From 0348dfc77a2116f836745c0aff0bdfd14b11ed41 Mon Sep 17 00:00:00 2001 From: Rafael Vuijk Date: Wed, 28 Oct 2026 19:55:37 +0000 Subject: [PATCH] =?UTF-8?q?The=20M=C3=B6bius,=20divisor=20and=20prime-coun?= =?UTF-8?q?ting=20functions?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit mobius(n), divisorsigma(k, n), primenu(n), primeomega(n) and primepi(x) were reserved by name in built by MathS.NumberTheory.Mobius, DivisorSigma, PrimeNu, PrimeOmega and PrimePi. mobius is the Möbius function: 0 where the square of a prime divides n, (-1)^k for a product of k distinct primes, and 1 at 1. moebiusmu, Mathematica's name for it, reads as the same function. divisorsigma(k, n) is sigma_k(n), the order first as the notation and Mathematica's DivisorSigma[k, n] write it. It is the product over the prime powers p^a in n of 1 + p^k + ... + p^(ak), exact for a rational order and an expression for any other number: divisorsigma(1/2, 4) is 3 + sqrt(2). primenu and primeomega are omega and Omega, the number of prime factors without and with multiplicity. The four are defined on the positive integers, NaN at any other number, and left as written for an expression. The factorisation is trial division up to a million. That settles every number up to 10^12, and a larger one whose part left after the small primes is below 10^12; anything else is left as written, and 2^100 is factorised at once. primepi(x) counts the primes up to floor(x) by a sieve over the odd numbers, for a real x up to ten million (94 ms there), and is NaN off the real line. They print by name, draw as \operatorname{\mu}(n), \operatorname{\sigma}_k(n), \operatorname{\omega}(n), \operatorname{\Omega}(n) and \operatorname{\pi}(x), so that a Greek letter is not read back as a variable times a bracket, and export to SymPy's mobius, divisor_sigma(n, k), primenu, primeomega and primepi. Their codomains are the integers, and the non-negative integers for the three counts. The MCP server's syntax document and the syntax page name them, and the native smoke test evaluates them. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura --- BREAKING-CHANGES.md | 22 +- Sources/.editorconfig | 3 + Sources/AngouriMath/Convenience/MathS.cs | 20 + Sources/AngouriMath/Core/Antlr/AngouriMath.g | 12 +- .../AngouriMath/Core/Antlr/AngouriMath.interp | 12 +- .../AngouriMath/Core/Antlr/AngouriMath.tokens | 114 ++-- .../Core/Antlr/AngouriMathLexer.cs | 603 +++++++++--------- .../Core/Antlr/AngouriMathLexer.interp | 14 +- .../Core/Antlr/AngouriMathLexer.tokens | 114 ++-- .../Core/Antlr/AngouriMathParser.cs | 132 ++-- Sources/AngouriMath/Core/CostModel.cs | 1 + Sources/AngouriMath/Core/Domains.Classes.cs | 45 ++ .../Discrete/Entity.Discrete.Classes.cs | 101 +++ .../Serialization/Entity.Serialization.cs | 5 + .../Transformations/Matching/MatchPattern.cs | 5 + .../Docs/Contributing/WritingARule.md | 2 +- Sources/AngouriMath/Docs/Usage/Syntax.md | 17 +- .../EquationSolver/InvertNode.Classes.cs | 35 + .../Evaluation.Discrete.Classes.cs | 86 +++ .../Functions/NumberTheory/Primes.cs | 85 +++ .../Output/Latex/Latex.Arithmetics.Classes.cs | 32 + .../ToString/ToString.Arithmetics.Classes.cs | 40 ++ .../ToSympy/ToSympy.Arithmetics.Classes.cs | 26 + Sources/AngouriMath/Functions/Substitute.cs | 35 + .../Functions/TreeAnalyzer/RealValued.cs | 7 +- .../Functions/TreeAnalyzer/Sort.Classes.cs | 25 + Sources/MCP/AngouriMath.Mcp/Resources.cs | 6 +- Sources/Tests/AotSmokeTest/Program.cs | 7 + Sources/Tests/UnitTests/Common/PublicApi.txt | 107 ++++ .../MissingFunctionNamesRefusedTest.cs | 10 +- .../Convenience/NumberTheoryFunctionsTest.cs | 137 ++++ .../Transformations/RuleAuthoringGuideTest.cs | 2 +- 32 files changed, 1339 insertions(+), 523 deletions(-) create mode 100644 Sources/Tests/UnitTests/Convenience/NumberTheoryFunctionsTest.cs diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md index 88096c1d9..e225fe99c 100644 --- a/BREAKING-CHANGES.md +++ b/BREAKING-CHANGES.md @@ -440,8 +440,7 @@ 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`, `mobius`, `moebiusmu`, `divisorsigma`, `primenu`, -`primeomega`, `primepi`, `harmonicnumber`, `catalannumber`, `multinomial`, `fallingfactorial`, `factorialpower`, +is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber`, `catalannumber`, `multinomial`, `fallingfactorial`, `factorialpower`, `risingfactorial`, `forwarddifference`, `laplacian`, `jacobian` and `hessian`. 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`. @@ -454,7 +453,24 @@ 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` | -| `"divisorsigma(k, n)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` | +| `"multinomial(a, b, c)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` | + +### The Möbius, divisor and prime-counting functions + +**Not silent: `mobius(n)`, `divisorsigma(k, n)`, `primenu(n)`, `primeomega(n)` and `primepi(x)` are now functions, where +they were read as products or, with two arguments, were a parse error.** `mobius` (also `moebiusmu`) is the Möbius +function μ, `divisorsigma(k, n)` the sum of the `k`-th powers of the divisors of `n`, and `primenu` and `primeomega` the +number of prime factors without and with multiplicity, ω and Ω. Each is defined on the positive integers and is `NaN` +elsewhere. `primepi(x)` counts the primes at most the real number `x` +([#2182](https://github.com/asc-community/AngouriMath/issues/2182)). + +| Input | Was (2.6.0) | Now | +|---|---|---| +| `"mobius(6)".ToEntity().Simplify()` | `6 * mobius` | `1` | +| `"divisorsigma(1, 6)".ToEntity().Simplify()` | throws `UnhandledParseException` | `12` | +| `"primeomega(12)".ToEntity().Simplify()` | `12 * primeomega` | `3` | +| `"primepi(10)".ToEntity().Evaled` | `primepi * 10` | `4` | +| `"mobius(0)".ToEntity().Simplify()` | `0` | `NaN` | ### A subscript may have a subscript **Not silent: what was a parse error is a name.** A name took at most one `_`, so `x_1_2` and `X_a_beta` were lexer diff --git a/Sources/.editorconfig b/Sources/.editorconfig index b7ff61155..83217939c 100644 --- a/Sources/.editorconfig +++ b/Sources/.editorconfig @@ -805,3 +805,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed [Tests/UnitTests/Common/SimplifyOverASymbolicCommonDenominatorTest.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/NumberTheoryFunctionsTest.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 33cfa5c2a..fb221da80 100644 --- a/Sources/AngouriMath/Convenience/MathS.cs +++ b/Sources/AngouriMath/Convenience/MathS.cs @@ -50,6 +50,26 @@ public static class NumberTheory /// public static Entity Phi(Entity integer) => new Phif(integer); + /// The Möbius function μ(n) of a positive integer + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity Mobius(Entity n) => new Mobiusf(n); + + /// The divisor function σ_k(n): the sum of the k-th powers of the divisors of n + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity DivisorSigma(Entity order, Entity n) => new DivisorSigmaf(order, n); + + /// The number of distinct prime factors ω(n) of a positive integer + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity PrimeNu(Entity n) => new PrimeNuf(n); + + /// The number of prime factors Ω(n) of a positive integer, with multiplicity + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity PrimeOmega(Entity n) => new PrimeOmegaf(n); + + /// The prime-counting function π(x): how many primes are at most x + /// https://github.com/asc-community/AngouriMath/issues/2182 + public static Entity PrimePi(Entity x) => new PrimePif(x); + /// /// The n-th prime, prime(n): prime(1) is 2 and /// prime(25) is 97. Defined on the positive whole numbers, and a diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g index 4b8ee1d56..45f70d93a 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g @@ -595,6 +595,12 @@ atom returns[Entity value] | 'phi(' args = function_arguments ')' { Assert("phi", 1, $args.list.Count); $value = MathS.NumberTheory.Phi($args.list[0]); } | 'prime(' args = function_arguments ')' { Assert("prime", 1, $args.list.Count); $value = MathS.NumberTheory.Prime($args.list[0]); } | 'valuation(' args = function_arguments ')' { Assert("valuation", 2, $args.list.Count); $value = MathS.NumberTheory.Valuation($args.list[0], $args.list[1]); } + | 'mobius(' args = function_arguments ')' { Assert("mobius", 1, $args.list.Count); $value = MathS.NumberTheory.Mobius($args.list[0]); } + | 'moebiusmu(' args = function_arguments ')' { Assert("moebiusmu", 1, $args.list.Count); $value = MathS.NumberTheory.Mobius($args.list[0]); } + | 'divisorsigma(' args = function_arguments ')' { Assert("divisorsigma", 2, $args.list.Count); $value = MathS.NumberTheory.DivisorSigma($args.list[0], $args.list[1]); } + | 'primenu(' args = function_arguments ')' { Assert("primenu", 1, $args.list.Count); $value = MathS.NumberTheory.PrimeNu($args.list[0]); } + | 'primeomega(' args = function_arguments ')' { Assert("primeomega", 1, $args.list.Count); $value = MathS.NumberTheory.PrimeOmega($args.list[0]); } + | 'primepi(' args = function_arguments ')' { Assert("primepi", 1, $args.list.Count); $value = MathS.NumberTheory.PrimePi($args.list[0]); } | 'card(' args = function_arguments ')' { Assert("card", 1, $args.list.Count); $value = MathS.Sets.Card($args.list[0]); } | 'powerset(' args = function_arguments ')' { Assert("powerset", 1, $args.list.Count); $value = MathS.Sets.PowerSet($args.list[0]); } | 'union(' args = function_arguments ')' { Assert("union", 2, $args.list.Count); $value = $args.list[1] is Entity.Set.Inf { Element: Variable } unionRange ? MathS.Sets.IndexedUnion($args.list[0], unionRange.Element, unionRange.SupSet) : throw new InvalidArgumentParseException("union expects its second argument to say which name ranges over which set, as in union(A_i, i in I)"); } @@ -681,12 +687,6 @@ 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"); } - | 'mobius(' args = function_arguments ')' { $value = NotImplementedFunction("mobius", "Mobius function yet"); } - | 'moebiusmu(' args = function_arguments ')' { $value = NotImplementedFunction("moebiusmu", "Mobius function yet"); } - | 'divisorsigma(' args = function_arguments ')' { $value = NotImplementedFunction("divisorsigma", "divisor function yet"); } - | 'primenu(' args = function_arguments ')' { $value = NotImplementedFunction("primenu", "count of distinct prime factors yet"); } - | 'primeomega(' args = function_arguments ')' { $value = NotImplementedFunction("primeomega", "count of prime factors with multiplicity yet"); } - | 'primepi(' args = function_arguments ')' { $value = NotImplementedFunction("primepi", "prime-counting function yet"); } | 'harmonicnumber(' args = function_arguments ')' { $value = NotImplementedFunction("harmonicnumber", "harmonic numbers yet"); } | 'catalannumber(' args = function_arguments ')' { $value = NotImplementedFunction("catalannumber", "Catalan numbers yet"); } | 'multinomial(' args = function_arguments ')' { $value = NotImplementedFunction("multinomial", "multinomial coefficients yet"); } diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp index 0bce64420..5ac2a10cf 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp @@ -150,6 +150,12 @@ null 'phi(' 'prime(' 'valuation(' +'mobius(' +'moebiusmu(' +'divisorsigma(' +'primenu(' +'primeomega(' +'primepi(' 'card(' 'powerset(' 'union(' @@ -201,12 +207,6 @@ null 'hurwitzzeta(' 'lambertw(' 'productlog(' -'mobius(' -'moebiusmu(' -'divisorsigma(' -'primenu(' -'primeomega(' -'primepi(' 'harmonicnumber(' 'catalannumber(' 'multinomial(' diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens index 62bf831c1..6813960bc 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens @@ -385,63 +385,63 @@ WS=237 'phi('=148 'prime('=149 'valuation('=150 -'card('=151 -'powerset('=152 -'union('=153 -'intersection('=154 -'complement('=155 -'image('=156 -'preimage('=157 -'floor('=158 -'ceil('=159 -'ceiling('=160 -'round('=161 -'min('=162 -'max('=163 -'argmax('=164 -'argmin('=165 -'gcd('=166 -'lcm('=167 -'binomial('=168 -'iverson('=169 -'aleph('=170 -'erf('=171 -'erfc('=172 -'erfi('=173 -'Ei('=174 -'li('=175 -'polygamma('=176 -'digamma('=177 -'Si('=178 -'Ci('=179 -'Shi('=180 -'Chi('=181 -'det('=182 -'transpose('=183 -'dot('=184 -'cross('=185 -'resultant('=186 -'conjugate('=187 -'conj('=188 -'arg('=189 -'Re('=190 -'Im('=191 -'re('=192 -'real('=193 -'im('=194 -'imag('=195 -'trunc('=196 -'zeta('=197 -'riemannzeta('=198 -'hurwitzzeta('=199 -'lambertw('=200 -'productlog('=201 -'mobius('=202 -'moebiusmu('=203 -'divisorsigma('=204 -'primenu('=205 -'primeomega('=206 -'primepi('=207 +'mobius('=151 +'moebiusmu('=152 +'divisorsigma('=153 +'primenu('=154 +'primeomega('=155 +'primepi('=156 +'card('=157 +'powerset('=158 +'union('=159 +'intersection('=160 +'complement('=161 +'image('=162 +'preimage('=163 +'floor('=164 +'ceil('=165 +'ceiling('=166 +'round('=167 +'min('=168 +'max('=169 +'argmax('=170 +'argmin('=171 +'gcd('=172 +'lcm('=173 +'binomial('=174 +'iverson('=175 +'aleph('=176 +'erf('=177 +'erfc('=178 +'erfi('=179 +'Ei('=180 +'li('=181 +'polygamma('=182 +'digamma('=183 +'Si('=184 +'Ci('=185 +'Shi('=186 +'Chi('=187 +'det('=188 +'transpose('=189 +'dot('=190 +'cross('=191 +'resultant('=192 +'conjugate('=193 +'conj('=194 +'arg('=195 +'Re('=196 +'Im('=197 +'re('=198 +'real('=199 +'im('=200 +'imag('=201 +'trunc('=202 +'zeta('=203 +'riemannzeta('=204 +'hurwitzzeta('=205 +'lambertw('=206 +'productlog('=207 'harmonicnumber('=208 'catalannumber('=209 'multinomial('=210 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs index 9a8c1c2af..c27a56182 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs @@ -153,20 +153,20 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu "'arcsech('", "'acosech('", "'arcosech('", "'arcsch('", "'arccosech('", "'acsch('", "'factorial('", "'gamma('", "'derivative('", "'integral('", "'limit('", "'limitleft('", "'limitright('", "'sum('", "'product('", "'signum('", - "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'card('", - "'powerset('", "'union('", "'intersection('", "'complement('", "'image('", - "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('", - "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", + "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'mobius('", + "'moebiusmu('", "'divisorsigma('", "'primenu('", "'primeomega('", "'primepi('", + "'card('", "'powerset('", "'union('", "'intersection('", "'complement('", + "'image('", "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", + "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", "'cross('", "'resultant('", "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'lambertw('", - "'productlog('", "'mobius('", "'moebiusmu('", "'divisorsigma('", "'primenu('", - "'primeomega('", "'primepi('", "'harmonicnumber('", "'catalannumber('", - "'multinomial('", "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", - "'forwarddifference('", "'laplacian('", "'jacobian('", "'hessian('", "'heaviside('", - "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", + "'productlog('", "'harmonicnumber('", "'catalannumber('", "'multinomial('", + "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", "'forwarddifference('", + "'laplacian('", "'jacobian('", "'hessian('", "'heaviside('", "'unitstep('", + "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" }; @@ -324,42 +324,42 @@ static AngouriMathLexer() { 1,145,1,145,1,145,1,145,1,145,1,145,1,146,1,146,1,146,1,146,1,146,1,147, 1,147,1,147,1,147,1,147,1,148,1,148,1,148,1,148,1,148,1,148,1,148,1,149, 1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,150,1,150, - 1,150,1,150,1,150,1,150,1,151,1,151,1,151,1,151,1,151,1,151,1,151,1,151, - 1,151,1,151,1,152,1,152,1,152,1,152,1,152,1,152,1,152,1,153,1,153,1,153, - 1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,154, - 1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,155, - 1,155,1,155,1,155,1,155,1,155,1,155,1,156,1,156,1,156,1,156,1,156,1,156, - 1,156,1,156,1,156,1,156,1,157,1,157,1,157,1,157,1,157,1,157,1,157,1,158, - 1,158,1,158,1,158,1,158,1,158,1,159,1,159,1,159,1,159,1,159,1,159,1,159, - 1,159,1,159,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,161,1,161,1,161, - 1,161,1,161,1,162,1,162,1,162,1,162,1,162,1,163,1,163,1,163,1,163,1,163, - 1,163,1,163,1,163,1,164,1,164,1,164,1,164,1,164,1,164,1,164,1,164,1,165, - 1,165,1,165,1,165,1,165,1,166,1,166,1,166,1,166,1,166,1,167,1,167,1,167, - 1,167,1,167,1,167,1,167,1,167,1,167,1,167,1,168,1,168,1,168,1,168,1,168, - 1,168,1,168,1,168,1,168,1,169,1,169,1,169,1,169,1,169,1,169,1,169,1,170, - 1,170,1,170,1,170,1,170,1,171,1,171,1,171,1,171,1,171,1,171,1,172,1,172, - 1,172,1,172,1,172,1,172,1,173,1,173,1,173,1,173,1,174,1,174,1,174,1,174, - 1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,176, - 1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,177,1,177,1,177,1,177, - 1,178,1,178,1,178,1,178,1,179,1,179,1,179,1,179,1,179,1,180,1,180,1,180, - 1,180,1,180,1,181,1,181,1,181,1,181,1,181,1,182,1,182,1,182,1,182,1,182, - 1,182,1,182,1,182,1,182,1,182,1,182,1,183,1,183,1,183,1,183,1,183,1,184, - 1,184,1,184,1,184,1,184,1,184,1,184,1,185,1,185,1,185,1,185,1,185,1,185, - 1,185,1,185,1,185,1,185,1,185,1,186,1,186,1,186,1,186,1,186,1,186,1,186, - 1,186,1,186,1,186,1,186,1,187,1,187,1,187,1,187,1,187,1,187,1,188,1,188, - 1,188,1,188,1,188,1,189,1,189,1,189,1,189,1,190,1,190,1,190,1,190,1,191, - 1,191,1,191,1,191,1,192,1,192,1,192,1,192,1,192,1,192,1,193,1,193,1,193, - 1,193,1,194,1,194,1,194,1,194,1,194,1,194,1,195,1,195,1,195,1,195,1,195, - 1,195,1,195,1,196,1,196,1,196,1,196,1,196,1,196,1,197,1,197,1,197,1,197, - 1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,197,1,198,1,198,1,198, - 1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,198,1,199,1,199, - 1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,199,1,200,1,200,1,200,1,200, - 1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,200,1,201,1,201,1,201,1,201, - 1,201,1,201,1,201,1,201,1,202,1,202,1,202,1,202,1,202,1,202,1,202,1,202, - 1,202,1,202,1,202,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203, - 1,203,1,203,1,203,1,203,1,203,1,204,1,204,1,204,1,204,1,204,1,204,1,204, - 1,204,1,204,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205, - 1,205,1,205,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,207, + 1,150,1,150,1,150,1,150,1,150,1,150,1,151,1,151,1,151,1,151,1,151,1,151, + 1,151,1,151,1,151,1,151,1,151,1,152,1,152,1,152,1,152,1,152,1,152,1,152, + 1,152,1,152,1,152,1,152,1,152,1,152,1,152,1,153,1,153,1,153,1,153,1,153, + 1,153,1,153,1,153,1,153,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154, + 1,154,1,154,1,154,1,154,1,155,1,155,1,155,1,155,1,155,1,155,1,155,1,155, + 1,155,1,156,1,156,1,156,1,156,1,156,1,156,1,157,1,157,1,157,1,157,1,157, + 1,157,1,157,1,157,1,157,1,157,1,158,1,158,1,158,1,158,1,158,1,158,1,158, + 1,159,1,159,1,159,1,159,1,159,1,159,1,159,1,159,1,159,1,159,1,159,1,159, + 1,159,1,159,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,160, + 1,160,1,160,1,161,1,161,1,161,1,161,1,161,1,161,1,161,1,162,1,162,1,162, + 1,162,1,162,1,162,1,162,1,162,1,162,1,162,1,163,1,163,1,163,1,163,1,163, + 1,163,1,163,1,164,1,164,1,164,1,164,1,164,1,164,1,165,1,165,1,165,1,165, + 1,165,1,165,1,165,1,165,1,165,1,166,1,166,1,166,1,166,1,166,1,166,1,166, + 1,167,1,167,1,167,1,167,1,167,1,168,1,168,1,168,1,168,1,168,1,169,1,169, + 1,169,1,169,1,169,1,169,1,169,1,169,1,170,1,170,1,170,1,170,1,170,1,170, + 1,170,1,170,1,171,1,171,1,171,1,171,1,171,1,172,1,172,1,172,1,172,1,172, + 1,173,1,173,1,173,1,173,1,173,1,173,1,173,1,173,1,173,1,173,1,174,1,174, + 1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,175,1,175,1,175,1,175,1,175, + 1,175,1,175,1,176,1,176,1,176,1,176,1,176,1,177,1,177,1,177,1,177,1,177, + 1,177,1,178,1,178,1,178,1,178,1,178,1,178,1,179,1,179,1,179,1,179,1,180, + 1,180,1,180,1,180,1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181, + 1,181,1,181,1,182,1,182,1,182,1,182,1,182,1,182,1,182,1,182,1,182,1,183, + 1,183,1,183,1,183,1,184,1,184,1,184,1,184,1,185,1,185,1,185,1,185,1,185, + 1,186,1,186,1,186,1,186,1,186,1,187,1,187,1,187,1,187,1,187,1,188,1,188, + 1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,188,1,189,1,189,1,189, + 1,189,1,189,1,190,1,190,1,190,1,190,1,190,1,190,1,190,1,191,1,191,1,191, + 1,191,1,191,1,191,1,191,1,191,1,191,1,191,1,191,1,192,1,192,1,192,1,192, + 1,192,1,192,1,192,1,192,1,192,1,192,1,192,1,193,1,193,1,193,1,193,1,193, + 1,193,1,194,1,194,1,194,1,194,1,194,1,195,1,195,1,195,1,195,1,196,1,196, + 1,196,1,196,1,197,1,197,1,197,1,197,1,198,1,198,1,198,1,198,1,198,1,198, + 1,199,1,199,1,199,1,199,1,200,1,200,1,200,1,200,1,200,1,200,1,201,1,201, + 1,201,1,201,1,201,1,201,1,201,1,202,1,202,1,202,1,202,1,202,1,202,1,203, + 1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203,1,203, + 1,204,1,204,1,204,1,204,1,204,1,204,1,204,1,204,1,204,1,204,1,204,1,204, + 1,204,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,205,1,206, + 1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,206,1,207, 1,207,1,207,1,207,1,207,1,207,1,207,1,207,1,207,1,207,1,207,1,207,1,207, 1,207,1,207,1,207,1,208,1,208,1,208,1,208,1,208,1,208,1,208,1,208,1,208, 1,208,1,208,1,208,1,208,1,208,1,208,1,209,1,209,1,209,1,209,1,209,1,209, @@ -505,20 +505,20 @@ static AngouriMathLexer() { 1221,1,0,0,0,275,1233,1,0,0,0,277,1243,1,0,0,0,279,1250,1,0,0,0,281,1261, 1,0,0,0,283,1273,1,0,0,0,285,1278,1,0,0,0,287,1287,1,0,0,0,289,1295,1, 0,0,0,291,1300,1,0,0,0,293,1306,1,0,0,0,295,1311,1,0,0,0,297,1316,1,0, - 0,0,299,1323,1,0,0,0,301,1334,1,0,0,0,303,1340,1,0,0,0,305,1350,1,0,0, - 0,307,1357,1,0,0,0,309,1371,1,0,0,0,311,1383,1,0,0,0,313,1390,1,0,0,0, - 315,1400,1,0,0,0,317,1407,1,0,0,0,319,1413,1,0,0,0,321,1422,1,0,0,0,323, - 1429,1,0,0,0,325,1434,1,0,0,0,327,1439,1,0,0,0,329,1447,1,0,0,0,331,1455, - 1,0,0,0,333,1460,1,0,0,0,335,1465,1,0,0,0,337,1475,1,0,0,0,339,1484,1, - 0,0,0,341,1491,1,0,0,0,343,1496,1,0,0,0,345,1502,1,0,0,0,347,1508,1,0, - 0,0,349,1512,1,0,0,0,351,1516,1,0,0,0,353,1527,1,0,0,0,355,1536,1,0,0, - 0,357,1540,1,0,0,0,359,1544,1,0,0,0,361,1549,1,0,0,0,363,1554,1,0,0,0, - 365,1559,1,0,0,0,367,1570,1,0,0,0,369,1575,1,0,0,0,371,1582,1,0,0,0,373, - 1593,1,0,0,0,375,1604,1,0,0,0,377,1610,1,0,0,0,379,1615,1,0,0,0,381,1619, - 1,0,0,0,383,1623,1,0,0,0,385,1627,1,0,0,0,387,1633,1,0,0,0,389,1637,1, - 0,0,0,391,1643,1,0,0,0,393,1650,1,0,0,0,395,1656,1,0,0,0,397,1669,1,0, - 0,0,399,1682,1,0,0,0,401,1692,1,0,0,0,403,1704,1,0,0,0,405,1712,1,0,0, - 0,407,1723,1,0,0,0,409,1737,1,0,0,0,411,1746,1,0,0,0,413,1758,1,0,0,0, + 0,0,299,1323,1,0,0,0,301,1334,1,0,0,0,303,1342,1,0,0,0,305,1353,1,0,0, + 0,307,1367,1,0,0,0,309,1376,1,0,0,0,311,1388,1,0,0,0,313,1397,1,0,0,0, + 315,1403,1,0,0,0,317,1413,1,0,0,0,319,1420,1,0,0,0,321,1434,1,0,0,0,323, + 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, + 0,0,349,1538,1,0,0,0,351,1547,1,0,0,0,353,1554,1,0,0,0,355,1559,1,0,0, + 0,357,1565,1,0,0,0,359,1571,1,0,0,0,361,1575,1,0,0,0,363,1579,1,0,0,0, + 365,1590,1,0,0,0,367,1599,1,0,0,0,369,1603,1,0,0,0,371,1607,1,0,0,0,373, + 1612,1,0,0,0,375,1617,1,0,0,0,377,1622,1,0,0,0,379,1633,1,0,0,0,381,1638, + 1,0,0,0,383,1645,1,0,0,0,385,1656,1,0,0,0,387,1667,1,0,0,0,389,1673,1, + 0,0,0,391,1678,1,0,0,0,393,1682,1,0,0,0,395,1686,1,0,0,0,397,1690,1,0, + 0,0,399,1696,1,0,0,0,401,1700,1,0,0,0,403,1706,1,0,0,0,405,1713,1,0,0, + 0,407,1719,1,0,0,0,409,1732,1,0,0,0,411,1745,1,0,0,0,413,1755,1,0,0,0, 415,1767,1,0,0,0,417,1783,1,0,0,0,419,1798,1,0,0,0,421,1811,1,0,0,0,423, 1829,1,0,0,0,425,1845,1,0,0,0,427,1862,1,0,0,0,429,1881,1,0,0,0,431,1892, 1,0,0,0,433,1902,1,0,0,0,435,1911,1,0,0,0,437,1922,1,0,0,0,439,1932,1, @@ -742,249 +742,248 @@ static AngouriMathLexer() { 1320,1321,5,101,0,0,1321,1322,5,40,0,0,1322,298,1,0,0,0,1323,1324,5,118, 0,0,1324,1325,5,97,0,0,1325,1326,5,108,0,0,1326,1327,5,117,0,0,1327,1328, 5,97,0,0,1328,1329,5,116,0,0,1329,1330,5,105,0,0,1330,1331,5,111,0,0,1331, - 1332,5,110,0,0,1332,1333,5,40,0,0,1333,300,1,0,0,0,1334,1335,5,99,0,0, - 1335,1336,5,97,0,0,1336,1337,5,114,0,0,1337,1338,5,100,0,0,1338,1339,5, - 40,0,0,1339,302,1,0,0,0,1340,1341,5,112,0,0,1341,1342,5,111,0,0,1342,1343, - 5,119,0,0,1343,1344,5,101,0,0,1344,1345,5,114,0,0,1345,1346,5,115,0,0, - 1346,1347,5,101,0,0,1347,1348,5,116,0,0,1348,1349,5,40,0,0,1349,304,1, - 0,0,0,1350,1351,5,117,0,0,1351,1352,5,110,0,0,1352,1353,5,105,0,0,1353, - 1354,5,111,0,0,1354,1355,5,110,0,0,1355,1356,5,40,0,0,1356,306,1,0,0,0, - 1357,1358,5,105,0,0,1358,1359,5,110,0,0,1359,1360,5,116,0,0,1360,1361, - 5,101,0,0,1361,1362,5,114,0,0,1362,1363,5,115,0,0,1363,1364,5,101,0,0, - 1364,1365,5,99,0,0,1365,1366,5,116,0,0,1366,1367,5,105,0,0,1367,1368,5, - 111,0,0,1368,1369,5,110,0,0,1369,1370,5,40,0,0,1370,308,1,0,0,0,1371,1372, - 5,99,0,0,1372,1373,5,111,0,0,1373,1374,5,109,0,0,1374,1375,5,112,0,0,1375, - 1376,5,108,0,0,1376,1377,5,101,0,0,1377,1378,5,109,0,0,1378,1379,5,101, - 0,0,1379,1380,5,110,0,0,1380,1381,5,116,0,0,1381,1382,5,40,0,0,1382,310, - 1,0,0,0,1383,1384,5,105,0,0,1384,1385,5,109,0,0,1385,1386,5,97,0,0,1386, - 1387,5,103,0,0,1387,1388,5,101,0,0,1388,1389,5,40,0,0,1389,312,1,0,0,0, - 1390,1391,5,112,0,0,1391,1392,5,114,0,0,1392,1393,5,101,0,0,1393,1394, - 5,105,0,0,1394,1395,5,109,0,0,1395,1396,5,97,0,0,1396,1397,5,103,0,0,1397, - 1398,5,101,0,0,1398,1399,5,40,0,0,1399,314,1,0,0,0,1400,1401,5,102,0,0, - 1401,1402,5,108,0,0,1402,1403,5,111,0,0,1403,1404,5,111,0,0,1404,1405, - 5,114,0,0,1405,1406,5,40,0,0,1406,316,1,0,0,0,1407,1408,5,99,0,0,1408, - 1409,5,101,0,0,1409,1410,5,105,0,0,1410,1411,5,108,0,0,1411,1412,5,40, - 0,0,1412,318,1,0,0,0,1413,1414,5,99,0,0,1414,1415,5,101,0,0,1415,1416, - 5,105,0,0,1416,1417,5,108,0,0,1417,1418,5,105,0,0,1418,1419,5,110,0,0, - 1419,1420,5,103,0,0,1420,1421,5,40,0,0,1421,320,1,0,0,0,1422,1423,5,114, - 0,0,1423,1424,5,111,0,0,1424,1425,5,117,0,0,1425,1426,5,110,0,0,1426,1427, - 5,100,0,0,1427,1428,5,40,0,0,1428,322,1,0,0,0,1429,1430,5,109,0,0,1430, - 1431,5,105,0,0,1431,1432,5,110,0,0,1432,1433,5,40,0,0,1433,324,1,0,0,0, - 1434,1435,5,109,0,0,1435,1436,5,97,0,0,1436,1437,5,120,0,0,1437,1438,5, - 40,0,0,1438,326,1,0,0,0,1439,1440,5,97,0,0,1440,1441,5,114,0,0,1441,1442, - 5,103,0,0,1442,1443,5,109,0,0,1443,1444,5,97,0,0,1444,1445,5,120,0,0,1445, - 1446,5,40,0,0,1446,328,1,0,0,0,1447,1448,5,97,0,0,1448,1449,5,114,0,0, - 1449,1450,5,103,0,0,1450,1451,5,109,0,0,1451,1452,5,105,0,0,1452,1453, - 5,110,0,0,1453,1454,5,40,0,0,1454,330,1,0,0,0,1455,1456,5,103,0,0,1456, - 1457,5,99,0,0,1457,1458,5,100,0,0,1458,1459,5,40,0,0,1459,332,1,0,0,0, - 1460,1461,5,108,0,0,1461,1462,5,99,0,0,1462,1463,5,109,0,0,1463,1464,5, - 40,0,0,1464,334,1,0,0,0,1465,1466,5,98,0,0,1466,1467,5,105,0,0,1467,1468, - 