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 cca217cfc..4e5862c8a 100644 --- a/Sources/.editorconfig +++ b/Sources/.editorconfig @@ -829,3 +829,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed [Tests/UnitTests/Convenience/CatalanNumberTest.cs] file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n + +[Tests/UnitTests/Convenience/HarmonicNumberTest.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 92e9c2218..2457c98c8 100644 --- a/Sources/AngouriMath/Convenience/MathS.cs +++ b/Sources/AngouriMath/Convenience/MathS.cs @@ -1387,6 +1387,14 @@ public static Entity VectorLength(Matrix v) [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Entity Binomial(Entity n, Entity k) => new Binomialf(n, k); + /// The harmonic number H_n = 1 + 1/2 + ... + 1/n + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity HarmonicNumber(Entity n) => new HarmonicNumberf(n, Integer.One); + + /// The generalized harmonic number H_n^(m) = 1 + 1/2^m + ... + 1/n^m + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity HarmonicNumber(Entity n, Entity m) => new HarmonicNumberf(n, m); + /// The Catalan number C_n = binomial(2n, n) / (n + 1) /// https://github.com/asc-community/AngouriMath/issues/2182 public static Entity CatalanNumber(Entity n) => new CatalanNumberf(n); diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g index 63f13c58d..0a4158223 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g @@ -627,6 +627,7 @@ atom returns[Entity value] | 'binomial(' args = function_arguments ')' { Assert("binomial", 2, $args.list.Count); $value = MathS.Binomial($args.list[0], $args.list[1]); } | 'multinomial(' args = function_arguments ')' { $value = ParsingHelpers.Multinomial($args.list); } | 'catalannumber(' args = function_arguments ')' { Assert("catalannumber", 1, $args.list.Count); $value = MathS.CatalanNumber($args.list[0]); } + | 'harmonicnumber(' args = function_arguments ')' { if (Assert("harmonicnumber", (2, 1), $args.list.Count)) $value = MathS.HarmonicNumber($args.list[0], $args.list[1]); else $value = MathS.HarmonicNumber($args.list[0]); } | 'fallingfactorial(' args = function_arguments ')' { Assert("fallingfactorial", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); } | 'factorialpower(' args = function_arguments ')' { Assert("factorialpower", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); } | 'risingfactorial(' args = function_arguments ')' { Assert("risingfactorial", 2, $args.list.Count); $value = MathS.RisingFactorial($args.list[0], $args.list[1]); } @@ -695,7 +696,6 @@ atom returns[Entity value] | '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"); } - | 'harmonicnumber(' args = function_arguments ')' { $value = NotImplementedFunction("harmonicnumber", "harmonic numbers yet"); } | 'forwarddifference(' args = function_arguments ')' { $value = NotImplementedFunction("forwarddifference", "forward difference yet"); } /* Names that will not be functions, refused with the spelling to use: what they mean is ambiguous between sources, or is already written exactly another way. */ diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp index f152344ea..391f8f3c9 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp @@ -176,6 +176,7 @@ null 'binomial(' 'multinomial(' 'catalannumber(' +'harmonicnumber(' 'fallingfactorial(' 'factorialpower(' 'risingfactorial(' @@ -215,7 +216,6 @@ null 'hurwitzzeta(' 'lambertw(' 'productlog(' -'harmonicnumber(' 'forwarddifference(' 'heaviside(' 'unitstep(' diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens index 8a98f19da..c48e79814 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens @@ -411,46 +411,46 @@ WS=237 'binomial('=174 'multinomial('=175 'catalannumber('=176 -'fallingfactorial('=177 -'factorialpower('=178 -'risingfactorial('=179 -'iverson('=180 -'aleph('=181 -'erf('=182 -'erfc('=183 -'erfi('=184 -'Ei('=185 -'li('=186 -'polygamma('=187 -'digamma('=188 -'Si('=189 -'Ci('=190 -'Shi('=191 -'Chi('=192 -'det('=193 -'transpose('=194 -'dot('=195 -'cross('=196 -'laplacian('=197 -'jacobian('=198 -'hessian('=199 -'resultant('=200 -'conjugate('=201 -'conj('=202 -'arg('=203 -'Re('=204 -'Im('=205 -'re('=206 -'real('=207 -'im('=208 -'imag('=209 -'trunc('=210 -'zeta('=211 -'riemannzeta('=212 -'hurwitzzeta('=213 -'lambertw('=214 -'productlog('=215 -'harmonicnumber('=216 +'harmonicnumber('=177 +'fallingfactorial('=178 +'factorialpower('=179 +'risingfactorial('=180 +'iverson('=181 +'aleph('=182 +'erf('=183 +'erfc('=184 +'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 +'jacobian('=199 +'hessian('=200 +'resultant('=201 +'conjugate('=202 +'conj('=203 +'arg('=204 +'Re('=205 +'Im('=206 +'re('=207 +'real('=208 +'im('=209 +'imag('=210 +'trunc('=211 +'zeta('=212 +'riemannzeta('=213 +'hurwitzzeta('=214 +'lambertw('=215 +'productlog('=216 'forwarddifference('=217 'heaviside('=218 'unitstep('=219 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs index ffda6f694..e44a51a39 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs @@ -158,15 +158,15 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu "'card('", "'powerset('", "'union('", "'intersection('", "'complement('", "'image('", "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", - "'multinomial('", "'catalannumber('", "'fallingfactorial('", "'factorialpower('", - "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", - "'Ei('", "'li('", "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", - "'Chi('", "'det('", "'transpose('", "'dot('", "'cross('", "'laplacian('", - "'jacobian('", "'hessian('", "'resultant('", "'conjugate('", "'conj('", - "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", - "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'lambertw('", "'productlog('", - "'harmonicnumber('", "'forwarddifference('", "'heaviside('", "'unitstep('", - "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", + "'multinomial('", "'catalannumber('", "'harmonicnumber('", "'fallingfactorial('", + "'factorialpower('", "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", + "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", + "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", + "'cross('", "'laplacian('", "'jacobian('", "'hessian('", "'resultant('", + "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", "'re('", "'real('", + "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", "'hurwitzzeta('", + "'lambertw('", "'productlog('", "'forwarddifference('", "'heaviside('", + "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" }; @@ -344,32 +344,32 @@ static AngouriMathLexer() { 1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,175, 1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175, 1,175,1,175,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,176, - 1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,177,1,177,1,177,1,177, + 1,176,1,176,1,176,1,176,1,176,1,176,1,177,1,177,1,177,1,177,1,177,1,177, 1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177, 1,178,1,178,1,178,1,178,1,178,1,178,1,178,1,178,1,178,1,178,1,178,1,178, - 1,178,1,178,1,178,1,178,1,178,1,179,1,179,1,179,1,179,1,179,1,179,1,179, - 1,179,1,179,1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,181,1,181,1,181, - 1,181,1,181,1,182,1,182,1,182,1,182,1,182,1,182,1,183,1,183,1,183,1,183, - 1,183,1,183,1,184,1,184,1,184,1,184,1,185,1,185,1,185,1,185,1,186,1,186, - 1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,187,1,187,1,187, - 1,187,1,187,1,187,1,187,1,187,1,187,1,188,1,188,1,188,1,188,1,189,1,189, - 