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,
- 1,0,0,0,1998,1999,5,113,0,0,1999,2000,5,117,0,0,2000,2001,5,111,0,0,2001,
- 2002,5,116,0,0,2002,2003,5,105,0,0,2003,2004,5,101,0,0,2004,2005,5,110,
- 0,0,2005,2006,5,116,0,0,2006,2007,5,40,0,0,2007,450,1,0,0,0,2008,2009,
- 5,100,0,0,2009,2010,5,111,0,0,2010,2011,5,109,0,0,2011,2012,5,97,0,0,2012,
- 2013,5,105,0,0,2013,2014,5,110,0,0,2014,2015,5,40,0,0,2015,452,1,0,0,0,
- 2016,2017,5,112,0,0,2017,2018,5,105,0,0,2018,2019,5,101,0,0,2019,2020,
- 5,99,0,0,2020,2021,5,101,0,0,2021,2022,5,119,0,0,2022,2023,5,105,0,0,2023,
- 2024,5,115,0,0,2024,2025,5,101,0,0,2025,2026,5,40,0,0,2026,454,1,0,0,0,
- 2027,2028,5,97,0,0,2028,2029,5,112,0,0,2029,2030,5,112,0,0,2030,2031,5,
- 108,0,0,2031,2032,5,121,0,0,2032,2033,5,40,0,0,2033,456,1,0,0,0,2034,2035,
- 5,108,0,0,2035,2036,5,97,0,0,2036,2037,5,109,0,0,2037,2038,5,98,0,0,2038,
- 2039,5,100,0,0,2039,2040,5,97,0,0,2040,2041,5,40,0,0,2041,458,1,0,0,0,
- 2042,2044,5,13,0,0,2043,2042,1,0,0,0,2043,2044,1,0,0,0,2044,2045,1,0,0,
- 0,2045,2047,5,10,0,0,2046,2043,1,0,0,0,2047,2048,1,0,0,0,2048,2046,1,0,
- 0,0,2048,2049,1,0,0,0,2049,2050,1,0,0,0,2050,2051,6,229,0,0,2051,460,1,
- 0,0,0,2052,2054,7,0,0,0,2053,2055,7,1,0,0,2054,2053,1,0,0,0,2054,2055,
- 1,0,0,0,2055,2057,1,0,0,0,2056,2058,2,48,57,0,2057,2056,1,0,0,0,2058,2059,
- 1,0,0,0,2059,2057,1,0,0,0,2059,2060,1,0,0,0,2060,462,1,0,0,0,2061,2063,
- 2,48,57,0,2062,2061,1,0,0,0,2063,2064,1,0,0,0,2064,2062,1,0,0,0,2064,2065,
- 1,0,0,0,2065,2066,1,0,0,0,2066,2070,5,46,0,0,2067,2069,2,48,57,0,2068,
- 2067,1,0,0,0,2069,2072,1,0,0,0,2070,2068,1,0,0,0,2070,2071,1,0,0,0,2071,
- 2074,1,0,0,0,2072,2070,1,0,0,0,2073,2075,3,461,230,0,2074,2073,1,0,0,0,
- 2074,2075,1,0,0,0,2075,2077,1,0,0,0,2076,2078,5,105,0,0,2077,2076,1,0,
- 0,0,2077,2078,1,0,0,0,2078,2095,1,0,0,0,2079,2081,5,46,0,0,2080,2079,1,
- 0,0,0,2080,2081,1,0,0,0,2081,2083,1,0,0,0,2082,2084,2,48,57,0,2083,2082,
- 1,0,0,0,2084,2085,1,0,0,0,2085,2083,1,0,0,0,2085,2086,1,0,0,0,2086,2088,
- 1,0,0,0,2087,2089,3,461,230,0,2088,2087,1,0,0,0,2088,2089,1,0,0,0,2089,
- 2091,1,0,0,0,2090,2092,5,105,0,0,2091,2090,1,0,0,0,2091,2092,1,0,0,0,2092,
- 2095,1,0,0,0,2093,2095,5,105,0,0,2094,2062,1,0,0,0,2094,2080,1,0,0,0,2094,