5,110,0,0,1468,1469,5,111,0,0,1469,1470,5,109,0,0,1470,1471,5,105,0,0, - 1471,1472,5,97,0,0,1472,1473,5,108,0,0,1473,1474,5,40,0,0,1474,336,1,0, - 0,0,1475,1476,5,105,0,0,1476,1477,5,118,0,0,1477,1478,5,101,0,0,1478,1479, - 5,114,0,0,1479,1480,5,115,0,0,1480,1481,5,111,0,0,1481,1482,5,110,0,0, - 1482,1483,5,40,0,0,1483,338,1,0,0,0,1484,1485,5,97,0,0,1485,1486,5,108, - 0,0,1486,1487,5,101,0,0,1487,1488,5,112,0,0,1488,1489,5,104,0,0,1489,1490, - 5,40,0,0,1490,340,1,0,0,0,1491,1492,5,101,0,0,1492,1493,5,114,0,0,1493, - 1494,5,102,0,0,1494,1495,5,40,0,0,1495,342,1,0,0,0,1496,1497,5,101,0,0, - 1497,1498,5,114,0,0,1498,1499,5,102,0,0,1499,1500,5,99,0,0,1500,1501,5, - 40,0,0,1501,344,1,0,0,0,1502,1503,5,101,0,0,1503,1504,5,114,0,0,1504,1505, - 5,102,0,0,1505,1506,5,105,0,0,1506,1507,5,40,0,0,1507,346,1,0,0,0,1508, - 1509,5,69,0,0,1509,1510,5,105,0,0,1510,1511,5,40,0,0,1511,348,1,0,0,0, - 1512,1513,5,108,0,0,1513,1514,5,105,0,0,1514,1515,5,40,0,0,1515,350,1, - 0,0,0,1516,1517,5,112,0,0,1517,1518,5,111,0,0,1518,1519,5,108,0,0,1519, - 1520,5,121,0,0,1520,1521,5,103,0,0,1521,1522,5,97,0,0,1522,1523,5,109, - 0,0,1523,1524,5,109,0,0,1524,1525,5,97,0,0,1525,1526,5,40,0,0,1526,352, - 1,0,0,0,1527,1528,5,100,0,0,1528,1529,5,105,0,0,1529,1530,5,103,0,0,1530, - 1531,5,97,0,0,1531,1532,5,109,0,0,1532,1533,5,109,0,0,1533,1534,5,97,0, - 0,1534,1535,5,40,0,0,1535,354,1,0,0,0,1536,1537,5,83,0,0,1537,1538,5,105, - 0,0,1538,1539,5,40,0,0,1539,356,1,0,0,0,1540,1541,5,67,0,0,1541,1542,5, - 105,0,0,1542,1543,5,40,0,0,1543,358,1,0,0,0,1544,1545,5,83,0,0,1545,1546, - 5,104,0,0,1546,1547,5,105,0,0,1547,1548,5,40,0,0,1548,360,1,0,0,0,1549, - 1550,5,67,0,0,1550,1551,5,104,0,0,1551,1552,5,105,0,0,1552,1553,5,40,0, - 0,1553,362,1,0,0,0,1554,1555,5,100,0,0,1555,1556,5,101,0,0,1556,1557,5, - 116,0,0,1557,1558,5,40,0,0,1558,364,1,0,0,0,1559,1560,5,116,0,0,1560,1561, - 5,114,0,0,1561,1562,5,97,0,0,1562,1563,5,110,0,0,1563,1564,5,115,0,0,1564, - 1565,5,112,0,0,1565,1566,5,111,0,0,1566,1567,5,115,0,0,1567,1568,5,101, - 0,0,1568,1569,5,40,0,0,1569,366,1,0,0,0,1570,1571,5,100,0,0,1571,1572, - 5,111,0,0,1572,1573,5,116,0,0,1573,1574,5,40,0,0,1574,368,1,0,0,0,1575, - 1576,5,99,0,0,1576,1577,5,114,0,0,1577,1578,5,111,0,0,1578,1579,5,115, - 0,0,1579,1580,5,115,0,0,1580,1581,5,40,0,0,1581,370,1,0,0,0,1582,1583, - 5,114,0,0,1583,1584,5,101,0,0,1584,1585,5,115,0,0,1585,1586,5,117,0,0, - 1586,1587,5,108,0,0,1587,1588,5,116,0,0,1588,1589,5,97,0,0,1589,1590,5, - 110,0,0,1590,1591,5,116,0,0,1591,1592,5,40,0,0,1592,372,1,0,0,0,1593,1594, - 5,99,0,0,1594,1595,5,111,0,0,1595,1596,5,110,0,0,1596,1597,5,106,0,0,1597, - 1598,5,117,0,0,1598,1599,5,103,0,0,1599,1600,5,97,0,0,1600,1601,5,116, - 0,0,1601,1602,5,101,0,0,1602,1603,5,40,0,0,1603,374,1,0,0,0,1604,1605, - 5,99,0,0,1605,1606,5,111,0,0,1606,1607,5,110,0,0,1607,1608,5,106,0,0,1608, - 1609,5,40,0,0,1609,376,1,0,0,0,1610,1611,5,97,0,0,1611,1612,5,114,0,0, - 1612,1613,5,103,0,0,1613,1614,5,40,0,0,1614,378,1,0,0,0,1615,1616,5,82, - 0,0,1616,1617,5,101,0,0,1617,1618,5,40,0,0,1618,380,1,0,0,0,1619,1620, - 5,73,0,0,1620,1621,5,109,0,0,1621,1622,5,40,0,0,1622,382,1,0,0,0,1623, - 1624,5,114,0,0,1624,1625,5,101,0,0,1625,1626,5,40,0,0,1626,384,1,0,0,0, - 1627,1628,5,114,0,0,1628,1629,5,101,0,0,1629,1630,5,97,0,0,1630,1631,5, - 108,0,0,1631,1632,5,40,0,0,1632,386,1,0,0,0,1633,1634,5,105,0,0,1634,1635, - 5,109,0,0,1635,1636,5,40,0,0,1636,388,1,0,0,0,1637,1638,5,105,0,0,1638, - 1639,5,109,0,0,1639,1640,5,97,0,0,1640,1641,5,103,0,0,1641,1642,5,40,0, - 0,1642,390,1,0,0,0,1643,1644,5,116,0,0,1644,1645,5,114,0,0,1645,1646,5, - 117,0,0,1646,1647,5,110,0,0,1647,1648,5,99,0,0,1648,1649,5,40,0,0,1649, - 392,1,0,0,0,1650,1651,5,122,0,0,1651,1652,5,101,0,0,1652,1653,5,116,0, - 0,1653,1654,5,97,0,0,1654,1655,5,40,0,0,1655,394,1,0,0,0,1656,1657,5,114, - 0,0,1657,1658,5,105,0,0,1658,1659,5,101,0,0,1659,1660,5,109,0,0,1660,1661, - 5,97,0,0,1661,1662,5,110,0,0,1662,1663,5,110,0,0,1663,1664,5,122,0,0,1664, - 1665,5,101,0,0,1665,1666,5,116,0,0,1666,1667,5,97,0,0,1667,1668,5,40,0, - 0,1668,396,1,0,0,0,1669,1670,5,104,0,0,1670,1671,5,117,0,0,1671,1672,5, - 114,0,0,1672,1673,5,119,0,0,1673,1674,5,105,0,0,1674,1675,5,116,0,0,1675, - 1676,5,122,0,0,1676,1677,5,122,0,0,1677,1678,5,101,0,0,1678,1679,5,116, - 0,0,1679,1680,5,97,0,0,1680,1681,5,40,0,0,1681,398,1,0,0,0,1682,1683,5, - 108,0,0,1683,1684,5,97,0,0,1684,1685,5,109,0,0,1685,1686,5,98,0,0,1686, - 1687,5,101,0,0,1687,1688,5,114,0,0,1688,1689,5,116,0,0,1689,1690,5,119, - 0,0,1690,1691,5,40,0,0,1691,400,1,0,0,0,1692,1693,5,112,0,0,1693,1694, - 5,114,0,0,1694,1695,5,111,0,0,1695,1696,5,100,0,0,1696,1697,5,117,0,0, - 1697,1698,5,99,0,0,1698,1699,5,116,0,0,1699,1700,5,108,0,0,1700,1701,5, - 111,0,0,1701,1702,5,103,0,0,1702,1703,5,40,0,0,1703,402,1,0,0,0,1704,1705, - 5,109,0,0,1705,1706,5,111,0,0,1706,1707,5,98,0,0,1707,1708,5,105,0,0,1708, - 1709,5,117,0,0,1709,1710,5,115,0,0,1710,1711,5,40,0,0,1711,404,1,0,0,0, - 1712,1713,5,109,0,0,1713,1714,5,111,0,0,1714,1715,5,101,0,0,1715,1716, - 5,98,0,0,1716,1717,5,105,0,0,1717,1718,5,117,0,0,1718,1719,5,115,0,0,1719, - 1720,5,109,0,0,1720,1721,5,117,0,0,1721,1722,5,40,0,0,1722,406,1,0,0,0, - 1723,1724,5,100,0,0,1724,1725,5,105,0,0,1725,1726,5,118,0,0,1726,1727, - 5,105,0,0,1727,1728,5,115,0,0,1728,1729,5,111,0,0,1729,1730,5,114,0,0, - 1730,1731,5,115,0,0,1731,1732,5,105,0,0,1732,1733,5,103,0,0,1733,1734, - 5,109,0,0,1734,1735,5,97,0,0,1735,1736,5,40,0,0,1736,408,1,0,0,0,1737, - 1738,5,112,0,0,1738,1739,5,114,0,0,1739,1740,5,105,0,0,1740,1741,5,109, - 0,0,1741,1742,5,101,0,0,1742,1743,5,110,0,0,1743,1744,5,117,0,0,1744,1745, - 5,40,0,0,1745,410,1,0,0,0,1746,1747,5,112,0,0,1747,1748,5,114,0,0,1748, - 1749,5,105,0,0,1749,1750,5,109,0,0,1750,1751,5,101,0,0,1751,1752,5,111, - 0,0,1752,1753,5,109,0,0,1753,1754,5,101,0,0,1754,1755,5,103,0,0,1755,1756, - 5,97,0,0,1756,1757,5,40,0,0,1757,412,1,0,0,0,1758,1759,5,112,0,0,1759, - 1760,5,114,0,0,1760,1761,5,105,0,0,1761,1762,5,109,0,0,1762,1763,5,101, - 0,0,1763,1764,5,112,0,0,1764,1765,5,105,0,0,1765,1766,5,40,0,0,1766,414, - 1,0,0,0,1767,1768,5,104,0,0,1768,1769,5,97,0,0,1769,1770,5,114,0,0,1770, - 1771,5,109,0,0,1771,1772,5,111,0,0,1772,1773,5,110,0,0,1773,1774,5,105, - 0,0,1774,1775,5,99,0,0,1775,1776,5,110,0,0,1776,1777,5,117,0,0,1777,1778, - 5,109,0,0,1778,1779,5,98,0,0,1779,1780,5,101,0,0,1780,1781,5,114,0,0,1781, - 1782,5,40,0,0,1782,416,1,0,0,0,1783,1784,5,99,0,0,1784,1785,5,97,0,0,1785, - 1786,5,116,0,0,1786,1787,5,97,0,0,1787,1788,5,108,0,0,1788,1789,5,97,0, - 0,1789,1790,5,110,0,0,1790,1791,5,110,0,0,1791,1792,5,117,0,0,1792,1793, - 5,109,0,0,1793,1794,5,98,0,0,1794,1795,5,101,0,0,1795,1796,5,114,0,0,1796, - 1797,5,40,0,0,1797,418,1,0,0,0,1798,1799,5,109,0,0,1799,1800,5,117,0,0, - 1800,1801,5,108,0,0,1801,1802,5,116,0,0,1802,1803,5,105,0,0,1803,1804, - 5,110,0,0,1804,1805,5,111,0,0,1805,1806,5,109,0,0,1806,1807,5,105,0,0, - 1807,1808,5,97,0,0,1808,1809,5,108,0,0,1809,1810,5,40,0,0,1810,420,1,0, - 0,0,1811,1812,5,102,0,0,1812,1813,5,97,0,0,1813,1814,5,108,0,0,1814,1815, - 5,108,0,0,1815,1816,5,105,0,0,1816,1817,5,110,0,0,1817,1818,5,103,0,0, - 1818,1819,5,102,0,0,1819,1820,5,97,0,0,1820,1821,5,99,0,0,1821,1822,5, - 116,0,0,1822,1823,5,111,0,0,1823,1824,5,114,0,0,1824,1825,5,105,0,0,1825, - 1826,5,97,0,0,1826,1827,5,108,0,0,1827,1828,5,40,0,0,1828,422,1,0,0,0, - 1829,1830,5,102,0,0,1830,1831,5,97,0,0,1831,1832,5,99,0,0,1832,1833,5, - 116,0,0,1833,1834,5,111,0,0,1834,1835,5,114,0,0,1835,1836,5,105,0,0,1836, - 1837,5,97,0,0,1837,1838,5,108,0,0,1838,1839,5,112,0,0,1839,1840,5,111, - 0,0,1840,1841,5,119,0,0,1841,1842,5,101,0,0,1842,1843,5,114,0,0,1843,1844, - 5,40,0,0,1844,424,1,0,0,0,1845,1846,5,114,0,0,1846,1847,5,105,0,0,1847, - 1848,5,115,0,0,1848,1849,5,105,0,0,1849,1850,5,110,0,0,1850,1851,5,103, - 0,0,1851,1852,5,102,0,0,1852,1853,5,97,0,0,1853,1854,5,99,0,0,1854,1855, - 5,116,0,0,1855,1856,5,111,0,0,1856,1857,5,114,0,0,1857,1858,5,105,0,0, - 1858,1859,5,97,0,0,1859,1860,5,108,0,0,1860,1861,5,40,0,0,1861,426,1,0, - 0,0,1862,1863,5,102,0,0,1863,1864,5,111,0,0,1864,1865,5,114,0,0,1865,1866, - 5,119,0,0,1866,1867,5,97,0,0,1867,1868,5,114,0,0,1868,1869,5,100,0,0,1869, - 1870,5,100,0,0,1870,1871,5,105,0,0,1871,1872,5,102,0,0,1872,1873,5,102, - 0,0,1873,1874,5,101,0,0,1874,1875,5,114,0,0,1875,1876,5,101,0,0,1876,1877, - 5,110,0,0,1877,1878,5,99,0,0,1878,1879,5,101,0,0,1879,1880,5,40,0,0,1880, - 428,1,0,0,0,1881,1882,5,108,0,0,1882,1883,5,97,0,0,1883,1884,5,112,0,0, - 1884,1885,5,108,0,0,1885,1886,5,97,0,0,1886,1887,5,99,0,0,1887,1888,5, - 105,0,0,1888,1889,5,97,0,0,1889,1890,5,110,0,0,1890,1891,5,40,0,0,1891, - 430,1,0,0,0,1892,1893,5,106,0,0,1893,1894,5,97,0,0,1894,1895,5,99,0,0, - 1895,1896,5,111,0,0,1896,1897,5,98,0,0,1897,1898,5,105,0,0,1898,1899,5, - 97,0,0,1899,1900,5,110,0,0,1900,1901,5,40,0,0,1901,432,1,0,0,0,1902,1903, - 5,104,0,0,1903,1904,5,101,0,0,1904,1905,5,115,0,0,1905,1906,5,115,0,0, - 1906,1907,5,105,0,0,1907,1908,5,97,0,0,1908,1909,5,110,0,0,1909,1910,5, - 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, - 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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 09f453712..172488a28 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp @@ -150,6 +150,12 @@ null 'phi(' 'prime(' 'valuation(' +'mobius(' +'moebiusmu(' +'divisorsigma(' +'primenu(' +'primeomega(' +'primepi(' 'card(' 'powerset(' 'union(' @@ -201,12 +207,6 @@ null 'hurwitzzeta(' 'lambertw(' 'productlog(' -'mobius(' -'moebiusmu(' -'divisorsigma(' -'primenu(' -'primeomega(' -'primepi(' 'harmonicnumber(' 'catalannumber(' 'multinomial(' @@ -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, 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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] \ No newline at end of file diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens index 62bf831c1..6813960bc 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens @@ -385,63 +385,63 @@ WS=237 'phi('=148 'prime('=149 'valuation('=150 -'card('=151 -'powerset('=152 -'union('=153 -'intersection('=154 -'complement('=155 -'image('=156 -'preimage('=157 -'floor('=158 -'ceil('=159 -'ceiling('=160 -'round('=161 -'min('=162 -'max('=163 -'argmax('=164 -'argmin('=165 -'gcd('=166 -'lcm('=167 -'binomial('=168 -'iverson('=169 -'aleph('=170 -'erf('=171 -'erfc('=172 -'erfi('=173 -'Ei('=174 -'li('=175 -'polygamma('=176 -'digamma('=177 -'Si('=178 -'Ci('=179 -'Shi('=180 -'Chi('=181 -'det('=182 -'transpose('=183 -'dot('=184 -'cross('=185 -'resultant('=186 -'conjugate('=187 -'conj('=188 -'arg('=189 -'Re('=190 -'Im('=191 -'re('=192 -'real('=193 -'im('=194 -'imag('=195 -'trunc('=196 -'zeta('=197 -'riemannzeta('=198 -'hurwitzzeta('=199 -'lambertw('=200 -'productlog('=201 -'mobius('=202 -'moebiusmu('=203 -'divisorsigma('=204 -'primenu('=205 -'primeomega('=206 -'primepi('=207 +'mobius('=151 +'moebiusmu('=152 +'divisorsigma('=153 +'primenu('=154 +'primeomega('=155 +'primepi('=156 +'card('=157 +'powerset('=158 +'union('=159 +'intersection('=160 +'complement('=161 +'image('=162 +'preimage('=163 +'floor('=164 +'ceil('=165 +'ceiling('=166 +'round('=167 +'min('=168 +'max('=169 +'argmax('=170 +'argmin('=171 +'gcd('=172 +'lcm('=173 +'binomial('=174 +'iverson('=175 +'aleph('=176 +'erf('=177 +'erfc('=178 +'erfi('=179 +'Ei('=180 +'li('=181 +'polygamma('=182 +'digamma('=183 +'Si('=184 +'Ci('=185 +'Shi('=186 +'Chi('=187 +'det('=188 +'transpose('=189 +'dot('=190 +'cross('=191 +'resultant('=192 +'conjugate('=193 +'conj('=194 +'arg('=195 +'Re('=196 +'Im('=197 +'re('=198 +'real('=199 +'im('=200 +'imag('=201 +'trunc('=202 +'zeta('=203 +'riemannzeta('=204 +'hurwitzzeta('=205 +'lambertw('=206 +'productlog('=207 'harmonicnumber('=208 'catalannumber('=209 'multinomial('=210 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs index 8a78f9292..5cef00db9 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs @@ -125,20 +125,20 @@ public const int "'arcsech('", "'acosech('", "'arcosech('", "'arcsch('", "'arccosech('", "'acsch('", "'factorial('", "'gamma('", "'derivative('", "'integral('", "'limit('", "'limitleft('", "'limitright('", "'sum('", "'product('", "'signum('", - "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'card('", - "'powerset('", "'union('", "'intersection('", "'complement('", "'image('", - "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('", - "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", + "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'mobius('", + "'moebiusmu('", "'divisorsigma('", "'primenu('", "'primeomega('", "'primepi('", + "'card('", "'powerset('", "'union('", "'intersection('", "'complement('", + "'image('", "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", + "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'polygamma('", "'digamma('", "'Si('", "'Ci('", "'Shi('", "'Chi('", "'det('", "'transpose('", "'dot('", "'cross('", "'resultant('", "'conjugate('", "'conj('", "'arg('", "'Re('", "'Im('", "'re('", "'real('", "'im('", "'imag('", "'trunc('", "'zeta('", "'riemannzeta('", "'hurwitzzeta('", "'lambertw('", - "'productlog('", "'mobius('", "'moebiusmu('", "'divisorsigma('", "'primenu('", - "'primeomega('", "'primepi('", "'harmonicnumber('", "'catalannumber('", - "'multinomial('", "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", - "'forwarddifference('", "'laplacian('", "'jacobian('", "'hessian('", "'heaviside('", - "'unitstep('", "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", + "'productlog('", "'harmonicnumber('", "'catalannumber('", "'multinomial('", + "'fallingfactorial('", "'factorialpower('", "'risingfactorial('", "'forwarddifference('", + "'laplacian('", "'jacobian('", "'hessian('", "'heaviside('", "'unitstep('", + "'isprime('", "'pochhammer('", "'doublefactorial('", "'factorial2('", "'fractionalpart('", "'quotient('", "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" }; @@ -4826,7 +4826,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 969; Match(T__32); - Assert("card", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.Card(_localctx.args.list[0]); + Assert("mobius", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.Mobius(_localctx.args.list[0]); } break; case 109: @@ -4838,7 +4838,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 974; Match(T__32); - Assert("powerset", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.PowerSet(_localctx.args.list[0]); + Assert("moebiusmu", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.Mobius(_localctx.args.list[0]); } break; case 110: @@ -4850,7 +4850,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 979; Match(T__32); - Assert("union", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } unionRange ? MathS.Sets.IndexedUnion(_localctx.args.list[0], unionRange.Element, unionRange.SupSet) : throw new InvalidArgumentParseException("union expects its second argument to say which name ranges over which set, as in union(A_i, i in I)"); + Assert("divisorsigma", 2, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.DivisorSigma(_localctx.args.list[0], _localctx.args.list[1]); } break; case 111: @@ -4862,7 +4862,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 984; Match(T__32); - Assert("intersection", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } intersectionRange ? MathS.Sets.IndexedIntersection(_localctx.args.list[0], intersectionRange.Element, intersectionRange.SupSet) : throw new InvalidArgumentParseException("intersection expects its second argument to say which name ranges over which set, as in intersection(A_i, i in I)"); + Assert("primenu", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.PrimeNu(_localctx.args.list[0]); } break; case 112: @@ -4874,7 +4874,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 989; Match(T__32); - Assert("complement", 2, _localctx.args.list.Count); _localctx.value = MathS.Sets.Complement(_localctx.args.list[0], _localctx.args.list[1]); + Assert("primeomega", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.PrimeOmega(_localctx.args.list[0]); } break; case 113: @@ -4886,7 +4886,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 994; Match(T__32); - Assert("image", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } imageRange ? MathS.Sets.Image(_localctx.args.list[0], imageRange.Element, imageRange.SupSet) : throw new InvalidArgumentParseException("image expects its second argument to say which name ranges over which set, as in image(f(x), x in A)"); + Assert("primepi", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.PrimePi(_localctx.args.list[0]); } break; case 114: @@ -4898,7 +4898,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 999; Match(T__32); - Assert("preimage", 3, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } preimageRange ? MathS.Sets.PreImage(_localctx.args.list[0], preimageRange.Element, preimageRange.SupSet, _localctx.args.list[2]) : throw new InvalidArgumentParseException("preimage expects its second argument to say which name ranges over which set, as in preimage(f(x), x in A, Y)"); + Assert("card", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.Card(_localctx.args.list[0]); } break; case 115: @@ -4910,7 +4910,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1004; Match(T__32); - Assert("floor", 1, _localctx.args.list.Count); _localctx.value = MathS.Floor(_localctx.args.list[0]); + Assert("powerset", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.PowerSet(_localctx.args.list[0]); } break; case 116: @@ -4922,7 +4922,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1009; Match(T__32); - Assert("ceil", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]); + Assert("union", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } unionRange ? MathS.Sets.IndexedUnion(_localctx.args.list[0], unionRange.Element, unionRange.SupSet) : throw new InvalidArgumentParseException("union expects its second argument to say which name ranges over which set, as in union(A_i, i in I)"); } break; case 117: @@ -4934,7 +4934,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1014; Match(T__32); - Assert("ceiling", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]); + Assert("intersection", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } intersectionRange ? MathS.Sets.IndexedIntersection(_localctx.args.list[0], intersectionRange.Element, intersectionRange.SupSet) : throw new InvalidArgumentParseException("intersection expects its second argument to say which name ranges over which set, as in intersection(A_i, i in I)"); } break; case 118: @@ -4946,7 +4946,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1019; Match(T__32); - Assert("round", 1, _localctx.args.list.Count); _localctx.value = MathS.Round(_localctx.args.list[0]); + Assert("complement", 2, _localctx.args.list.Count); _localctx.value = MathS.Sets.Complement(_localctx.args.list[0], _localctx.args.list[1]); } break; case 119: @@ -4958,7 +4958,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1024; Match(T__32); - AssertAtLeast("min", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Count == 1 && _localctx.args.list[0] is Entity.Set minSet ? MathS.Minimum(Variable.CreateUnique(minSet, "x"), Variable.CreateUnique(minSet, "x"), minSet) : _localctx.args.list.Count == 2 && AngouriMath.Functions.ExtremumOverSet.AsRange(_localctx.args.list[1]) is var (minVar, minOver) ? MathS.Minimum(_localctx.args.list[0], minVar, minOver) : _localctx.args.list.Aggregate((a, b) => MathS.Min(a, b)); + Assert("image", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } imageRange ? MathS.Sets.Image(_localctx.args.list[0], imageRange.Element, imageRange.SupSet) : throw new InvalidArgumentParseException("image expects its second argument to say which name ranges over which set, as in image(f(x), x in A)"); } break; case 120: @@ -4970,7 +4970,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1029; Match(T__32); - AssertAtLeast("max", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Count == 1 && _localctx.args.list[0] is Entity.Set maxSet ? MathS.Maximum(Variable.CreateUnique(maxSet, "x"), Variable.CreateUnique(maxSet, "x"), maxSet) : _localctx.args.list.Count == 2 && AngouriMath.Functions.ExtremumOverSet.AsRange(_localctx.args.list[1]) is var (maxVar, maxOver) ? MathS.Maximum(_localctx.args.list[0], maxVar, maxOver) : _localctx.args.list.Aggregate((a, b) => MathS.Max(a, b)); + Assert("preimage", 3, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } preimageRange ? MathS.Sets.PreImage(_localctx.args.list[0], preimageRange.Element, preimageRange.SupSet, _localctx.args.list[2]) : throw new InvalidArgumentParseException("preimage expects its second argument to say which name ranges over which set, as in preimage(f(x), x in A, Y)"); } break; case 121: @@ -4982,7 +4982,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1034; Match(T__32); - Assert("argmax", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } argmaxRange ? MathS.Argmax(_localctx.args.list[0], argmaxRange.Element, argmaxRange.SupSet) : throw new InvalidArgumentParseException("argmax expects its second argument to say which variable ranges over which set, as in argmax(f(t), t in S)"); + Assert("floor", 1, _localctx.args.list.Count); _localctx.value = MathS.Floor(_localctx.args.list[0]); } break; case 122: @@ -4994,7 +4994,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1039; Match(T__32); - Assert("argmin", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } argminRange ? MathS.Argmin(_localctx.args.list[0], argminRange.Element, argminRange.SupSet) : throw new InvalidArgumentParseException("argmin expects its second argument to say which variable ranges over which set, as in argmin(f(t), t in S)"); + Assert("ceil", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]); } break; case 123: @@ -5006,7 +5006,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1044; Match(T__32); - AssertAtLeast("gcd", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Gcd(a, b)); + Assert("ceiling", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]); } break; case 124: @@ -5018,7 +5018,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1049; Match(T__32); - AssertAtLeast("lcm", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Lcm(a, b)); + Assert("round", 1, _localctx.args.list.Count); _localctx.value = MathS.Round(_localctx.args.list[0]); } break; case 125: @@ -5030,7 +5030,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1054; Match(T__32); - Assert("binomial", 2, _localctx.args.list.Count); _localctx.value = MathS.Binomial(_localctx.args.list[0], _localctx.args.list[1]); + AssertAtLeast("min", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Count == 1 && _localctx.args.list[0] is Entity.Set minSet ? MathS.Minimum(Variable.CreateUnique(minSet, "x"), Variable.CreateUnique(minSet, "x"), minSet) : _localctx.args.list.Count == 2 && AngouriMath.Functions.ExtremumOverSet.AsRange(_localctx.args.list[1]) is var (minVar, minOver) ? MathS.Minimum(_localctx.args.list[0], minVar, minOver) : _localctx.args.list.Aggregate((a, b) => MathS.Min(a, b)); } break; case 126: @@ -5042,7 +5042,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1059; Match(T__32); - Assert("iverson", 1, _localctx.args.list.Count); _localctx.value = MathS.Iverson(_localctx.args.list[0]); + AssertAtLeast("max", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Count == 1 && _localctx.args.list[0] is Entity.Set maxSet ? MathS.Maximum(Variable.CreateUnique(maxSet, "x"), Variable.CreateUnique(maxSet, "x"), maxSet) : _localctx.args.list.Count == 2 && AngouriMath.Functions.ExtremumOverSet.AsRange(_localctx.args.list[1]) is var (maxVar, maxOver) ? MathS.Maximum(_localctx.args.list[0], maxVar, maxOver) : _localctx.args.list.Aggregate((a, b) => MathS.Max(a, b)); } break; case 127: @@ -5054,7 +5054,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1064; Match(T__32); - Assert("aleph", 1, _localctx.args.list.Count); _localctx.value = MathS.Aleph(_localctx.args.list[0]); + Assert("argmax", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } argmaxRange ? MathS.Argmax(_localctx.args.list[0], argmaxRange.Element, argmaxRange.SupSet) : throw new InvalidArgumentParseException("argmax expects its second argument to say which variable ranges over which set, as in argmax(f(t), t in S)"); } break; case 128: @@ -5066,7 +5066,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1069; Match(T__32); - Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]); + Assert("argmin", 2, _localctx.args.list.Count); _localctx.value = _localctx.args.list[1] is Entity.Set.Inf { Element: Variable } argminRange ? MathS.Argmin(_localctx.args.list[0], argminRange.Element, argminRange.SupSet) : throw new InvalidArgumentParseException("argmin expects its second argument to say which variable ranges over which set, as in argmin(f(t), t in S)"); } break; case 129: @@ -5078,7 +5078,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1074; Match(T__32); - Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]); + AssertAtLeast("gcd", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Gcd(a, b)); } break; case 130: @@ -5090,7 +5090,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1079; Match(T__32); - Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]); + AssertAtLeast("lcm", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Lcm(a, b)); } break; case 131: @@ -5102,7 +5102,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1084; Match(T__32); - Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]); + Assert("binomial", 2, _localctx.args.list.Count); _localctx.value = MathS.Binomial(_localctx.args.list[0], _localctx.args.list[1]); } break; case 132: @@ -5114,7 +5114,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1089; Match(T__32); - Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]); + Assert("iverson", 1, _localctx.args.list.Count); _localctx.value = MathS.Iverson(_localctx.args.list[0]); } break; case 133: @@ -5126,7 +5126,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1094; Match(T__32); - Assert("polygamma", 2, _localctx.args.list.Count); _localctx.value = MathS.Polygamma(_localctx.args.list[0], _localctx.args.list[1]); + Assert("aleph", 1, _localctx.args.list.Count); _localctx.value = MathS.Aleph(_localctx.args.list[0]); } break; case 134: @@ -5138,7 +5138,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1099; Match(T__32); - Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_localctx.args.list[0]); + Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]); } break; case 135: @@ -5150,7 +5150,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1104; Match(T__32); - Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); + Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]); } break; case 