1,189,1,189,1,190,1,190,1,190,1,190,1,190,1,191,1,191,1,191,1,191,1,191, - 1,192,1,192,1,192,1,192,1,192,1,193,1,193,1,193,1,193,1,193,1,193,1,193, - 1,193,1,193,1,193,1,193,1,194,1,194,1,194,1,194,1,194,1,195,1,195,1,195, - 1,195,1,195,1,195,1,195,1,196,1,196,1,196,1,196,1,196,1,196,1,196,1,196, - 1,196,1,196,1,196,1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,197, - 1,197,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,199,1,199, - 1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,200,1,200,1,200, - 1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,201,1,201,1,201,1,201, - 1,201,1,201,1,202,1,202,1,202,1,202,1,202,1,203,1,203,1,203,1,203,1,204, - 1,204,1,204,1,204,1,205,1,205,1,205,1,205,1,206,1,206,1,206,1,206,1,206, - 1,206,1,207,1,207,1,207,1,207,1,208,1,208,1,208,1,208,1,208,1,208,1,209, - 1,209,1,209,1,209,1,209,1,209,1,209,1,210,1,210,1,210,1,210,1,210,1,210, - 1,211,1,211,1,211,1,211,1,211,1,211,1,211,1,211,1,211,1,211,1,211,1,211, - 1,211,1,212,1,212,1,212,1,212,1,212,1,212,1,212,1,212,1,212,1,212,1,212, - 1,212,1,212,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213,1,213, - 1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214,1,214, - 1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215, + 1,178,1,178,1,178,1,178,1,179,1,179,1,179,1,179,1,179,1,179,1,179,1,179, + 1,179,1,179,1,179,1,179,1,179,1,179,1,179,1,179,1,179,1,180,1,180,1,180, + 1,180,1,180,1,180,1,180,1,180,1,180,1,181,1,181,1,181,1,181,1,181,1,181, + 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, + 1,192,1,192,1,192,1,192,1,193,1,193,1,193,1,193,1,193,1,194,1,194,1,194, + 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, + 1,198,1,198,1,198,1,198,1,198,1,199,1,199,1,199,1,199,1,199,1,199,1,199, + 1,199,1,199,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200, + 1,200,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201,1,201, + 1,202,1,202,1,202,1,202,1,202,1,202,1,203,1,203,1,203,1,203,1,203,1,204, + 1,204,1,204,1,204,1,205,1,205,1,205,1,205,1,206,1,206,1,206,1,206,1,207, + 1,207,1,207,1,207,1,207,1,207,1,208,1,208,1,208,1,208,1,209,1,209,1,209, + 1,209,1,209,1,209,1,210,1,210,1,210,1,210,1,210,1,210,1,210,1,211,1,211, + 1,211,1,211,1,211,1,211,1,212,1,212,1,212,1,212,1,212,1,212,1,212,1,212, + 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, + 1,214,1,214,1,214,1,214,1,215,1,215,1,215,1,215,1,215,1,215,1,215,1,215, 1,215,1,215,1,215,1,215,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216, 1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,216,1,217, 1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,217,1,218,1,218, @@ -511,16 +511,16 @@ static AngouriMathLexer() { 1446,1,0,0,0,325,1453,1,0,0,0,327,1463,1,0,0,0,329,1470,1,0,0,0,331,1476, 1,0,0,0,333,1485,1,0,0,0,335,1492,1,0,0,0,337,1497,1,0,0,0,339,1502,1, 0,0,0,341,1510,1,0,0,0,343,1518,1,0,0,0,345,1523,1,0,0,0,347,1528,1,0, - 0,0,349,1538,1,0,0,0,351,1551,1,0,0,0,353,1566,1,0,0,0,355,1584,1,0,0, - 0,357,1600,1,0,0,0,359,1617,1,0,0,0,361,1626,1,0,0,0,363,1633,1,0,0,0, - 365,1638,1,0,0,0,367,1644,1,0,0,0,369,1650,1,0,0,0,371,1654,1,0,0,0,373, - 1658,1,0,0,0,375,1669,1,0,0,0,377,1678,1,0,0,0,379,1682,1,0,0,0,381,1686, - 1,0,0,0,383,1691,1,0,0,0,385,1696,1,0,0,0,387,1701,1,0,0,0,389,1712,1, - 0,0,0,391,1717,1,0,0,0,393,1724,1,0,0,0,395,1735,1,0,0,0,397,1745,1,0, - 0,0,399,1754,1,0,0,0,401,1765,1,0,0,0,403,1776,1,0,0,0,405,1782,1,0,0, - 0,407,1787,1,0,0,0,409,1791,1,0,0,0,411,1795,1,0,0,0,413,1799,1,0,0,0, - 415,1805,1,0,0,0,417,1809,1,0,0,0,419,1815,1,0,0,0,421,1822,1,0,0,0,423, - 1828,1,0,0,0,425,1841,1,0,0,0,427,1854,1,0,0,0,429,1864,1,0,0,0,431,1876, + 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, + 0,0,399,1761,1,0,0,0,401,1770,1,0,0,0,403,1781,1,0,0,0,405,1792,1,0,0, + 0,407,1798,1,0,0,0,409,1803,1,0,0,0,411,1807,1,0,0,0,413,1811,1,0,0,0, + 415,1815,1,0,0,0,417,1821,1,0,0,0,419,1825,1,0,0,0,421,1831,1,0,0,0,423, + 1838,1,0,0,0,425,1844,1,0,0,0,427,1857,1,0,0,0,429,1870,1,0,0,0,431,1880, 1,0,0,0,433,1892,1,0,0,0,435,1911,1,0,0,0,437,1922,1,0,0,0,439,1932,1, 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, @@ -806,185 +806,184 @@ static AngouriMathLexer() { 108,0,0,1556,1557,5,97,0,0,1557,1558,5,110,0,0,1558,1559,5,110,0,0,1559, 1560,5,117,0,0,1560,1561,5,109,0,0,1561,1562,5,98,0,0,1562,1563,5,101, 0,0,1563,1564,5,114,0,0,1564,1565,5,40,0,0,1565,352,1,0,0,0,1566,1567, - 5,102,0,0,1567,1568,5,97,0,0,1568,1569,5,108,0,0,1569,1570,5,108,0,0,1570, - 1571,5,105,0,0,1571,1572,5,110,0,0,1572,1573,5,103,0,0,1573,1574,5,102, - 0,0,1574,1575,5,97,0,0,1575,1576,5,99,0,0,1576,1577,5,116,0,0,1577,1578, - 5,111,0,0,1578,1579,5,114,0,0,1579,1580,5,105,0,0,1580,1581,5,97,0,0,1581, - 1582,5,108,0,0,1582,1583,5,40,0,0,1583,354,1,0,0,0,1584,1585,5,102,0,0, - 1585,1586,5,97,0,0,1586,1587,5,99,0,0,1587,1588,5,116,0,0,1588,1589,5, - 111,0,0,1589,1590,5,114,0,0,1590,1591,5,105,0,0,1591,1592,5,97,0,0,1592, - 1593,5,108,0,0,1593,1594,5,112,0,0,1594,1595,5,111,0,0,1595,1596,5,119, - 0,0,1596,1597,5,101,0,0,1597,1598,5,114,0,0,1598,1599,5,40,0,0,1599,356, - 1,0,0,0,1600,1601,5,114,0,0,1601,1602,5,105,0,0,1602,1603,5,115,0,0,1603, - 1604,5,105,0,0,1604,1605,5,110,0,0,1605,1606,5,103,0,0,1606,1607,5,102, - 0,0,1607,1608,5,97,0,0,1608,1609,5,99,0,0,1609,1610,5,116,0,0,1610,1611, - 5,111,0,0,1611,1612,5,114,0,0,1612,1613,5,105,0,0,1613,1614,5,97,0,0,1614, - 1615,5,108,0,0,1615,1616,5,40,0,0,1616,358,1,0,0,0,1617,1618,5,105,0,0, - 1618,1619,5,118,0,0,1619,1620,5,101,0,0,1620,1621,5,114,0,0,1621,1622, - 5,115,0,0,1622,1623,5,111,0,0,1623,1624,5,110,0,0,1624,1625,5,40,0,0,1625, - 360,1,0,0,0,1626,1627,5,97,0,0,1627,1628,5,108,0,0,1628,1629,5,101,0,0, - 1629,1630,5,112,0,0,1630,1631,5,104,0,0,1631,1632,5,40,0,0,1632,362,1, - 0,0,0,1633,1634,5,101,0,0,1634,1635,5,114,0,0,1635,1636,5,102,0,0,1636, - 1637,5,40,0,0,1637,364,1,0,0,0,1638,1639,5,101,0,0,1639,1640,5,114,0,0, - 1640,1641,5,102,0,0,1641,1642,5,99,0,0,1642,1643,5,40,0,0,1643,366,1,0, - 0,0,1644,1645,5,101,0,0,1645,1646,5,114,0,0,1646,1647,5,102,0,0,1647,1648, - 5,105,0,0,1648,1649,5,40,0,0,1649,368,1,0,0,0,1650,1651,5,69,0,0,1651, - 1652,5,105,0,0,1652,1653,5,40,0,0,1653,370,1,0,0,0,1654,1655,5,108,0,0, - 1655,1656,5,105,0,0,1656,1657,5,40,0,0,1657,372,1,0,0,0,1658,1659,5,112, - 0,0,1659,1660,5,111,0,0,1660,1661,5,108,0,0,1661,1662,5,121,0,0,1662,1663, - 5,103,0,0,1663,1664,5,97,0,0,1664,1665,5,109,0,0,1665,1666,5,109,0,0,1666, - 1667,5,97,0,0,1667,1668,5,40,0,0,1668,374,1,0,0,0,1669,1670,5,100,0,0, - 1670,1671,5,105,0,0,1671,1672,5,103,0,0,1672,1673,5,97,0,0,1673,1674,5, - 109,0,0,1674,1675,5,109,0,0,1675,1676,5,97,0,0,1676,1677,5,40,0,0,1677, - 376,1,0,0,0,1678,1679,5,83,0,0,1679,1680,5,105,0,0,1680,1681,5,40,0,0, - 1681,378,1,0,0,0,1682,1683,5,67,0,0,1683,1684,5,105,0,0,1684,1685,5,40, - 0,0,1685,380,1,0,0,0,1686,1687,5,83,0,0,1687,1688,5,104,0,0,1688,1689, - 5,105,0,0,1689,1690,5,40,0,0,1690,382,1,0,0,0,1691,1692,5,67,0,0,1692, - 1693,5,104,0,0,1693,1694,5,105,0,0,1694,1695,5,40,0,0,1695,384,1,0,0,0, - 1696,1697,5,100,0,0,1697,1698,5,101,0,0,1698,1699,5,116,0,0,1699,1700, - 5,40,0,0,1700,386,1,0,0,0,1701,1702,5,116,0,0,1702,1703,5,114,0,0,1703, - 1704,5,97,0,0,1704,1705,5,110,0,0,1705,1706,5,115,0,0,1706,1707,5,112, - 0,0,1707,1708,5,111,0,0,1708,1709,5,115,0,0,1709,1710,5,101,0,0,1710,1711, - 5,40,0,0,1711,388,1,0,0,0,1712,1713,5,100,0,0,1713,1714,5,111,0,0,1714, - 1715,5,116,0,0,1715,1716,5,40,0,0,1716,390,1,0,0,0,1717,1718,5,99,0,0, - 1718,1719,5,114,0,0,1719,1720,5,111,0,0,1720,1721,5,115,0,0,1721,1722, - 