- 2093,1,0,0,0,2095,464,1,0,0,0,2096,2097,5,67,0,0,2097,2115,5,67,0,0,2098,
- 2099,5,82,0,0,2099,2115,5,82,0,0,2100,2101,5,81,0,0,2101,2115,5,81,0,0,
- 2102,2103,5,90,0,0,2103,2115,5,90,0,0,2104,2105,5,66,0,0,2105,2115,5,66,
- 0,0,2106,2107,5,90,0,0,2107,2108,5,90,0,0,2108,2115,5,42,0,0,2109,2110,
- 5,90,0,0,2110,2111,5,90,0,0,2111,2115,5,43,0,0,2112,2113,5,80,0,0,2113,
- 2115,5,80,0,0,2114,2096,1,0,0,0,2114,2098,1,0,0,0,2114,2100,1,0,0,0,2114,
- 2102,1,0,0,0,2114,2104,1,0,0,0,2114,2106,1,0,0,0,2114,2109,1,0,0,0,2114,
- 2112,1,0,0,0,2115,466,1,0,0,0,2116,2117,5,116,0,0,2117,2118,5,114,0,0,
- 2118,2119,5,117,0,0,2119,2135,5,101,0,0,2120,2121,5,84,0,0,2121,2122,5,
- 114,0,0,2122,2123,5,117,0,0,2123,2135,5,101,0,0,2124,2125,5,102,0,0,2125,
- 2126,5,97,0,0,2126,2127,5,108,0,0,2127,2128,5,115,0,0,2128,2135,5,101,
- 0,0,2129,2130,5,70,0,0,2130,2131,5,97,0,0,2131,2132,5,108,0,0,2132,2133,
- 5,115,0,0,2133,2135,5,101,0,0,2134,2116,1,0,0,0,2134,2120,1,0,0,0,2134,
- 2124,1,0,0,0,2134,2129,1,0,0,0,2135,468,1,0,0,0,2136,2137,5,78,0,0,2137,
- 2138,5,97,0,0,2138,2139,5,78,0,0,2139,470,1,0,0,0,2140,2142,7,2,0,0,2141,
- 2140,1,0,0,0,2142,2143,1,0,0,0,2143,2141,1,0,0,0,2143,2144,1,0,0,0,2144,
- 2153,1,0,0,0,2145,2147,5,95,0,0,2146,2148,7,3,0,0,2147,2146,1,0,0,0,2148,
- 2149,1,0,0,0,2149,2147,1,0,0,0,2149,2150,1,0,0,0,2150,2152,1,0,0,0,2151,
- 2145,1,0,0,0,2152,2155,1,0,0,0,2153,2151,1,0,0,0,2153,2154,1,0,0,0,2154,
- 472,1,0,0,0,2155,2153,1,0,0,0,2156,2157,5,47,0,0,2157,2158,5,47,0,0,2158,
- 2162,1,0,0,0,2159,2161,8,4,0,0,2160,2159,1,0,0,0,2161,2164,1,0,0,0,2162,
- 2160,1,0,0,0,2162,2163,1,0,0,0,2163,2169,1,0,0,0,2164,2162,1,0,0,0,2165,
- 2167,5,13,0,0,2166,2165,1,0,0,0,2166,2167,1,0,0,0,2167,2168,1,0,0,0,2168,
- 2170,5,10,0,0,2169,2166,1,0,0,0,2169,2170,1,0,0,0,2170,2183,1,0,0,0,2171,
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+ 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,
+ 5,114,0,0,1995,1996,5,116,0,0,1996,1997,5,40,0,0,1997,448,1,0,0,0,1998,
+ 1999,5,113,0,0,1999,2000,5,117,0,0,2000,2001,5,111,0,0,2001,2002,5,116,
+ 0,0,2002,2003,5,105,0,0,2003,2004,5,101,0,0,2004,2005,5,110,0,0,2005,2006,
+ 5,116,0,0,2006,2007,5,40,0,0,2007,450,1,0,0,0,2008,2009,5,100,0,0,2009,
+ 2010,5,111,0,0,2010,2011,5,109,0,0,2011,2012,5,97,0,0,2012,2013,5,105,