136: @@ -5162,7 +5162,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1109; Match(T__32); - Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); + Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]); } break; case 137: @@ -5174,7 +5174,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1114; Match(T__32); - Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); + Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]); } break; case 138: @@ -5186,7 +5186,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1119; Match(T__32); - Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); + Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]); } break; case 139: @@ -5198,7 +5198,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1124; Match(T__32); - Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_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 140: @@ -5210,7 +5210,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1129; Match(T__32); - Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); + Assert("digamma", 1, _localctx.args.list.Count); _localctx.value = MathS.Digamma(_localctx.args.list[0]); } break; case 141: @@ -5222,7 +5222,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1134; Match(T__32); - Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_localctx.args.list[0], _localctx.args.list[1]); + Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]); } break; case 142: @@ -5234,7 +5234,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1139; Match(T__32); - Assert("cross", (1, 2), _localctx.args.list.Count); _localctx.value = ParsingHelpers.Cross(_localctx.args.list); + Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]); } break; case 143: @@ -5246,7 +5246,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1144; 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("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]); } break; case 144: @@ -5258,7 +5258,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1149; Match(T__32); - Assert("conjugate", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); + Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]); } break; case 145: @@ -5270,7 +5270,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1154; Match(T__32); - Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); + Assert("det", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Determinant(_localctx.args.list[0]); } break; case 146: @@ -5282,7 +5282,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1159; Match(T__32); - Assert("arg", 1, _localctx.args.list.Count); _localctx.value = MathS.Arg(_localctx.args.list[0]); + Assert("transpose", 1, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Transposed(_localctx.args.list[0]); } break; case 147: @@ -5294,7 +5294,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1164; Match(T__32); - Assert("Re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("dot", 2, _localctx.args.list.Count); _localctx.value = ParsingHelpers.Dot(_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("Im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); + Assert("cross", (1, 2), _localctx.args.list.Count); _localctx.value = ParsingHelpers.Cross(_localctx.args.list); } break; case 149: @@ -5318,7 +5318,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1174; Match(T__32); - Assert("re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_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 150: @@ -5330,7 +5330,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1179; Match(T__32); - Assert("real", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); + Assert("conjugate", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 151: @@ -5342,7 +5342,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1184; Match(T__32); - Assert("im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); + Assert("conj", 1, _localctx.args.list.Count); _localctx.value = MathS.Conjugate(_localctx.args.list[0]); } break; case 152: @@ -5354,7 +5354,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1189; Match(T__32); - Assert("imag", 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 153: @@ -5366,7 +5366,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1194; Match(T__32); - _localctx.value = NotImplementedFunction("trunc", "rounding functions"); + Assert("Re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 154: @@ -5378,7 +5378,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1199; Match(T__32); - _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); + Assert("Im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 155: @@ -5390,7 +5390,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1204; Match(T__32); - _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); + Assert("re", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 156: @@ -5402,7 +5402,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1209; Match(T__32); - _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); + Assert("real", 1, _localctx.args.list.Count); _localctx.value = MathS.Re(_localctx.args.list[0]); } break; case 157: @@ -5414,7 +5414,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1214; Match(T__32); - _localctx.value = NotImplementedFunction("lambertw", "Lambert W function yet"); + Assert("im", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 158: @@ -5426,7 +5426,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1219; Match(T__32); - _localctx.value = NotImplementedFunction("productlog", "Lambert W function yet"); + Assert("imag", 1, _localctx.args.list.Count); _localctx.value = MathS.Im(_localctx.args.list[0]); } break; case 159: @@ -5438,7 +5438,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1224; Match(T__32); - _localctx.value = NotImplementedFunction("mobius", "Mobius function yet"); + _localctx.value = NotImplementedFunction("trunc", "rounding functions"); } break; case 160: @@ -5450,7 +5450,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1229; Match(T__32); - _localctx.value = NotImplementedFunction("moebiusmu", "Mobius function yet"); + _localctx.value = NotImplementedFunction("zeta", "Riemann or Hurwitz zeta function yet"); } break; case 161: @@ -5462,7 +5462,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1234; Match(T__32); - _localctx.value = NotImplementedFunction("divisorsigma", "divisor function yet"); + _localctx.value = NotImplementedFunction("riemannzeta", "Riemann zeta function yet"); } break; case 162: @@ -5474,7 +5474,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1239; Match(T__32); - _localctx.value = NotImplementedFunction("primenu", "count of distinct prime factors yet"); + _localctx.value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); } break; case 163: @@ -5486,7 +5486,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1244; Match(T__32); - _localctx.value = NotImplementedFunction("primeomega", "count of prime factors with multiplicity yet"); + _localctx.value = NotImplementedFunction("lambertw", "Lambert W function yet"); } break; case 164: @@ -5498,7 +5498,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1249; Match(T__32); - _localctx.value = NotImplementedFunction("primepi", "prime-counting function yet"); + _localctx.value = NotImplementedFunction("productlog", "Lambert W function yet"); } break; case 165: diff --git a/Sources/AngouriMath/Core/CostModel.cs b/Sources/AngouriMath/Core/CostModel.cs index 86c924ba3..01501141f 100644 --- a/Sources/AngouriMath/Core/CostModel.cs +++ b/Sources/AngouriMath/Core/CostModel.cs @@ -176,6 +176,7 @@ private static double Feature(Entity expr, Func predicate) Powf(_, Real { IsNegative: true }) => HeavyWeight + ChildrenCost(expr), // Number of negative powers Logf => TinyWeight + ChildrenCost(expr), // Number of logarithms Phif => ExtraHeavyWeight + ChildrenCost(expr), // Number of phi functions + Mobiusf or DivisorSigmaf or PrimeNuf or PrimeOmegaf or PrimePif => ExtraHeavyWeight + ChildrenCost(expr), Primef => ExtraHeavyWeight + ChildrenCost(expr), Valuationf => ExtraHeavyWeight + ChildrenCost(expr), Real { IsNegative: true } => MajorWeight + ChildrenCost(expr), // Number of negative reals diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs index 747e69a65..13d7d81ac 100644 --- a/Sources/AngouriMath/Core/Domains.Classes.cs +++ b/Sources/AngouriMath/Core/Domains.Classes.cs @@ -764,6 +764,51 @@ partial record Primef internal override Domain DefaultCodomain => Domain.Prime; } + partial record Mobiusf + { + // -1, 0 or 1. + /// + public override Domain Codomain { get; protected init; } = Domain.Integer; + /// + internal override Domain DefaultCodomain => Domain.Integer; + } + + partial record PrimeNuf + { + // A count. + /// + public override Domain Codomain { get; protected init; } = Domain.NonNegativeInteger; + /// + internal override Domain DefaultCodomain => Domain.NonNegativeInteger; + } + + partial record PrimeOmegaf + { + // A count. + /// + public override Domain Codomain { get; protected init; } = Domain.NonNegativeInteger; + /// + internal override Domain DefaultCodomain => Domain.NonNegativeInteger; + } + + partial record PrimePif + { + // A count. + /// + public override Domain Codomain { get; protected init; } = Domain.NonNegativeInteger; + /// + internal override Domain DefaultCodomain => Domain.NonNegativeInteger; + } + + partial record DivisorSigmaf + { + // A sum of powers, complex for a complex order. + /// + 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/Discrete/Entity.Discrete.Classes.cs b/Sources/AngouriMath/Core/Entity/Discrete/Entity.Discrete.Classes.cs index 2d5250982..9ee4b840b 100644 --- a/Sources/AngouriMath/Core/Entity/Discrete/Entity.Discrete.Classes.cs +++ b/Sources/AngouriMath/Core/Entity/Discrete/Entity.Discrete.Classes.cs @@ -451,6 +451,107 @@ internal Phif New(Entity argument) protected override Entity[] InitDirectChildren() => new[] { Argument }; } + /// + /// The Möbius function mobius(n), μ(n): 0 where a square of a prime divides the positive integer n, and (-1)^k where n is a product of k distinct primes, so μ(1) = 1. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + public sealed partial record Mobiusf(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + internal Mobiusf New(Entity argument) + => ReferenceEquals(argument, Argument) ? this : new(argument) { Codomain = Codomain }; + + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + + /// + /// The number of distinct prime factors primenu(n), ω(n), of a positive integer: ω(12) = 2 and ω(1) = 0. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + public sealed partial record PrimeNuf(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + internal PrimeNuf New(Entity argument) + => ReferenceEquals(argument, Argument) ? this : new(argument) { Codomain = Codomain }; + + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + + /// + /// The number of prime factors primeomega(n), Ω(n), of a positive integer, counted with multiplicity: Ω(12) = 3. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + public sealed partial record PrimeOmegaf(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + internal PrimeOmegaf New(Entity argument) + => ReferenceEquals(argument, Argument) ? this : new(argument) { Codomain = Codomain }; + + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + + /// + /// The prime-counting function primepi(x), π(x): how many primes are at most the real number x, so π(10) = 4. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + public sealed partial record PrimePif(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + internal PrimePif New(Entity argument) + => ReferenceEquals(argument, Argument) ? this : new(argument) { Codomain = Codomain }; + + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + + /// + /// The divisor function divisorsigma(k, n), σ_k(n): the sum of the k-th powers of + /// the positive divisors of the positive integer n, so σ_0 counts them and σ_1 sums + /// them. The order first, as the notation and Mathematica's DivisorSigma[k, n] read. + /// + /// https://github.com/asc-community/AngouriMath/issues/2182 + public sealed partial record DivisorSigmaf(Entity Order, Entity Argument) : Function, IBinaryNode + { + /// + public Entity NodeFirstChild => Order; + + /// + public Entity NodeSecondChild => Argument; + + internal DivisorSigmaf New(Entity order, Entity argument) + => ReferenceEquals(Order, order) && ReferenceEquals(Argument, argument) ? this : new(order, argument) { Codomain = Codomain }; + + /// + public override Entity Replace(Func func) + => func(New(Order.Replace(func), Argument.Replace(func))); + + /// + protected override Entity[] InitDirectChildren() => new[] { Order, Argument }; + } + /// /// This node represents whether the first argument divides the second: a divides b /// is the statement that b is a whole multiple of a, which for integers is diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs index 86ec85bd3..7ca88e183 100644 --- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs +++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs @@ -77,6 +77,11 @@ [EntityJsonConverter] partial record Number } [EntityJsonConverter] partial record Orf; [EntityJsonConverter] partial record Phif; + [EntityJsonConverter] partial record Mobiusf; + [EntityJsonConverter] partial record DivisorSigmaf; + [EntityJsonConverter] partial record PrimeNuf; + [EntityJsonConverter] partial record PrimeOmegaf; + [EntityJsonConverter] partial record PrimePif; [EntityJsonConverter] partial record Primef; [EntityJsonConverter] partial record Valuationf; [EntityJsonConverter] partial record Dividesf; diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs index 9e1d89590..de4602657 100644 --- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs +++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs @@ -494,6 +494,11 @@ internal abstract bool ETryBuild( [typeof(Entity.Roundf)] = (1, static c => new Entity.Roundf(c[0])), [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.PrimeNuf)] = (1, static c => new Entity.PrimeNuf(c[0])), + [typeof(Entity.PrimeOmegaf)] = (1, static c => new Entity.PrimeOmegaf(c[0])), + [typeof(Entity.PrimePif)] = (1, static c => new Entity.PrimePif(c[0])), + [typeof(Entity.DivisorSigmaf)] = (2, static c => new Entity.DivisorSigmaf(c[0], c[1])), [typeof(Entity.Primef)] = (1, static c => new Entity.Primef(c[0])), [typeof(Entity.Valuationf)] = (2, static c => new Entity.Valuationf(c[0], c[1])), [typeof(Entity.Cardf)] = (1, static c => new Entity.Cardf(c[0])), diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md index 12a2cc306..9516d5229 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 **68** such types. +pattern used as a **replacement** must be one the library can construct: there are **73** 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 8af6ee492..770072b4f 100644 --- a/Sources/AngouriMath/Docs/Usage/Syntax.md +++ b/Sources/AngouriMath/Docs/Usage/Syntax.md @@ -272,7 +272,15 @@ one argument is base 10, so `log(100)` is 2; `log10` and `log2` say it in the na for the `n`-th prime (`prime(25)` is `97`, `NaN` off the positive whole numbers, left as written for a symbol or an index past a million); `valuation(n, p)` for the `p`-adic valuation, the exponent of the prime `p` in `n` (`valuation(12, 2)` is `2`, `valuation(12, 5)` is `0`, `+oo` at -`n = 0`, `NaN` where `p` is not prime; `v_p(n)` in LaTeX); `#S` (or `card(S)`) for the number of elements of a set, counted for a finite set of numbers and left as written for an infinite one; `#` binds like a function call, so a set expression needs parentheses (`#(A \/ B)`). +`n = 0`, `NaN` where `p` is not prime; `v_p(n)` in LaTeX); `mobius(n)` for the Möbius function +`μ(n)`, 0 where the square of a prime divides `n` and `(-1)^k` for a product of `k` distinct primes +(`mobius(30)` is `-1`, `mobius(12)` is `0`; `moebiusmu` is the same); `divisorsigma(k, n)` for the +sum of the `k`-th powers of the divisors of `n` (`divisorsigma(1, 12)` is `28`, `divisorsigma(0, 12)` +counts them, `6`); `primenu(n)` and `primeomega(n)` for the number of prime factors without and with +multiplicity, `ω(n)` and `Ω(n)` (`2` and `3` at `12`); these four are defined on the positive whole +numbers, `NaN` elsewhere, and left as written for a number whose factorisation would need trial +division past a million. `primepi(x)` counts the primes at most the real number `x` (`primepi(100)` +is `25`, left as written past ten million); `#S` (or `card(S)`) for the number of elements of a set, counted for a finite set of numbers and left as written for an infinite one; `#` binds like a function call, so a set expression needs parentheses (`#(A \/ B)`). **Complex conjugate, argument and parts** — `conjugate(z)`, or `conj(z)`, printed `conjugate(z)` and drawn as `\overline{z}`. It is carried through sums, differences, products, quotients and whole powers, so @@ -476,8 +484,8 @@ ZZ*` is `True`, `0 in ZZ+` is `False`, `-3 in ZZ*` is `False`) and left as writt `7 in PP` is `True`, `8 in PP` and `1 in PP` are `False`, `x in PP` stays as written, and a whole number past the machine word is left open rather than tested slowly. It is cut by an interval to its members where there are few enough to list — `PP /\ [1; 30]` is -`{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }`, so `card(PP /\ [1; n])` is the prime-counting function, -`25` at `100` — and `min(PP)` is `2`, `min(x, x in PP and x > 14)` the next prime, `17` +`{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }`, so `card(PP /\ [1; n])` is the prime-counting function +`primepi(n)`, `25` at `100` — and `min(PP)` is `2`, `min(x, x in PP and x > 14)` the next prime, `17` ([#1450](https://github.com/asc-community/AngouriMath/issues/1450)). The eight special sets nest, `PP ⊂ ZZ+ ⊂ ZZ* ⊂ ZZ ⊂ QQ ⊂ RR ⊂ CC` with `BB` beside them, and the set operators answer for two of them: `ZZ unite QQ` is `QQ`, `BB intersect ZZ` is `{}`, `ZZ* \ ZZ+` is `{ 0 }`, `ZZ \ ZZ*` is @@ -485,8 +493,7 @@ 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` `mobius` `moebiusmu` `divisorsigma` `primenu` `primeomega` -`primepi` `harmonicnumber` `catalannumber` `multinomial` `fallingfactorial` `factorialpower` +`hurwitzzeta` `lambertw` `productlog` `harmonicnumber` `catalannumber` `multinomial` `fallingfactorial` `factorialpower` `risingfactorial` `forwarddifference` `laplacian` `jacobian` `hessian`. 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 5ad4cd1f9..ec542d99d 100644 --- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs +++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs @@ -905,6 +905,41 @@ partial record Primef => null; } + partial record Mobiusf + { + // Every argument with a given value is a set no list of values of x is. Left unsolved. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + + partial record DivisorSigmaf + { + // Every argument with a given value is a set no list of values of x is. Left unsolved. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + + partial record PrimeNuf + { + // Every argument with a given value is a set no list of values of x is. Left unsolved. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + + partial record PrimeOmegaf + { + // Every argument with a given value is a set no list of values of x is. Left unsolved. + private protected override IEnumerable? InvertNode(Entity value, Entity x) + => null; + } + + partial record PrimePif + { + // Every argument with a given value is a set no list of values of x is. Left unsolved. + 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.Discrete/Evaluation.Discrete.Classes.cs b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs index f717f659d..4934a9bd7 100644 --- a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs +++ b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs @@ -688,6 +688,92 @@ protected override Entity InnerSimplify(bool isExact) private const int LargestIndex = 1000000; } + partial record Mobiusf + { + // Defined on the positive integers, as are the other functions of a factorisation. + private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.PositiveIntegers); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => OfAFactorization(a, factors => factors.Any(factor => factor.Power > 1) ? Integer.Zero + : factors.Count % 2 == 0 ? Integer.One : Integer.MinusOne), + (@this, a) => ((Mobiusf)@this).New(a), isExact); + } + + partial record PrimeNuf + { + private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.PositiveIntegers); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => OfAFactorization(a, factors => Integer.Create(factors.Count)), + (@this, a) => ((PrimeNuf)@this).New(a), isExact); + } + + partial record PrimeOmegaf + { + private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.PositiveIntegers); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => OfAFactorization(a, factors => Integer.Create(factors.Sum(factor => factor.Power))), + (@this, a) => ((PrimeOmegaf)@this).New(a), isExact); + } + + partial record DivisorSigmaf + { + // Any complex order; the divisors are those of a positive integer. + private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.PositiveIntegers); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnTwoArguments(Order, Argument, + (k, n) => k is Number ? OfAFactorization(n, factors => Multiplicatively(k, factors).InnerSimplified(isExact)) : null, + (@this, k, n) => ((DivisorSigmaf)@this).New(k, n), isExact); + + // The function is multiplicative: the product over the prime powers p^a dividing n of + // 1 + p^k + p^(2k) + ... + p^(ak). + private static Entity Multiplicatively(Entity order, List<(EInteger Prime, int Power)> factors) + => factors.Select(factor => (Entity)Enumerable.Range(0, factor.Power + 1) + .Select(j => (Entity)Integer.Create(factor.Prime.Pow(j)).Pow(order)) + .Aggregate((sum, term) => sum + term)) + .Aggregate(Integer.One as Entity, (product, sum) => product * sum); + } + + partial record PrimePif + { + // A count of the primes up to any real number. + private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.R); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => a switch + { + Real { IsFinite: true } x when Functions.Primes.CountUpTo(x.EDecimal.RoundToExponent(EInteger.Zero, ERounding.Floor).ToEInteger()) is { } count + => Integer.Create(count), + Real => null, + Number => MathS.NaN, + _ => null + }, + (@this, a) => ((PrimePif)@this).New(a), isExact); + } + + /// + /// A function of the factorisation of a positive integer; not a number for any other + /// number, and left as written for an expression or an integer too large to factorise. + /// + private static Entity? OfAFactorization(Entity argument, System.Func, Entity> function) + => argument switch + { + Integer { EInteger.Sign: > 0 } positive => Functions.Primes.Factorization(positive.EInteger) is { } factors ? function(factors) : null, + Number => MathS.NaN, + _ => null + }; + partial record Phif { // Euler's totient function is defined for all integers in this library. diff --git a/Sources/AngouriMath/Functions/NumberTheory/Primes.cs b/Sources/AngouriMath/Functions/NumberTheory/Primes.cs index e3eb52bbb..2aaa7046c 100644 --- a/Sources/AngouriMath/Functions/NumberTheory/Primes.cs +++ b/Sources/AngouriMath/Functions/NumberTheory/Primes.cs @@ -174,6 +174,91 @@ static void AddPrimeI() /// How far a search for a prime, or a listing of them, is taken before the set is left as written. private const int LongestSearch = 100000; + /// + /// The prime factors of a positive whole number with their multiplicities, smallest first, + /// or where trial division up to + /// leaves a part it cannot call prime: every number up to its square is factorised, and + /// a larger one is whenever what is left after the small primes is below that square. + /// https://github.com/asc-community/AngouriMath/issues/2182 + /// + internal static List<(EInteger Prime, int Power)>? Factorization(EInteger n) + { + var factors = new List<(EInteger, int)>(); + var rest = n; + for (long divisor = 2; divisor <= LargestTrialDivisor; divisor += divisor == 2 ? 1 : 2) + { + if (rest.CanFitInInt64()) + return Finish(rest.ToInt64Checked(), divisor); + var asInteger = EInteger.FromInt64(divisor); + var power = 0; + while (rest.Remainder(asInteger).IsZero) + { + rest = rest.Divide(asInteger); + power++; + } + if (power > 0) + factors.Add((asInteger, power)); + } + return null; + + // The same division on a machine word, once what is left fits one. + List<(EInteger, int)>? Finish(long left, long from) + { + for (var divisor = from; divisor <= LargestTrialDivisor && divisor * divisor <= left; divisor += divisor == 2 ? 