5,115,0,0,1722,1723,5,40,0,0,1723,392,1,0,0,0,1724,1725,5,108,0,0,1725, - 1726,5,97,0,0,1726,1727,5,112,0,0,1727,1728,5,108,0,0,1728,1729,5,97,0, - 0,1729,1730,5,99,0,0,1730,1731,5,105,0,0,1731,1732,5,97,0,0,1732,1733, - 5,110,0,0,1733,1734,5,40,0,0,1734,394,1,0,0,0,1735,1736,5,106,0,0,1736, - 1737,5,97,0,0,1737,1738,5,99,0,0,1738,1739,5,111,0,0,1739,1740,5,98,0, - 0,1740,1741,5,105,0,0,1741,1742,5,97,0,0,1742,1743,5,110,0,0,1743,1744, - 5,40,0,0,1744,396,1,0,0,0,1745,1746,5,104,0,0,1746,1747,5,101,0,0,1747, - 1748,5,115,0,0,1748,1749,5,115,0,0,1749,1750,5,105,0,0,1750,1751,5,97, - 0,0,1751,1752,5,110,0,0,1752,1753,5,40,0,0,1753,398,1,0,0,0,1754,1755, - 5,114,0,0,1755,1756,5,101,0,0,1756,1757,5,115,0,0,1757,1758,5,117,0,0, - 1758,1759,5,108,0,0,1759,1760,5,116,0,0,1760,1761,5,97,0,0,1761,1762,5, - 110,0,0,1762,1763,5,116,0,0,1763,1764,5,40,0,0,1764,400,1,0,0,0,1765,1766, - 5,99,0,0,1766,1767,5,111,0,0,1767,1768,5,110,0,0,1768,1769,5,106,0,0,1769, - 1770,5,117,0,0,1770,1771,5,103,0,0,1771,1772,5,97,0,0,1772,1773,5,116, - 0,0,1773,1774,5,101,0,0,1774,1775,5,40,0,0,1775,402,1,0,0,0,1776,1777, - 5,99,0,0,1777,1778,5,111,0,0,1778,1779,5,110,0,0,1779,1780,5,106,0,0,1780, - 1781,5,40,0,0,1781,404,1,0,0,0,1782,1783,5,97,0,0,1783,1784,5,114,0,0, - 1784,1785,5,103,0,0,1785,1786,5,40,0,0,1786,406,1,0,0,0,1787,1788,5,82, - 0,0,1788,1789,5,101,0,0,1789,1790,5,40,0,0,1790,408,1,0,0,0,1791,1792, - 5,73,0,0,1792,1793,5,109,0,0,1793,1794,5,40,0,0,1794,410,1,0,0,0,1795, - 1796,5,114,0,0,1796,1797,5,101,0,0,1797,1798,5,40,0,0,1798,412,1,0,0,0, - 1799,1800,5,114,0,0,1800,1801,5,101,0,0,1801,1802,5,97,0,0,1802,1803,5, - 108,0,0,1803,1804,5,40,0,0,1804,414,1,0,0,0,1805,1806,5,105,0,0,1806,1807, - 5,109,0,0,1807,1808,5,40,0,0,1808,416,1,0,0,0,1809,1810,5,105,0,0,1810, - 1811,5,109,0,0,1811,1812,5,97,0,0,1812,1813,5,103,0,0,1813,1814,5,40,0, - 0,1814,418,1,0,0,0,1815,1816,5,116,0,0,1816,1817,5,114,0,0,1817,1818,5, - 117,0,0,1818,1819,5,110,0,0,1819,1820,5,99,0,0,1820,1821,5,40,0,0,1821, - 420,1,0,0,0,1822,1823,5,122,0,0,1823,1824,5,101,0,0,1824,1825,5,116,0, - 0,1825,1826,5,97,0,0,1826,1827,5,40,0,0,1827,422,1,0,0,0,1828,1829,5,114, - 0,0,1829,1830,5,105,0,0,1830,1831,5,101,0,0,1831,1832,5,109,0,0,1832,1833, - 5,97,0,0,1833,1834,5,110,0,0,1834,1835,5,110,0,0,1835,1836,5,122,0,0,1836, - 1837,5,101,0,0,1837,1838,5,116,0,0,1838,1839,5,97,0,0,1839,1840,5,40,0, - 0,1840,424,1,0,0,0,1841,1842,5,104,0,0,1842,1843,5,117,0,0,1843,1844,5, - 114,0,0,1844,1845,5,119,0,0,1845,1846,5,105,0,0,1846,1847,5,116,0,0,1847, - 1848,5,122,0,0,1848,1849,5,122,0,0,1849,1850,5,101,0,0,1850,1851,5,116, - 0,0,1851,1852,5,97,0,0,1852,1853,5,40,0,0,1853,426,1,0,0,0,1854,1855,5, - 108,0,0,1855,1856,5,97,0,0,1856,1857,5,109,0,0,1857,1858,5,98,0,0,1858, - 1859,5,101,0,0,1859,1860,5,114,0,0,1860,1861,5,116,0,0,1861,1862,5,119, - 0,0,1862,1863,5,40,0,0,1863,428,1,0,0,0,1864,1865,5,112,0,0,1865,1866, - 5,114,0,0,1866,1867,5,111,0,0,1867,1868,5,100,0,0,1868,1869,5,117,0,0, - 1869,1870,5,99,0,0,1870,1871,5,116,0,0,1871,1872,5,108,0,0,1872,1873,5, - 111,0,0,1873,1874,5,103,0,0,1874,1875,5,40,0,0,1875,430,1,0,0,0,1876,1877, - 5,104,0,0,1877,1878,5,97,0,0,1878,1879,5,114,0,0,1879,1880,5,109,0,0,1880, - 1881,5,111,0,0,1881,1882,5,110,0,0,1882,1883,5,105,0,0,1883,1884,5,99, - 0,0,1884,1885,5,110,0,0,1885,1886,5,117,0,0,1886,1887,5,109,0,0,1887,1888, - 5,98,0,0,1888,1889,5,101,0,0,1889,1890,5,114,0,0,1890,1891,5,40,0,0,1891, - 432,1,0,0,0,1892,1893,5,102,0,0,1893,1894,5,111,0,0,1894,1895,5,114,0, - 0,1895,1896,5,119,0,0,1896,1897,5,97,0,0,1897,1898,5,114,0,0,1898,1899, - 5,100,0,0,1899,1900,5,100,0,0,1900,1901,5,105,0,0,1901,1902,5,102,0,0, - 1902,1903,5,102,0,0,1903,1904,5,101,0,0,1904,1905,5,114,0,0,1905,1906, - 5,101,0,0,1906,1907,5,110,0,0,1907,1908,5,99,0,0,1908,1909,5,101,0,0,1909, - 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, - 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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, + 106,0,0,1752,1753,5,97,0,0,1753,1754,5,99,0,0,1754,1755,5,111,0,0,1755, + 1756,5,98,0,0,1756,1757,5,105,0,0,1757,1758,5,97,0,0,1758,1759,5,110,0, + 0,1759,1760,5,40,0,0,1760,398,1,0,0,0,1761,1762,5,104,0,0,1762,1763,5, + 101,0,0,1763,1764,5,115,0,0,1764,1765,5,115,0,0,1765,1766,5,105,0,0,1766, + 1767,5,97,0,0,1767,1768,5,110,0,0,1768,1769,5,40,0,0,1769,400,1,0,0,0, + 1770,1771,5,114,0,0,1771,1772,5,101,0,0,1772,1773,5,115,0,0,1773,1774, + 5,117,0,0,1774,1775,5,108,0,0,1775,1776,5,116,0,0,1776,1777,5,97,0,0,1777, + 1778,5,110,0,0,1778,1779,5,116,0,0,1779,1780,5,40,0,0,1780,402,1,0,0,0, + 1781,1782,5,99,0,0,1782,1783,5,111,0,0,1783,1784,5,110,0,0,1784,1785,5, + 106,0,0,1785,1786,5,117,0,0,1786,1787,5,103,0,0,1787,1788,5,97,0,0,1788, + 1789,5,116,0,0,1789,1790,5,101,0,0,1790,1791,5,40,0,0,1791,404,1,0,0,0, + 1792,1793,5,99,0,0,1793,1794,5,111,0,0,1794,1795,5,110,0,0,1795,1796,5, + 106,0,0,1796,1797,5,40,0,0,1797,406,1,0,0,0,1798,1799,5,97,0,0,1799,1800, + 5,114,0,0,1800,1801,5,103,0,0,1801,1802,5,40,0,0,1802,408,1,0,0,0,1803, + 1804,5,82,0,0,1804,1805,5,101,0,0,1805,1806,5,40,0,0,1806,410,1,0,0,0, + 1807,1808,5,73,0,0,1808,1809,5,109,0,0,1809,1810,5,40,0,0,1810,412,1,0, + 0,0,1811,1812,5,114,0,0,1812,1813,5,101,0,0,1813,1814,5,40,0,0,1814,414, + 1,0,0,0,1815,1816,5,114,0,0,1816,1817,5,101,0,0,1817,1818,5,97,0,0,1818, + 1819,5,108,0,0,1819,1820,5,40,0,0,1820,416,1,0,0,0,1821,1822,5,105,0,0, + 1822,1823,5,109,0,0,1823,1824,5,40,0,0,1824,418,1,0,0,0,1825,1826,5,105, + 0,0,1826,1827,5,109,0,0,1827,1828,5,97,0,0,1828,1829,5,103,0,0,1829,1830, + 5,40,0,0,1830,420,1,0,0,0,1831,1832,5,116,0,0,1832,1833,5,114,0,0,1833, + 1834,5,117,0,0,1834,1835,5,110,0,0,1835,1836,5,99,0,0,1836,1837,5,40,0, + 0,1837,422,1,0,0,0,1838,1839,5,122,0,0,1839,1840,5,101,0,0,1840,1841,5, + 116,0,0,1841,1842,5,97,0,0,1842,1843,5,40,0,0,1843,424,1,0,0,0,1844,1845, + 5,114,0,0,1845,1846,5,105,0,0,1846,1847,5,101,0,0,1847,1848,5,109,0,0, + 1848,1849,5,97,0,0,1849,1850,5,110,0,0,1850,1851,5,110,0,0,1851,1852,5, + 122,0,0,1852,1853,5,101,0,0,1853,1854,5,116,0,0,1854,1855,5,97,0,0,1855, + 1856,5,40,0,0,1856,426,1,0,0,0,1857,1858,5,104,0,0,1858,1859,5,117,0,0, + 1859,1860,5,114,0,0,1860,1861,5,119,0,0,1861,1862,5,105,0,0,1862,1863, + 5,116,0,0,1863,1864,5,122,0,0,1864,1865,5,122,0,0,1865,1866,5,101,0,0, + 1866,1867,5,116,0,0,1867,1868,5,97,0,0,1868,1869,5,40,0,0,1869,428,1,0, + 0,0,1870,1871,5,108,0,0,1871,1872,5,97,0,0,1872,1873,5,109,0,0,1873,1874, + 5,98,0,0,1874,1875,5,101,0,0,1875,1876,5,114,0,0,1876,1877,5,116,0,0,1877, + 1878,5,119,0,0,1878,1879,5,40,0,0,1879,430,1,0,0,0,1880,1881,5,112,0,0, + 1881,1882,5,114,0,0,1882,1883,5,111,0,0,1883,1884,5,100,0,0,1884,1885, + 5,117,0,0,1885,1886,5,99,0,0,1886,1887,5,116,0,0,1887,1888,5,108,0,0,1888, + 1889,5,111,0,0,1889,1890,5,103,0,0,1890,1891,5,40,0,0,1891,432,1,0,0,0, + 1892,1893,5,102,0,0,1893,1894,5,111,0,0,1894,1895,5,114,0,0,1895,1896, + 5,119,0,0,1896,1897,5,97,0,0,1897,1898,5,114,0,0,1898,1899,5,100,0,0,1899, + 1900,5,100,0,0,1900,1901,5,105,0,0,1901,1902,5,102,0,0,1902,1903,5,102, + 0,0,1903,1904,5,101,0,0,1904,1905,5,114,0,0,1905,1906,5,101,0,0,1906,1907, + 5,110,0,0,1907,1908,5,99,0,0,1908,1909,5,101,0,0,1909,1910,5,40,0,0,1910, + 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, + 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 aa565818c..42abde5c4 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp @@ -176,6 +176,7 @@ null 'binomial(' 'multinomial(' 'catalannumber(' +'harmonicnumber(' 'fallingfactorial(' 'factorialpower(' 'risingfactorial(' @@ -215,7 +216,6 @@ null 'hurwitzzeta(' 'lambertw(' 'productlog(' -'harmonicnumber(' 'forwarddifference(' 'heaviside(' 'unitstep(' @@ -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, 1, 32, 1, 32, 1, 33, 1, 33, 1, 33, 1, 33, 1, 34, 1, 34, 1, 34, 1, 34, 1, 35, 1, 35, 1, 36, 1, 36, 1, 36, 1, 36, 1, 37, 1, 37, 1, 37, 1, 38, 1, 38, 1, 38, 1, 38, 1, 38, 1, 38, 1, 38, 1, 38, 1, 39, 1, 39, 1, 39, 1, 40, 1, 40, 1, 40, 1, 40, 1, 40, 1, 40, 1, 40, 1, 40, 1, 40, 1, 41, 1, 41, 1, 41, 1, 42, 1, 42, 1, 43, 1, 43, 1, 43, 1, 43, 1, 43, 1, 43, 1, 43, 1, 44, 1, 44, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 46, 1, 46, 1, 46, 1, 47, 1, 47, 1, 47, 1, 47, 1, 47, 1, 47, 1, 47, 1, 48, 1, 48, 1, 49, 1, 49, 1, 50, 1, 50, 1, 51, 1, 51, 1, 51, 1, 51, 1, 52, 1, 52, 1, 52, 1, 52, 1, 53, 1, 53, 1, 53, 1, 54, 1, 54, 1, 54, 1, 55, 1, 55, 1, 56, 1, 56, 1, 57, 1, 57, 1, 57, 1, 58, 1, 58, 1, 59, 1, 59, 1, 60, 1, 60, 1, 61, 1, 61, 1, 61, 1, 61, 1, 61, 1, 62, 1, 62, 1, 62, 1, 62, 1, 62, 1, 62, 1, 62, 1, 63, 1, 63, 1, 63, 1, 63, 1, 63, 1, 63, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 65, 1, 65, 1, 65, 1, 65, 1, 65, 1, 65, 1, 66, 1, 66, 1, 66, 1, 66, 1, 66, 1, 66, 1, 67, 1, 67, 1, 67, 1, 67, 1, 67, 1, 68, 1, 68, 1, 68, 1, 68, 1, 69, 1, 69, 1, 69, 1, 69, 1, 69, 1, 70, 1, 70, 1, 70, 1, 70, 1, 70, 1, 71, 1, 71, 1, 71, 1, 71, 1, 71, 1, 72, 1, 72, 1, 72, 1, 72, 1, 72, 1, 73, 1, 73, 1, 73, 1, 73, 1, 73, 1, 73, 1, 73, 1, 74, 1, 74, 1, 74, 1, 74, 1, 74, 1, 75, 1, 75, 1, 75, 1, 75, 1, 75, 1, 76, 1, 76, 1, 76, 1, 76, 1, 76, 1, 76, 1, 76, 1, 77, 1, 77, 1, 77, 1, 77, 1, 77, 1, 78, 1, 78, 1, 78, 1, 78, 1, 78, 1, 78, 1, 78, 1, 78, 1, 79, 1, 79, 1, 79, 1, 79, 1, 79, 1, 79, 1, 79, 1, 79, 1, 80, 1, 80, 1, 80, 1, 80, 1, 80, 1, 80, 1, 80, 1, 80, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 81, 1, 82, 1, 82, 1, 82, 1, 82, 1, 82, 1, 82, 1, 82, 1, 82, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 83, 1, 84, 1, 84, 1, 84, 1, 84, 1, 84, 1, 84, 1, 84, 1, 84, 1, 85, 1, 85, 1, 85, 1, 85, 1, 85, 1, 85, 1, 86, 1, 86, 1, 86, 1, 86, 1, 86, 1, 86, 1, 87, 1, 87, 1, 87, 1, 87, 1, 87, 1, 87, 1, 88, 1, 88, 1, 88, 1, 88, 1, 88, 1, 88, 1, 89, 1, 89, 1, 89, 1, 89, 1, 89, 1, 89, 1, 89, 1, 89, 1, 90, 1, 90, 1, 90, 1, 90, 1, 90, 1, 90, 1, 91, 1, 91, 1, 91, 1, 91, 1, 91, 1, 91, 1, 91, 1, 91, 1, 92, 1, 92, 1, 92, 1, 92, 1, 92, 1, 92, 1, 93, 1, 93, 1, 93, 1, 93, 1, 93, 1, 93, 1, 93, 1, 93, 1, 94, 1, 94, 1, 94, 1, 94, 1, 94, 1, 94, 1, 95, 1, 95, 1, 95, 1, 95, 1, 96, 1, 96, 1, 96, 1, 96, 1, 96, 1, 96, 1, 97, 1, 97, 1, 97, 1, 97, 1, 98, 1, 98, 1, 98, 1, 98, 1, 98, 1, 98, 1, 99, 1, 99, 1, 99, 1, 99, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 101, 1, 101, 1, 101, 1, 101, 1, 101, 1, 101, 1, 102, 1, 102, 1, 102, 1, 102, 1, 102, 1, 103, 1, 103, 1, 103, 1, 103, 1, 103, 1, 103, 1, 104, 1, 104, 1, 104, 1, 104, 1, 104, 1, 105, 1, 105, 1, 105, 1, 105, 1, 105, 1, 105, 1, 105, 1, 105, 1, 106, 1, 106, 1, 106, 1, 106, 1, 106, 1, 106, 1, 107, 1, 107, 1, 107, 1, 107, 1, 107, 1, 107, 1, 107, 1, 108, 1, 108, 1, 108, 1, 108, 1, 108, 1, 108, 1, 108, 1, 108, 1, 109, 1, 109, 1, 109, 1, 109, 1, 109, 1, 109, 1, 110, 1, 110, 1, 110, 1, 110, 1, 110, 1, 110, 1, 110, 1, 110, 1, 110, 1, 111, 1, 111, 1, 111, 1, 111, 1, 111, 1, 111, 1, 111, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 113, 1, 113, 1, 113, 1, 113, 1, 113, 1, 113, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 115, 1, 115, 1, 115, 1, 115, 1, 115, 1, 115, 1, 115, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 117, 1, 117, 1, 117, 1, 117, 1, 117, 1, 117, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 121, 1, 121, 1, 121, 1, 121, 1, 121, 1, 121, 1, 121, 1, 121, 1, 121, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 122, 1, 123, 1, 123, 1, 123, 1, 123, 1, 123, 1, 123, 1, 123, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 124, 1, 125, 1, 125, 1, 125, 1, 125, 1, 125, 1, 125, 1, 125, 1, 126, 1, 126, 1, 126, 1, 126, 1, 126, 1, 126, 1, 126, 1, 126, 1, 127, 1, 127, 1, 127, 1, 127, 1, 127, 1, 127, 1, 127, 1, 128, 1, 128, 1, 128, 1, 128, 1, 128, 1, 128, 1, 128, 1, 128, 1, 128, 1, 129, 1, 129, 1, 129, 1, 129, 1, 129, 1, 129, 1, 129, 1, 129, 1, 129, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 130, 1, 131, 1, 131, 1, 131, 1, 131, 1, 131, 1, 131, 1, 131, 1, 131, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 132, 1, 133, 1, 133, 1, 133, 1, 133, 1, 133, 1, 133, 1, 133, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 134, 1, 135, 1, 135, 1, 135, 1, 135, 1, 135, 1, 135, 1, 135, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 136, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 137, 1, 138, 1, 138, 1, 138, 1, 138, 1, 138, 1, 138, 1, 138, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 1, 139, 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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] \ No newline at end of file diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens index 8a98f19da..c48e79814 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens @@ -411,46 +411,46 @@ WS=237 'binomial('=174 'multinomial('=175 'catalannumber('=176 -'fallingfactorial('=177 -'factorialpower('=178 -'risingfactorial('=179 -'iverson('=180 -'aleph('=181 -'erf('=182 -'erfc('=183 -'erfi('=184 -'Ei('=185 -'li('=186 -'polygamma('=187 -'digamma('=188 -'Si('=189 -'Ci('=190 -'Shi('=191 -'Chi('=192 -'det('=193 -'transpose('=194 -'dot('=195 -'cross('=196 -'laplacian('=197 -'jacobian('=198 -'hessian('=199 -'resultant('=200 -'conjugate('=201 -'conj('=202 -'arg('=203 -'Re('=204 -'Im('=205 -'re('=206 -'real('=207 -'im('=208 -'imag('=209 -'trunc('=210 -'zeta('=211 -'riemannzeta('=212 -'hurwitzzeta('=213 -'lambertw('=214 -'productlog('=215 -'harmonicnumber('=216 +'harmonicnumber('=177 +'fallingfactorial('=178 +'factorialpower('=179 +'risingfactorial('=180 +'iverson('=181 +'aleph('=182 +'erf('=183 +'erfc('=184 +'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 +'jacobian('=199 +'hessian('=200 +'resultant('=201 +'conjugate('=202 +'conj('=203 +'arg('=204 +'Re('=205 +'Im('=206 +'re('=207 +'real('=208 +'im('=209 +'imag('=210 +'trunc('=211 +'zeta('=212 +'riemannzeta('=213 +'hurwitzzeta('=214 +'lambertw('=215 +'productlog('=216 'forwarddifference('=217 'heaviside('=218 'unitstep('=219 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs index b856182c6..2325acc20 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs @@ -130,15 +130,15 @@ public const int "'card('", "'powerset('", "'union('", "'intersection('", "'complement('", "'image('", "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", - "'multinomial('", "'catalannumber('", "'fallingfactorial('", "'factorialpower('", - "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", - "'Ei('", "'li('", "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", - "'Chi('", "'det('", "'transpose('", "'dot('", "'cross('", "'laplacian('", - "'jacobian('", "'hessian('", "'resultant('", "'conjugate('", "'conj('", - "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", - "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'lambertw('", "'productlog('", - "'harmonicnumber('", "'forwarddifference('", "'heaviside('", "'unitstep('", - "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", + "'multinomial('", "'catalannumber('", "'harmonicnumber('", "'fallingfactorial('", + "'factorialpower('", "'risingfactorial('", "'iverson('", "'aleph('", "'erf('", + "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", + "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", + "'cross('", "'laplacian('", "'jacobian('", "'hessian('", "'resultant('", + "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", "'re('", "'real('", + "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", "'hurwitzzeta('", + "'lambertw('", "'productlog('", "'forwarddifference('", "'heaviside('", + "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" }; @@ -5138,7 +5138,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1099; Match(T__32); - Assert("fallingfactorial", 2, _localctx.args.list.Count); _localctx.value = MathS.FallingFactorial(_localctx.args.list[0], _localctx.args.list[1]); + if (Assert("harmonicnumber", (2, 1), _localctx.args.list.Count)) _localctx.value = MathS.HarmonicNumber(_localctx.args.list[0], _localctx.args.list[1]); else _localctx.value = MathS.HarmonicNumber(_localctx.args.list[0]); } break; case 135: @@ -5150,7 +5150,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1104; Match(T__32); - Assert("factorialpower", 2, _localctx.args.list.Count); _localctx.value = MathS.FallingFactorial(_localctx.args.list[0], _localctx.args.list[1]); + Assert("fallingfactorial", 2, _localctx.args.list.Count); _localctx.value = MathS.FallingFactorial(_localctx.args.list[0], _localctx.args.list[1]); } break; case 136: @@ -5162,7 +5162,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1109; Match(T__32); - Assert("risingfactorial", 2, _localctx.args.list.Count); _localctx.value = MathS.RisingFactorial(_localctx.args.list[0], _localctx.args.list[1]); + Assert("factorialpower", 2, _localctx.args.list.Count); _localctx.value = MathS.FallingFactorial(_localctx.args.list[0], _localctx.args.list[1]); } break; case 137: @@ -5174,7 +5174,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1114; Match(T__32); - Assert("iverson", 1, _localctx.args.list.Count); _localctx.value = MathS.Iverson(_localctx.args.list[0]); + Assert("risingfactorial", 2, _localctx.args.list.Count); _localctx.value = MathS.RisingFactorial(_localctx.args.list[0], _localctx.args.list[1]); } break; case 138: @@ -5186,7 +5186,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1119; Match(T__32); - Assert("aleph", 1, _localctx.args.list.Count); _localctx.value = MathS.Aleph(_localctx.args.list[0]); + Assert("iverson", 1, _localctx.args.list.Count); _localctx.value = MathS.Iverson(_localctx.args.list[0]); } break; case 139: @@ -5198,7 +5198,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1124; Match(T__32); - Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]); + Assert("aleph", 1, _localctx.args.list.Count); _localctx.value = MathS.Aleph(_localctx.args.list[0]); } break; case 140: @@ -5210,7 +5210,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1129; Match(T__32); - Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]); + Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]); } break; case 141: @@ -5222,7 +5222,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1134; Match(T__32); - Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]); + Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]); } break; case 142: @@ -5234,7 +5234,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1139; Match(T__32); - Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]); + Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]); } break; case 143: @@ -5246,7 +5246,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1144; Match(T__32); - Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]); + Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]); } break; case 144: @@ -5258,7 +5258,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1149; Match(T__32); - Assert("polygamma", 2, _localctx.args.list.Count); _localctx.value = MathS.Polygamma(_localctx.args.list[0], _localctx.args.list[1]); + Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]); } break; case 145: @@ -5270,7 +5270,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1154; Match(T__32); - Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_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 146: @@ -5282,7 +5282,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1159; Match(T__32); - Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); + Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_localctx.args.list[0]); } break; case 147: @@ -5294,7 +5294,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1164; Match(T__32); - Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); + Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); } break; case 148: @@ -5306,7 +5306,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1169; Match(T__32); - Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); + Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); } break; case 149: @@ -5318,7 +5318,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1174; Match(T__32); - Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); + Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); } break; case 150: @@ -5330,7 +5330,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1179; Match(T__32); - Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_localctx.args.list[0]); + Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); } break; case 151: @@ -5342,7 +5342,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1184; Match(T__32); - Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); + Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_localctx.args.list[0]); } break; case 152: @@ -5354,7 +5354,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1189; Match(T__32); - Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_localctx.args.list[0], _localctx.args.list[1]); + Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); } break; case 153: @@ -5366,7 +5366,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1194; Match(T__32); - Assert("cross", (1, 2), _localctx.args.list.Count); _localctx.value = ParsingHelpers.Cross(_localctx.args.list); + Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_localctx.args.list[0], _localctx.args.list[1]); } break; case 154: @@ -5378,7 +5378,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1199; Match(T__32); - Assert("laplacian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Laplacian(_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 155: @@ -5390,7 +5390,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1204; 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 156: @@ -5402,7 +5402,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1209; Match(T__32); - Assert("hessian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Hessian(_localctx.args.list[0], _localctx.args.list[1]); + Assert("jacobian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Jacobian(_localctx.args.list[0], _localctx.args.list[1]); } break; case 157: @@ -5414,7 +5414,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1214; 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("hessian", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Hessian(_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("conjugate", 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 159: @@ -5438,7 +5438,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1224; Match(T__32); - Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); + Assert("conjugate", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 160: @@ -5450,7 +5450,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1229; Match(T__32); - Assert("arg", 