1 : 2) + { + var power = 0; + while (left % divisor == 0) + { + left /= divisor; + power++; + } + if (power > 0) + factors.Add((EInteger.FromInt64(divisor), power)); + } + if (left > 1) + { + // No divisor up to the bound, so what is left is prime if it is below the square. + if (left / LargestTrialDivisor >= LargestTrialDivisor) + return null; + factors.Add((EInteger.FromInt64(left), 1)); + } + return factors; + } + } + + /// How far trial division goes: far enough to factorise every number up to 10^12. + private const long LargestTrialDivisor = 1000000; + + /// + /// How many primes are at most , by a sieve over the odd numbers, or + /// above . + /// https://github.com/asc-community/AngouriMath/issues/2182 + /// + internal static int? CountUpTo(EInteger n) + { + if (n.CompareTo(EInteger.FromInt32(2)) < 0) + return 0; + if (n.CompareTo(EInteger.FromInt32(LargestCounted)) > 0) + return null; + var last = n.ToInt32Checked(); + // composite[i] is whether 2i + 1 is composite. + var composite = new System.Collections.BitArray(last / 2 + 1); + var count = 1; + for (var i = 1; 2 * i + 1 <= last; i++) + { + if (composite[i]) + continue; + count++; + long odd = 2 * i + 1; + for (var multiple = odd * odd; multiple <= last; multiple += 2 * odd) + composite[(int)(multiple / 2)] = true; + } + return count; + } + + /// How far sieves before a count is left as written. + private const int LargestCounted = 10000000; + internal static Integer GetPrime(int index) { // One volatile read, then an array that is never written again. diff --git a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs index 413bcb9cb..e5f29bb0b 100644 --- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs @@ -368,6 +368,38 @@ partial record Primef private protected override string LatexizeNode() => $@"\operatorname{{prime}}\left({Argument.Latexize()}\right)"; } + // A Greek letter that could be a variable is wrapped in \operatorname, as phi is, since + // mu * (n + 1) draws as \mu \left(n+1\right). https://github.com/asc-community/AngouriMath/issues/2182 + partial record Mobiusf + { + /// + private protected override string LatexizeNode() => $@"\operatorname{{\mu}}\left({Argument.Latexize()}\right)"; + } + + partial record PrimeNuf + { + /// + private protected override string LatexizeNode() => $@"\operatorname{{\omega}}\left({Argument.Latexize()}\right)"; + } + + partial record PrimeOmegaf + { + /// + private protected override string LatexizeNode() => $@"\operatorname{{\Omega}}\left({Argument.Latexize()}\right)"; + } + + partial record PrimePif + { + /// + private protected override string LatexizeNode() => $@"\operatorname{{\pi}}\left({Argument.Latexize()}\right)"; + } + + partial record DivisorSigmaf + { + /// + private protected override string LatexizeNode() => $@"\operatorname{{\sigma}}_{{{Order.Latexize()}}}\left({Argument.Latexize()}\right)"; + } + partial record Valuationf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs index b5d8250b1..059fa6a3a 100644 --- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs @@ -105,6 +105,46 @@ partial record Primef public override string ToString() => Stringize(); } + partial record Mobiusf + { + /// + private protected override string StringizeNode() => $@"mobius({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + + partial record PrimeNuf + { + /// + private protected override string StringizeNode() => $@"primenu({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + + partial record PrimeOmegaf + { + /// + private protected override string StringizeNode() => $@"primeomega({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + + partial record PrimePif + { + /// + private protected override string StringizeNode() => $@"primepi({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + + partial record DivisorSigmaf + { + /// + private protected override string StringizeNode() => $@"divisorsigma({Order.Stringize()}, {Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + partial record Valuationf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs index 6d877aca7..a81259009 100644 --- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs @@ -271,6 +271,32 @@ public partial record Primef internal override string ToSymPy() => $"sympy.prime({Argument.ToSymPy()})"; } + public partial record Mobiusf + { + internal override string ToSymPy() => $"sympy.mobius({Argument.ToSymPy()})"; + } + + public partial record PrimeNuf + { + internal override string ToSymPy() => $"sympy.primenu({Argument.ToSymPy()})"; + } + + public partial record PrimeOmegaf + { + internal override string ToSymPy() => $"sympy.primeomega({Argument.ToSymPy()})"; + } + + public partial record PrimePif + { + internal override string ToSymPy() => $"sympy.primepi({Argument.ToSymPy()})"; + } + + public partial record DivisorSigmaf + { + // SymPy takes the argument first and the order second. + internal override string ToSymPy() => $"sympy.divisor_sigma({Argument.ToSymPy()}, {Order.ToSymPy()})"; + } + public partial record Valuationf { internal override string ToSymPy() => $"sympy.multiplicity({Prime.ToSymPy()}, {Argument.ToSymPy()})"; diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs index fa2ae88ab..b14d043a0 100644 --- a/Sources/AngouriMath/Functions/Substitute.cs +++ b/Sources/AngouriMath/Functions/Substitute.cs @@ -540,6 +540,41 @@ public override Entity Substitute(Entity x, Entity value) => this == x ? value : New(Argument.Substitute(x, value)); } + partial record Mobiusf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + + partial record PrimeNuf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + + partial record PrimeOmegaf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + + partial record PrimePif + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + + partial record DivisorSigmaf + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Order.Substitute(x, value), Argument.Substitute(x, value)); + } + partial record Valuationf { /// diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs index 13ba086be..a13eb8c26 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs @@ -71,8 +71,9 @@ or Arctanf or Arccotanf or Signumf or Erff or Erfcf or Erfif or Eif or Sif or Sh case Polygammaf(var order, var argument) when !order.ContainsNode(x): return IsRealValued(argument, x); // A modulus is real whatever it is taken of, and so are an argument and a real - // and an imaginary part; an Iverson bracket is 0 or 1. - case Absf or Iversonf or Argf or Ref or Imf: + // and an imaginary part; an Iverson bracket is 0 or 1, and the Möbius function and + // the counts of primes are integers. + case Absf or Iversonf or Argf or Ref or Imf or Mobiusf or PrimeNuf or PrimeOmegaf or PrimePif: return true; default: return false; @@ -157,7 +158,7 @@ or Arctanf or Arccotanf or Signumf or Erff or Erfcf or Erfif or Eif or Sif or Sh return GatherTheBasesOfRoots(expr.DirectChildren[0], x, bases); case Polygammaf(var order, var argument) when !order.ContainsNode(x): return GatherTheBasesOfRoots(argument, x, bases); - case Absf or Iversonf or Argf or Ref or Imf: + case Absf or Iversonf or Argf or Ref or Imf or Mobiusf or PrimeNuf or PrimeOmegaf or PrimePif: return true; default: return false; diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs index 67be1763c..88bae0113 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs @@ -563,6 +563,31 @@ partial record Primef private protected override string SortHashName(SortLevel level) => "prime_"; } + partial record Mobiusf + { + private protected override string SortHashName(SortLevel level) => "mobius_"; + } + + partial record DivisorSigmaf + { + private protected override string SortHashName(SortLevel level) => "divisorsigma_"; + } + + partial record PrimeNuf + { + private protected override string SortHashName(SortLevel level) => "primenu_"; + } + + partial record PrimeOmegaf + { + private protected override string SortHashName(SortLevel level) => "primeomega_"; + } + + partial record PrimePif + { + private protected override string SortHashName(SortLevel level) => "primepi_"; + } + partial record Valuationf { private protected override string SortHashName(SortLevel level) => "valuation_"; diff --git a/Sources/MCP/AngouriMath.Mcp/Resources.cs b/Sources/MCP/AngouriMath.Mcp/Resources.cs index 02711bd9e..8b3655564 100644 --- a/Sources/MCP/AngouriMath.Mcp/Resources.cs +++ b/Sources/MCP/AngouriMath.Mcp/Resources.cs @@ -96,7 +96,9 @@ that every response returns. - complex numbers: `conjugate`, also spelled `conj`; `arg`, the principal argument in `(-pi, pi]`; `Re` and `Im`, also spelled `re`, `im`, `real` and `imag`, `Im(x + i y)` being `y` - `floor ceil ceiling round min max gcd lcm` - - `gamma factorial binomial phi prime valuation`, and the postfix `n!` and `n!!` (the double factorial, not `(n!)!`) + - `gamma factorial binomial phi prime valuation`, the postfix `n!` and `n!!` (the double factorial, not `(n!)!`), + 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 upper incomplete gamma function - sets: `card powerset union intersection complement image preimage domain aleph @@ -113,7 +115,7 @@ apply lambda` | You might write | Reality | |---|---| | `arcsinh(x)` | **refused.** The inverse hyperbolics are area functions: write `arsinh`, `asinh` or `arsh` | - | `trunc`, `zeta`, `lambertw`, `mobius`, `divisorsigma`, `primepi`, `harmonicnumber`, `catalannumber`, `multinomial`, `fallingfactorial`, `risingfactorial` and other long names of functions to come | refused by name — not yet in the library | + | `trunc`, `zeta`, `lambertw`, `harmonicnumber`, `catalannumber`, `multinomial`, `fallingfactorial`, `risingfactorial` 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 2b6d97b3b..cab4a9dea 100644 --- a/Sources/Tests/AotSmokeTest/Program.cs +++ b/Sources/Tests/AotSmokeTest/Program.cs @@ -118,6 +118,13 @@ private static void Parsing() // The double factorial is a postfix the parser builds. https://github.com/asc-community/AngouriMath/issues/2182 var doubleFactorial = MathS.FromString("x!! + 0"); CheckClose("x!! at x = 7", At(doubleFactorial, "x", 7), 105); + + // The functions of a factorisation, and the count of primes by a sieve. + // https://github.com/asc-community/AngouriMath/issues/2182 + var mobius = MathS.FromString("mobius(n) + divisorsigma(1, n) + primeomega(n)"); + CheckClose("mu + sigma + Omega at n = 12", At(mobius, "n", 12), 0 + 28 + 3); + var primes = MathS.FromString("primepi(x)"); + CheckClose("primepi at x = 100", At(primes, "x", 100), 25); } private static void Simplification() diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt index 87e90d342..72ffb6819 100644 --- a/Sources/Tests/UnitTests/Common/PublicApi.txt +++ b/Sources/Tests/UnitTests/Common/PublicApi.txt @@ -978,6 +978,27 @@ AngouriMath.Entity+Dividesf.ToString() : System.String AngouriMath.Entity+Dividesf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Dividesf.op_Equality(AngouriMath.Entity+Dividesf, AngouriMath.Entity+Dividesf) : System.Boolean AngouriMath.Entity+Dividesf.op_Inequality(AngouriMath.Entity+Dividesf, AngouriMath.Entity+Dividesf) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.$() : AngouriMath.Entity+DivisorSigmaf +AngouriMath.Entity+DivisorSigmaf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+DivisorSigmaf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void +AngouriMath.Entity+DivisorSigmaf.EqualityContract { } : System.Type +AngouriMath.Entity+DivisorSigmaf.Equals(AngouriMath.Entity+DivisorSigmaf) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.GetHashCode() : System.Int32 +AngouriMath.Entity+DivisorSigmaf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+DivisorSigmaf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.NodeFirstChild { } : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.NodeSecondChild { } : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.Order { } : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+DivisorSigmaf.ToString() : System.String +AngouriMath.Entity+DivisorSigmaf.ctor(AngouriMath.Entity, AngouriMath.Entity) +AngouriMath.Entity+DivisorSigmaf.op_Equality(AngouriMath.Entity+DivisorSigmaf, AngouriMath.Entity+DivisorSigmaf) : System.Boolean +AngouriMath.Entity+DivisorSigmaf.op_Inequality(AngouriMath.Entity+DivisorSigmaf, AngouriMath.Entity+DivisorSigmaf) : System.Boolean AngouriMath.Entity+DoubleFactorialf.$() : AngouriMath.Entity+DoubleFactorialf AngouriMath.Entity+DoubleFactorialf.Argument { } : AngouriMath.Entity AngouriMath.Entity+DoubleFactorialf.Codomain { } : AngouriMath.Core.Domain @@ -1666,6 +1687,25 @@ AngouriMath.Entity+Minusf.ToString() : System.String AngouriMath.Entity+Minusf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Minusf.op_Equality(AngouriMath.Entity+Minusf, AngouriMath.Entity+Minusf) : System.Boolean AngouriMath.Entity+Minusf.op_Inequality(AngouriMath.Entity+Minusf, AngouriMath.Entity+Minusf) : System.Boolean +AngouriMath.Entity+Mobiusf.$() : AngouriMath.Entity+Mobiusf +AngouriMath.Entity+Mobiusf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+Mobiusf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+Mobiusf.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+Mobiusf.EqualityContract { } : System.Type +AngouriMath.Entity+Mobiusf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+Mobiusf.Equals(AngouriMath.Entity+Mobiusf) : System.Boolean +AngouriMath.Entity+Mobiusf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+Mobiusf.GetHashCode() : System.Int32 +AngouriMath.Entity+Mobiusf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+Mobiusf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+Mobiusf.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+Mobiusf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+Mobiusf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+Mobiusf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+Mobiusf.ToString() : System.String +AngouriMath.Entity+Mobiusf.ctor(AngouriMath.Entity) +AngouriMath.Entity+Mobiusf.op_Equality(AngouriMath.Entity+Mobiusf, AngouriMath.Entity+Mobiusf) : System.Boolean +AngouriMath.Entity+Mobiusf.op_Inequality(AngouriMath.Entity+Mobiusf, AngouriMath.Entity+Mobiusf) : System.Boolean AngouriMath.Entity+Modf.$() : AngouriMath.Entity+Modf AngouriMath.Entity+Modf.Codomain { } : AngouriMath.Core.Domain AngouriMath.Entity+Modf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void @@ -2131,6 +2171,63 @@ AngouriMath.Entity+Powf.ToString() : System.String AngouriMath.Entity+Powf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Powf.op_Equality(AngouriMath.Entity+Powf, AngouriMath.Entity+Powf) : System.Boolean AngouriMath.Entity+Powf.op_Inequality(AngouriMath.Entity+Powf, AngouriMath.Entity+Powf) : System.Boolean +AngouriMath.Entity+PrimeNuf.$() : AngouriMath.Entity+PrimeNuf +AngouriMath.Entity+PrimeNuf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+PrimeNuf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+PrimeNuf.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+PrimeNuf.EqualityContract { } : System.Type +AngouriMath.Entity+PrimeNuf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+PrimeNuf.Equals(AngouriMath.Entity+PrimeNuf) : System.Boolean +AngouriMath.Entity+PrimeNuf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+PrimeNuf.GetHashCode() : System.Int32 +AngouriMath.Entity+PrimeNuf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+PrimeNuf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+PrimeNuf.