1, _localctx.args.list.Count); _localctx.value = MathS.Arg(_localctx.args.list[0]); + Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 161: @@ -5462,7 +5462,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1234; Match(T__32); - Assert("Re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("arg", 1, _localctx.args.list.Count); _localctx.value = MathS.Arg(_localctx.args.list[0]); } break; case 162: @@ -5474,7 +5474,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1239; 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 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("Im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 164: @@ -5498,7 +5498,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1249; Match(T__32); - Assert("real", 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 165: @@ -5510,7 +5510,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1254; Match(T__32); - Assert("im", 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 166: @@ -5522,7 +5522,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1259; Match(T__32); - Assert("imag", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_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); - _localctx.value = NotImplementedFunction("trunc", "rounding functions"); + Assert("imag", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 168: @@ -5546,7 +5546,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1269; Match(T__32); - _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); + _localctx.value = NotImplementedFunction("trunc", "rounding functions"); } break; case 169: @@ -5558,7 +5558,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1274; Match(T__32); - _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); + _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); } break; case 170: @@ -5570,7 +5570,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1279; Match(T__32); - _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); + _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); } break; case 171: @@ -5582,7 +5582,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1284; Match(T__32); - _localctx.value = NotImplementedFunction("lambertw", "Lambert W function yet"); + _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); } break; case 172: @@ -5594,7 +5594,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1289; Match(T__32); - _localctx.value = NotImplementedFunction("productlog", "Lambert W function yet"); + _localctx.value = NotImplementedFunction("lambertw", "Lambert W function yet"); } break; case 173: @@ -5606,7 +5606,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1294; Match(T__32); - _localctx.value = NotImplementedFunction("harmonicnumber", "harmonic numbers yet"); + _localctx.value = NotImplementedFunction("productlog", "Lambert W function yet"); } break; case 174: diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs index 9a54c0e07..988920208 100644 --- a/Sources/AngouriMath/Core/Domains.Classes.cs +++ b/Sources/AngouriMath/Core/Domains.Classes.cs @@ -833,6 +833,14 @@ partial record CatalanNumberf internal override Domain DefaultCodomain => Domain.Complex; } + partial record HarmonicNumberf + { + /// + public override Domain Codomain { get; protected init; } = Domain.Complex; + /// + internal override Domain DefaultCodomain => Domain.Complex; + } + partial record Phif { /// diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Factorial.Classes.cs b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Factorial.Classes.cs index 72be6e0f3..d9e2d399d 100644 --- a/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Factorial.Classes.cs +++ b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Factorial.Classes.cs @@ -87,6 +87,33 @@ private Binomialf New(Entity upper, Entity lower) => protected override Entity[] InitDirectChildren() => new[] { Upper, Lower }; } + /// + /// The harmonic number harmonicnumber(n), H_n = 1 + 1/2 + ... + 1/n, and the + /// generalized one harmonicnumber(n, m), H_n^(m) = 1 + 1/2^m + ... + 1/n^m. + /// + /// + /// Off the whole numbers it is ζ(m) - ζ(m, n + 1), as Mathematica's HarmonicNumber + /// is: ψ(n + 1) - ψ(1) for m = 1, which is 2 - 2 ln 2 at n = 1/2. It + /// has no value at a negative integer n, a pole of the Hurwitz zeta function, but for a + /// whole order m <= 0, where it is a polynomial in n. + /// https://github.com/asc-community/AngouriMath/issues/2182 + /// + public sealed partial record HarmonicNumberf(Entity Argument, Entity Order) : Function, IBinaryNode + { + /// + public Entity NodeFirstChild => Argument; + + /// + public Entity NodeSecondChild => Order; + + internal HarmonicNumberf New(Entity argument, Entity order) => + ReferenceEquals(Argument, argument) && ReferenceEquals(Order, order) ? this : new(argument, order) { Codomain = Codomain }; + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func), Order.Replace(func))); + /// + protected override Entity[] InitDirectChildren() => new[] { Argument, Order }; + } + /// /// The Catalan number catalannumber(n), C_n = binomial(2n, n) / (n + 1): 1, 1, 2, 5, /// 14 from n = 0, the number of ways to bracket a product of n + 1 factors. diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs index 2d2cc2add..b1c0563ea 100644 --- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs +++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs @@ -79,6 +79,7 @@ [EntityJsonConverter] partial record Number } [EntityJsonConverter] partial record Orf; [EntityJsonConverter] partial record Phif; + [EntityJsonConverter] partial record HarmonicNumberf; [EntityJsonConverter] partial record CatalanNumberf; [EntityJsonConverter] partial record Mobiusf; [EntityJsonConverter] partial record DivisorSigmaf; diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs index eab071bdf..290797cec 100644 --- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs +++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs @@ -495,6 +495,7 @@ internal abstract bool ETryBuild( [typeof(Entity.Factorialf)] = (1, static c => new Entity.Factorialf(c[0])), [typeof(Entity.Phif)] = (1, static c => new Entity.Phif(c[0])), [typeof(Entity.Mobiusf)] = (1, static c => new Entity.Mobiusf(c[0])), + [typeof(Entity.HarmonicNumberf)] = (2, static c => new Entity.HarmonicNumberf(c[0], c[1])), [typeof(Entity.CatalanNumberf)] = (1, static c => new Entity.CatalanNumberf(c[0])), [typeof(Entity.PrimeNuf)] = (1, static c => new Entity.PrimeNuf(c[0])), [typeof(Entity.PrimeOmegaf)] = (1, static c => new Entity.PrimeOmegaf(c[0])), diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md index a451db8df..14410ac05 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 **76** such types. +pattern used as a **replacement** must be one the library can construct: there are **77** 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 0280c764b..bd162262b 100644 --- a/Sources/AngouriMath/Docs/Usage/Syntax.md +++ b/Sources/AngouriMath/Docs/Usage/Syntax.md @@ -354,6 +354,13 @@ drawn `\operatorname{C}_{n}`. Off the whole numbers it is `4^n Γ(n + 1/2) / ( `catalan` is, so `catalannumber(-1)` is `-1/2`, it is `0` at every whole number below that, and a negative half-integer is a pole ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). +**Harmonic numbers** — `harmonicnumber(n)`, `1 + 1/2 + ... + 1/n`, and `harmonicnumber(n, m)`, +`1 + 1/2^m + ... + 1/n^m`, drawn `\operatorname{H}_{n}` and `\operatorname{H}_{n}^{(m)}`: +`harmonicnumber(4)` is `25/12`. Off the whole numbers they are `ζ(m) - ζ(m, n + 1)`, as Mathematica's +`HarmonicNumber` is, evaluated numerically for a whole `m >= 1`: `harmonicnumber(1/2)` is `2 - 2 ln 2`. +A negative integer `n` has no value but for a whole `m <= 0` +([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). + **Iverson bracket** — `iverson(P)`. `1` where the statement `P` holds and `0` where it does not, which is how a count is written as a sum: `sum(iverson(k divides 12), k, 1, 12)` is `6`, the number of divisors of `12`. A statement that is not decided keeps the node, which prints as `[\![P]\!]` in @@ -525,7 +532,7 @@ 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` `harmonicnumber` +`hurwitzzeta` `lambertw` `productlog` `forwarddifference`. 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 diff --git a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs index 8cc48a324..ff6406412 100644 --- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs +++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs @@ -964,6 +964,14 @@ partial record CatalanNumberf => null; } + partial record HarmonicNumberf + { + // A harmonic number takes a value at arguments no list here gives. Left unsolved rather + // than answered with none. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + partial record Phif { // We can't easily calculate (compute) all solutions there are for this function 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 41ac629c6..b5399996b 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 @@ -699,6 +699,47 @@ Complex value when !isExact private const int LargestIndex = 1000; } + public partial record HarmonicNumberf + { + // No value at a negative integer n, a pole of ζ(m, n + 1), but for a whole order m <= 0, + // where it is a polynomial in n. + private protected override Entity IntrinsicCondition => + !(Argument.In(MathS.Sets.Z) & Argument < 0) | (Order.In(MathS.Sets.Z) & Order <= 0); + + /// + protected override Entity InnerSimplify(bool isExact) => + ExpandOnTwoArguments(Argument, Order, + (n, m) => (n, m) switch + { + // A whole n >= 0: the sum, exact for a rational order. + (Integer { EInteger: var whole }, Number order) when whole.Sign >= 0 && whole.CompareTo(PeterO.Numbers.EInteger.FromInt32(LongestSum)) <= 0 + => Sum(whole.ToInt32Checked(), order).InnerSimplified(isExact), + (Integer { EInteger.Sign: >= 0 }, Number) => null, + (Integer { EInteger.Sign: < 0 }, Number order) when order is not Integer { EInteger.Sign: <= 0 } => MathS.NaN, + // Elsewhere, numerically: ψ(n + 1) - ψ(1) for m = 1, and through the polygamma + // function for a whole m >= 2, as ζ(m) - ζ(m, n + 1) is. + (Complex value, Integer { EInteger: var order }) when !isExact && order.Sign > 0 && order.CompareTo(PeterO.Numbers.EInteger.FromInt32(LargestOrder)) <= 0 + => Numerically(value, order.ToInt32Checked()), + _ => null + }, + (@this, n, m) => ((HarmonicNumberf)@this).New(n, m), isExact); + + private static Entity Sum(int n, Number order) + => n == 0 ? Integer.Zero + : Enumerable.Range(1, n).Select(k => MathS.Pow(Integer.Create(k), -order)).Aggregate((sum, term) => sum + term); + + // (-1)^m / (m - 1)! (ψ^(m - 1)(1) - ψ^(m - 1)(n + 1)), which is ψ(n + 1) - ψ(1) at m = 1. + private static Entity Numerically(Complex n, int m) + => (MathS.Pow(-1, m) / MathS.Factorial(m - 1) + * (MathS.Polygamma(m - 1, Integer.One) - MathS.Polygamma(m - 1, n + 1))).Evaled; + + /// How long a sum is built before the node is left as written. + private const int LongestSum = 10000; + + /// The largest order evaluated through the polygamma function. + private const int LargestOrder = 64; + } + 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 3362c87f4..e460ffd55 100644 --- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs @@ -434,6 +434,13 @@ partial record CatalanNumberf private protected override string LatexizeNode() => $@"\operatorname{{C}}_{{{Argument.Latexize()}}}"; } + partial record HarmonicNumberf + { + /// + private protected override string LatexizeNode() + => Order == Integer.One ? $@"\operatorname{{H}}_{{{Argument.Latexize()}}}" : $@"\operatorname{{H}}_{{{Argument.Latexize()}}}^{{\left({Order.Latexize()}\right)}}"; + } + partial record Phif { /// diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs index 2bad09f48..f28fc478d 100644 --- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs @@ -97,6 +97,15 @@ partial record CatalanNumberf public override string ToString() => Stringize(); } + partial record HarmonicNumberf + { + /// + private protected override string StringizeNode() + => Order == Integer.One ? $@"harmonicnumber({Argument.Stringize()})" : $@"harmonicnumber({Argument.Stringize()}, {Order.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + partial record Phif { /// diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs index de3b9f707..cba300dfb 100644 --- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs @@ -276,6 +276,12 @@ public partial record CatalanNumberf internal override string ToSymPy() => $"sympy.catalan({Argument.ToSymPy()})"; } + public partial record HarmonicNumberf + { + internal override string ToSymPy() + => Order == Integer.One ? $"sympy.harmonic({Argument.ToSymPy()})" : $"sympy.harmonic({Argument.ToSymPy()}, {Order.ToSymPy()})"; + } + public partial record Phif { internal override string ToSymPy() => $"sympy.totient({Argument.ToSymPy()})"; diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs index 25c842bec..9b50e4930 100644 --- a/Sources/AngouriMath/Functions/Substitute.cs +++ b/Sources/AngouriMath/Functions/Substitute.cs @@ -547,6 +547,13 @@ public override Entity Substitute(Entity x, Entity value) => this == x ? value : New(Argument.Substitute(x, value)); } + partial record HarmonicNumberf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value), Order.Substitute(x, value)); + } + partial record Phif { /// diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs index 2662def63..f2fcc9b57 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs @@ -181,6 +181,11 @@ public partial record CatalanNumberf private protected override string SortHashName(SortLevel level) => "catalannumberf_"; } + public partial record HarmonicNumberf + { + private protected override string SortHashName(SortLevel level) => "harmonicnumberf_"; + } + public partial record Binomialf { private protected override string SortHashName(SortLevel level) => "binomialf_"; diff --git a/Sources/MCP/AngouriMath.Mcp/Resources.cs b/Sources/MCP/AngouriMath.Mcp/Resources.cs index d2bc14ba6..f98838188 100644 --- a/Sources/MCP/AngouriMath.Mcp/Resources.cs +++ b/Sources/MCP/AngouriMath.Mcp/Resources.cs @@ -99,7 +99,7 @@ that every response returns. - `gamma factorial binomial phi prime valuation`, the postfix `n!` and `n!!` (the double factorial, not `(n!)!`), `fallingfactorial(x, n)` (also `factorialpower`) and `risingfactorial(x, n)`, the factorial powers, `multinomial(k_1, ..., k_m)`, which is `(k_1 + ... + k_m)! / (k_1! ... k_m!)` once parsed, - `catalannumber(n)`, the Catalan numbers, + `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 @@ -120,7 +120,7 @@ apply lambda` | You might write | Reality | |---|---| | `arcsinh(x)` | **refused.