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+PrimeNuf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+PrimeNuf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+PrimeNuf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+PrimeNuf.ToString() : System.String +AngouriMath.Entity+PrimeNuf.ctor(AngouriMath.Entity) +AngouriMath.Entity+PrimeNuf.op_Equality(AngouriMath.Entity+PrimeNuf, AngouriMath.Entity+PrimeNuf) : System.Boolean +AngouriMath.Entity+PrimeNuf.op_Inequality(AngouriMath.Entity+PrimeNuf, AngouriMath.Entity+PrimeNuf) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.$() : AngouriMath.Entity+PrimeOmegaf +AngouriMath.Entity+PrimeOmegaf.Argument { } : AngouriMath.Entity +AngouriMath.Entity+PrimeOmegaf.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+PrimeOmegaf.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+PrimeOmegaf.EqualityContract { } : System.Type +AngouriMath.Entity+PrimeOmegaf.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.Equals(AngouriMath.Entity+PrimeOmegaf) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.Equals(System.Object) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.GetHashCode() : System.Int32 +AngouriMath.Entity+PrimeOmegaf.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+PrimeOmegaf.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+PrimeOmegaf.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+PrimeOmegaf.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+PrimeOmegaf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+PrimeOmegaf.ToString() : System.String +AngouriMath.Entity+PrimeOmegaf.ctor(AngouriMath.Entity) +AngouriMath.Entity+PrimeOmegaf.op_Equality(AngouriMath.Entity+PrimeOmegaf, AngouriMath.Entity+PrimeOmegaf) : System.Boolean +AngouriMath.Entity+PrimeOmegaf.op_Inequality(AngouriMath.Entity+PrimeOmegaf, AngouriMath.Entity+PrimeOmegaf) : System.Boolean +AngouriMath.Entity+PrimePif.$() : AngouriMath.Entity+PrimePif +AngouriMath.Entity+PrimePif.Argument { } : AngouriMath.Entity +AngouriMath.Entity+PrimePif.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+PrimePif.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+PrimePif.EqualityContract { } : System.Type +AngouriMath.Entity+PrimePif.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+PrimePif.Equals(AngouriMath.Entity+PrimePif) : System.Boolean +AngouriMath.Entity+PrimePif.Equals(System.Object) : System.Boolean +AngouriMath.Entity+PrimePif.GetHashCode() : System.Int32 +AngouriMath.Entity+PrimePif.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+PrimePif.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+PrimePif.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+PrimePif.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+PrimePif.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+PrimePif.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+PrimePif.ToString() : System.String +AngouriMath.Entity+PrimePif.ctor(AngouriMath.Entity) +AngouriMath.Entity+PrimePif.op_Equality(AngouriMath.Entity+PrimePif, AngouriMath.Entity+PrimePif) : System.Boolean +AngouriMath.Entity+PrimePif.op_Inequality(AngouriMath.Entity+PrimePif, AngouriMath.Entity+PrimePif) : System.Boolean AngouriMath.Entity+Primef.$() : AngouriMath.Entity+Primef AngouriMath.Entity+Primef.Argument { } : AngouriMath.Entity AngouriMath.Entity+Primef.Codomain { } : AngouriMath.Core.Domain @@ -3216,11 +3313,16 @@ AngouriMath.MathS+Multithreading.SetLocalCancellationToken(System.Threading.Canc AngouriMath.MathS+NumberTheory.Congruent(AngouriMath.Entity, AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+NumberTheory.CountDivisors(AngouriMath.Entity+Number+Integer) : AngouriMath.Entity+Number+Integer AngouriMath.MathS+NumberTheory.Divides(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS+NumberTheory.DivisorSigma(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+NumberTheory.Factorize(AngouriMath.Entity+Number+Integer) : System.Collections.Generic.IEnumerable> AngouriMath.MathS+NumberTheory.GreatestCommonDivisor(AngouriMath.Entity+Number+Integer, AngouriMath.Entity+Number+Integer) : AngouriMath.Entity+Number+Integer +AngouriMath.MathS+NumberTheory.Mobius(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+NumberTheory.ModularInverse(AngouriMath.Entity+Number+Integer, AngouriMath.Entity+Number+Integer) : AngouriMath.Entity+Number+Integer AngouriMath.MathS+NumberTheory.Phi(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+NumberTheory.Prime(AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS+NumberTheory.PrimeNu(AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS+NumberTheory.PrimeOmega(AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS+NumberTheory.PrimePi(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+NumberTheory.Valuation(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS+Numbers.Create(PeterO.Numbers.EDecimal) : AngouriMath.Entity+Number+Real AngouriMath.MathS+Numbers.Create(PeterO.Numbers.EDecimal, PeterO.Numbers.EDecimal) : AngouriMath.Entity+Number+Complex @@ -3530,6 +3632,7 @@ class AngouriMath.Entity+Cotanf class AngouriMath.Entity+Derivativef class AngouriMath.Entity+Divf class AngouriMath.Entity+Dividesf +class AngouriMath.Entity+DivisorSigmaf class AngouriMath.Entity+DoubleFactorialf class AngouriMath.Entity+Eif class AngouriMath.Entity+Equalsf @@ -3563,6 +3666,7 @@ class AngouriMath.Entity+Maximumf class AngouriMath.Entity+Minf class AngouriMath.Entity+Minimumf class AngouriMath.Entity+Minusf +class AngouriMath.Entity+Mobiusf class AngouriMath.Entity+Modf class AngouriMath.Entity+Mulf class AngouriMath.Entity+Notf @@ -3576,6 +3680,9 @@ class AngouriMath.Entity+Phif class AngouriMath.Entity+Piecewise class AngouriMath.Entity+Polygammaf class AngouriMath.Entity+Powf +class AngouriMath.Entity+PrimeNuf +class AngouriMath.Entity+PrimeOmegaf +class AngouriMath.Entity+PrimePif class AngouriMath.Entity+Primef class AngouriMath.Entity+Productf class AngouriMath.Entity+Providedf diff --git a/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs b/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs index a6df013ed..da626a502 100644 --- a/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs +++ b/Sources/Tests/UnitTests/Convenience/MissingFunctionNamesRefusedTest.cs @@ -35,7 +35,9 @@ public sealed class MissingFunctionNamesRefusedTest // and det until https://github.com/asc-community/AngouriMath/issues/2147. // And the long names of the functions to come, reserved until each is implemented, and the // 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. + // https://github.com/asc-community/AngouriMath/issues/2182. zeta(s) was zeta * s. mobius, + // moebiusmu, divisorsigma, primenu, primeomega and primepi were among them until they were + // implemented, in the same issue. [Theory] [InlineData("trunc(x)")] [InlineData("zeta(s)")] @@ -44,12 +46,6 @@ public sealed class MissingFunctionNamesRefusedTest [InlineData("hurwitzzeta(s, a)")] [InlineData("lambertw(x)")] [InlineData("productlog(x)")] - [InlineData("mobius(n)")] - [InlineData("moebiusmu(n)")] - [InlineData("divisorsigma(k, n)")] - [InlineData("primenu(n)")] - [InlineData("primeomega(n)")] - [InlineData("primepi(n)")] [InlineData("harmonicnumber(n)")] [InlineData("catalannumber(n)")] [InlineData("multinomial(a, b, c)")] diff --git a/Sources/Tests/UnitTests/Convenience/NumberTheoryFunctionsTest.cs b/Sources/Tests/UnitTests/Convenience/NumberTheoryFunctionsTest.cs new file mode 100644 index 000000000..637095fef --- /dev/null +++ b/Sources/Tests/UnitTests/Convenience/NumberTheoryFunctionsTest.cs @@ -0,0 +1,137 @@ +// +// 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 Xunit; +using static AngouriMath.Entity; + +namespace AngouriMath.Tests.Convenience +{ + /// + /// The Möbius function, the divisor function, the two counts of prime factors and the + /// prime-counting function. Each name was read as a product, mobius(6) as + /// mobius * 6. #2182 + /// + [Trait("Area", "Convenience")] + public sealed class NumberTheoryFunctionsTest + { + [Theory] + [InlineData("mobius(1)", "1")] + [InlineData("mobius(2)", "-1")] + [InlineData("mobius(4)", "0")] + [InlineData("mobius(6)", "1")] + [InlineData("mobius(30)", "-1")] + [InlineData("mobius(2 * 3 * 5 * 7)", "1")] + [InlineData("moebiusmu(12)", "0")] + [InlineData("primenu(1)", "0")] + [InlineData("primenu(12)", "2")] + [InlineData("primenu(30)", "3")] + [InlineData("primeomega(1)", "0")] + [InlineData("primeomega(12)", "3")] + [InlineData("primeomega(1024)", "10")] + [InlineData("divisorsigma(0, 12)", "6")] + [InlineData("divisorsigma(1, 12)", "28")] + [InlineData("divisorsigma(2, 6)", "50")] + [InlineData("divisorsigma(1, 1)", "1")] + [InlineData("divisorsigma(-1, 6)", "2")] + [InlineData("divisorsigma(-2, 2)", "5/4")] + [InlineData("primepi(1)", "0")] + [InlineData("primepi(2)", "1")] + [InlineData("primepi(10)", "4")] + [InlineData("primepi(10.5)", "4")] + [InlineData("primepi(100)", "25")] + [InlineData("primepi(-3)", "0")] + [InlineData("primepi(1000000)", "78498")] + public void TheyAreComputedOnTheirDomains(string written, string expected) + => Assert.Equal(expected.ToEntity().InnerSimplified, written.ToEntity().InnerSimplified); + + /// Any order: the square roots of the divisors of 4 are 1, sqrt(2) and 2. + [Fact] + public void TheDivisorFunctionTakesAnyOrder() + => Assert.Equal(Number.Integer.Zero, ("divisorsigma(1/2, 4) - (3 + sqrt(2))".ToEntity()).Simplify()); + + /// + /// The functions of a factorisation are defined on the positive integers, and the + /// prime-counting function on the reals. + /// + [Theory] + [InlineData("mobius(0)")] + [InlineData("mobius(-6)")] + [InlineData("mobius(1/2)")] + [InlineData("primenu(0)")] + [InlineData("primeomega(-4)")] + [InlineData("divisorsigma(1, 0)")] + [InlineData("divisorsigma(1, 3/2)")] + [InlineData("primepi(i)")] + public void TheyHaveNoValueOffTheirDomains(string written) + => Assert.Equal(MathS.NaN, written.ToEntity().InnerSimplified); + + /// + /// A number whose part left after trial division up to a million is too large to call + /// prime is not factorised, and a count of primes past ten million is not sieved; both are + /// left as written rather than answered slowly. 1000003 and 1000033 are primes. + /// + [Theory] + [InlineData("mobius(1000003 * 1000033)")] + [InlineData("primeomega(2305843009213693951)")] + [InlineData("primepi(10000001)")] + [InlineData("mobius(n)")] + [InlineData("divisorsigma(k, 6)")] + [InlineData("divisorsigma(2, n)")] + public void TheyAreLeftAsWrittenWhereTheyAreNotComputed(string written) + => Assert.IsAssignableFrom(written.ToEntity().InnerSimplified); + + /// A small prime factor is found past the machine word: 2^100 is not square-free. + [Fact] + public void ALargeNumberWithSmallFactorsIsFactorised() + { + Assert.Equal(Number.Integer.Zero, MathS.NumberTheory.Mobius(Number.Integer.Create(PeterO.Numbers.EInteger.One.ShiftLeft(100))).InnerSimplified); + Assert.Equal(Number.Integer.Create(100), MathS.NumberTheory.PrimeOmega(Number.Integer.Create(PeterO.Numbers.EInteger.One.ShiftLeft(100))).InnerSimplified); + } + + /// The sum of mu(d) over the divisors d of n is 1 at n = 1 and 0 above it. + [Theory] + [InlineData(1, 1)] + [InlineData(12, 0)] + [InlineData(30, 0)] + [InlineData(97, 0)] + public void TheMobiusFunctionSumsToZeroOverTheDivisors(int n, int sum) + { + Entity total = 0; + for (var d = 1; d <= n; d++) + if (n % d == 0) + total += MathS.NumberTheory.Mobius(d); + Assert.Equal(Number.Integer.Create(sum), total.InnerSimplified); + } + + [Theory] + [InlineData("mobius(n)", "mobius(n)", @"\operatorname{\mu}\left(n\right)", "sympy.mobius(n)")] + [InlineData("divisorsigma(k, n)", "divisorsigma(k, n)", @"\operatorname{\sigma}_{k}\left(n\right)", "sympy.divisor_sigma(n, k)")] + [InlineData("primenu(n)", "primenu(n)", @"\operatorname{\omega}\left(n\right)", "sympy.primenu(n)")] + [InlineData("primeomega(n)", "primeomega(n)", @"\operatorname{\Omega}\left(n\right)", "sympy.primeomega(n)")] + [InlineData("primepi(x)", "primepi(x)", @"\operatorname{\pi}\left(x\right)", "sympy.primepi(x)")] + [InlineData("moebiusmu(n + 1)", "mobius(n + 1)", @"\operatorname{\mu}\left(n+1\right)", "sympy.mobius(n + 1)")] + public void TheyAreWrittenByName(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()); + } + + [Fact] + public void TheyAreIntegers() + { + Assert.Equal(AngouriMath.Core.Domain.Integer, MathS.NumberTheory.Mobius("n").Codomain); + Assert.Equal(AngouriMath.Core.Domain.NonNegativeInteger, MathS.NumberTheory.PrimeNu("n").Codomain); + Assert.Equal(AngouriMath.Core.Domain.NonNegativeInteger, MathS.NumberTheory.PrimeOmega("n").Codomain); + Assert.Equal(AngouriMath.Core.Domain.NonNegativeInteger, MathS.NumberTheory.PrimePi("x").Codomain); + } + } +} diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs index 35d67181d..c2d4e8036 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(68, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); + => Stated(73, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); [Fact] public void ReplacementAPatternOrCode()