** The inverse hyperbolics are area functions: write `arsinh`, `asinh` or `arsh` | - | `trunc`, `zeta`, `lambertw`, `harmonicnumber` and other long names of functions to come | refused by name — not yet in the library | + | `trunc`, `zeta`, `lambertw` 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 bd3dee8b4..ebed4dc62 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 harmonic = MathS.FromString("harmonicnumber(x, 2)"); + CheckClose("harmonicnumber(x, 2) at x = 4", At(harmonic, "x", 4), 205.0 / 144); } private static void Simplification() diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt index b29e06d1c..3d6457d02 100644 --- a/Sources/Tests/UnitTests/Common/PublicApi.txt +++ b/Sources/Tests/UnitTests/Common/PublicApi.txt @@ -1310,6 +1310,27 @@ AngouriMath.Entity+Greaterf.ToString() : System.String AngouriMath.Entity+Greaterf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Greaterf.op_Equality(AngouriMath.Entity+Greaterf, AngouriMath.Entity+Greaterf) : System.Boolean AngouriMath.Entity+Greaterf.op_Inequality(AngouriMath.Entity+Greaterf, AngouriMath.Entity+Greaterf) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.$() : AngouriMath.Entity+HarmonicNumberf +AngouriMath.Entity+HarmonicNumberf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+HarmonicNumberf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void +AngouriMath.Entity+HarmonicNumberf.EqualityContract { } : System.Type +AngouriMath.Entity+HarmonicNumberf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.Equals(AngouriMath.Entity+HarmonicNumberf) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.GetHashCode() : System.Int32 +AngouriMath.Entity+HarmonicNumberf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+HarmonicNumberf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.NodeFirstChild { } : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.NodeSecondChild { } : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.Order { } : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+HarmonicNumberf.ToString() : System.String +AngouriMath.Entity+HarmonicNumberf.ctor(AngouriMath.Entity, AngouriMath.Entity) +AngouriMath.Entity+HarmonicNumberf.op_Equality(AngouriMath.Entity+HarmonicNumberf, AngouriMath.Entity+HarmonicNumberf) : System.Boolean +AngouriMath.Entity+HarmonicNumberf.op_Inequality(AngouriMath.Entity+HarmonicNumberf, AngouriMath.Entity+HarmonicNumberf) : System.Boolean AngouriMath.Entity+Imf.$() : AngouriMath.Entity+Imf AngouriMath.Entity+Imf.Argument { } : AngouriMath.Entity AngouriMath.Entity+Imf.Codomain { } : AngouriMath.Core.Domain @@ -3515,6 +3536,8 @@ AngouriMath.MathS.Gamma(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Gcd(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.GreaterOrEqualThan(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.GreaterThan(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.HarmonicNumber(AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.HarmonicNumber(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.I_1 : AngouriMath.Entity+Matrix AngouriMath.MathS.I_2 : AngouriMath.Entity+Matrix AngouriMath.MathS.I_3 : AngouriMath.Entity+Matrix @@ -3714,6 +3737,7 @@ class AngouriMath.Entity+Function class AngouriMath.Entity+Gcdf class AngouriMath.Entity+GreaterOrEqualf class AngouriMath.Entity+Greaterf +class AngouriMath.Entity+HarmonicNumberf class AngouriMath.Entity+Imf class AngouriMath.Entity+Impliesf class AngouriMath.Entity+IncompleteGammaf diff --git a/Sources/Tests/UnitTests/Convenience/HarmonicNumberTest.cs b/Sources/Tests/UnitTests/Convenience/HarmonicNumberTest.cs new file mode 100644 index 000000000..4d44e33c7 --- /dev/null +++ b/Sources/Tests/UnitTests/Convenience/HarmonicNumberTest.cs @@ -0,0 +1,81 @@ +// +// 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 harmonic numbers, 1 + 1/2^m + ... + 1/n^m on the whole numbers and + /// ζ(m) - ζ(m, n + 1) off them, as Mathematica's HarmonicNumber. The name was refused. + /// #2182 + /// + [Trait("Area", "Convenience")] + public sealed class HarmonicNumberTest + { + [Theory] + [InlineData("harmonicnumber(0)", "0")] + [InlineData("harmonicnumber(1)", "1")] + [InlineData("harmonicnumber(4)", "25/12")] + [InlineData("harmonicnumber(4, 2)", "205/144")] + [InlineData("harmonicnumber(3, 0)", "3")] + [InlineData("harmonicnumber(3, -1)", "6")] + [InlineData("harmonicnumber(2, 1/2)", "1 + 1/sqrt(2)")] + public void ItIsTheSumOnTheWholeNumbers(string written, string expected) + => Assert.Equal(Number.Integer.Zero, (written.ToEntity() - expected.ToEntity()).Simplify()); + + /// A negative integer is a pole of ζ(m, n + 1), for an order that is not a whole number <= 0. + [Theory] + [InlineData("harmonicnumber(-1)")] + [InlineData("harmonicnumber(-3, 2)")] + public void ItHasNoValueAtANegativeInteger(string written) + => Assert.Equal(MathS.NaN, written.ToEntity().InnerSimplified); + + /// Against mpmath, to 30 digits: H(1/2) = 2 - 2 ln 2, H(-1/2) = -2 ln 2. + [Theory] + [InlineData("harmonicnumber(1/2)", "0.613705638880109381165535757084")] + [InlineData("harmonicnumber(5/2)", "1.68037230554677604783220242375")] + [InlineData("harmonicnumber(-1/2)", "-1.38629436111989061883446424292")] + [InlineData("harmonicnumber(1/2, 2)", "0.710131866303547127055169666708")] + public void OffTheWholeNumbersItIsThePolygammaForm(string written, string expected) + { + var value = Assert.IsAssignableFrom(written.ToEntity().EvalNumerical()); + var difference = value.EDecimal.Subtract(EDecimal.FromString(expected)).Abs(); + Assert.True(difference.CompareTo(EDecimal.FromString("1e-25")) < 0, value.Stringize()); + } + + /// H(n) - H(n - 1) = 1/n, at n = 7/3 as well as at a whole n. + [Fact] + public void ConsecutiveHarmonicNumbersDifferByAReciprocal() + { + var at = (Entity)Number.Rational.Create(7, 3); + var difference = (MathS.HarmonicNumber(at) - MathS.HarmonicNumber(at - 1)).EvalNumerical(); + var expected = (1 / at).EvalNumerical(); + Assert.True(((Number.Real)(difference - expected).EvalNumerical()).EDecimal.Abs().CompareTo(EDecimal.FromString("1e-25")) < 0, difference.Stringize()); + } + + [Fact] + public void ASymbolKeepsTheNode() + => Assert.IsType("harmonicnumber(n)".ToEntity().InnerSimplified); + + [Theory] + [InlineData("harmonicnumber(n)", "harmonicnumber(n)", @"\operatorname{H}_{n}", "sympy.harmonic(n)")] + [InlineData("harmonicnumber(n, 2)", "harmonicnumber(n, 2)", @"\operatorname{H}_{n}^{\left(2\right)}", "sympy.harmonic(n, 2)")] + public void ItIsWrittenAsASubscriptedH(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 45d44a3c5..b6038ebb3 100644 --- a/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs +++ b/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs @@ -37,8 +37,8 @@ public sealed class MissingFunctionNamesRefusedTest // names that will not be functions, refused with the spelling to use: // 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 and catalannumber were - // among them until they were implemented, in the same issue. + // fallingfactorial, factorialpower and risingfactorial, multinomial, catalannumber and + // harmonicnumber were among them until they were implemented, in the same issue. [Theory] [InlineData("trunc(x)")] [InlineData("zeta(s)")] @@ -47,7 +47,6 @@ public sealed class MissingFunctionNamesRefusedTest [InlineData("hurwitzzeta(s, a)")] [InlineData("lambertw(x)")] [InlineData("productlog(x)")] - [InlineData("harmonicnumber(n)")] [InlineData("forwarddifference(f, k)")] [InlineData("heaviside(x)")] [InlineData("unitstep(x)")] diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs index 7b811500c..2fe9072cc 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(76, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); + => Stated(77, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); [Fact] public void ReplacementAPatternOrCode()