+ 0,0,2013,2014,5,110,0,0,2014,2015,5,40,0,0,2015,452,1,0,0,0,2016,2017,
+ 5,112,0,0,2017,2018,5,105,0,0,2018,2019,5,101,0,0,2019,2020,5,99,0,0,2020,
+ 2021,5,101,0,0,2021,2022,5,119,0,0,2022,2023,5,105,0,0,2023,2024,5,115,
+ 0,0,2024,2025,5,101,0,0,2025,2026,5,40,0,0,2026,454,1,0,0,0,2027,2028,
+ 5,97,0,0,2028,2029,5,112,0,0,2029,2030,5,112,0,0,2030,2031,5,108,0,0,2031,
+ 2032,5,121,0,0,2032,2033,5,40,0,0,2033,456,1,0,0,0,2034,2035,5,108,0,0,
+ 2035,2036,5,97,0,0,2036,2037,5,109,0,0,2037,2038,5,98,0,0,2038,2039,5,
+ 100,0,0,2039,2040,5,97,0,0,2040,2041,5,40,0,0,2041,458,1,0,0,0,2042,2044,
+ 5,13,0,0,2043,2042,1,0,0,0,2043,2044,1,0,0,0,2044,2045,1,0,0,0,2045,2047,
+ 5,10,0,0,2046,2043,1,0,0,0,2047,2048,1,0,0,0,2048,2046,1,0,0,0,2048,2049,
+ 1,0,0,0,2049,2050,1,0,0,0,2050,2051,6,229,0,0,2051,460,1,0,0,0,2052,2054,
+ 7,0,0,0,2053,2055,7,1,0,0,2054,2053,1,0,0,0,2054,2055,1,0,0,0,2055,2057,
+ 1,0,0,0,2056,2058,2,48,57,0,2057,2056,1,0,0,0,2058,2059,1,0,0,0,2059,2057,
+ 1,0,0,0,2059,2060,1,0,0,0,2060,462,1,0,0,0,2061,2063,2,48,57,0,2062,2061,
+ 1,0,0,0,2063,2064,1,0,0,0,2064,2062,1,0,0,0,2064,2065,1,0,0,0,2065,2066,
+ 1,0,0,0,2066,2070,5,46,0,0,2067,2069,2,48,57,0,2068,2067,1,0,0,0,2069,
+ 2072,1,0,0,0,2070,2068,1,0,0,0,2070,2071,1,0,0,0,2071,2074,1,0,0,0,2072,
+ 2070,1,0,0,0,2073,2075,3,461,230,0,2074,2073,1,0,0,0,2074,2075,1,0,0,0,
+ 2075,2077,1,0,0,0,2076,2078,5,105,0,0,2077,2076,1,0,0,0,2077,2078,1,0,
+ 0,0,2078,2095,1,0,0,0,2079,2081,5,46,0,0,2080,2079,1,0,0,0,2080,2081,1,
+ 0,0,0,2081,2083,1,0,0,0,2082,2084,2,48,57,0,2083,2082,1,0,0,0,2084,2085,
+ 1,0,0,0,2085,2083,1,0,0,0,2085,2086,1,0,0,0,2086,2088,1,0,0,0,2087,2089,
+ 3,461,230,0,2088,2087,1,0,0,0,2088,2089,1,0,0,0,2089,2091,1,0,0,0,2090,
+ 2092,5,105,0,0,2091,2090,1,0,0,0,2091,2092,1,0,0,0,2092,2095,1,0,0,0,2093,
+ 2095,5,105,0,0,2094,2062,1,0,0,0,2094,2080,1,0,0,0,2094,2093,1,0,0,0,2095,
+ 464,1,0,0,0,2096,2097,5,67,0,0,2097,2115,5,67,0,0,2098,2099,5,82,0,0,2099,
+ 2115,5,82,0,0,2100,2101,5,81,0,0,2101,2115,5,81,0,0,2102,2103,5,90,0,0,
+ 2103,2115,5,90,0,0,2104,2105,5,66,0,0,2105,2115,5,66,0,0,2106,2107,5,90,
+ 0,0,2107,2108,5,90,0,0,2108,2115,5,42,0,0,2109,2110,5,90,0,0,2110,2111,
+ 5,90,0,0,2111,2115,5,43,0,0,2112,2113,5,80,0,0,2113,2115,5,80,0,0,2114,
+ 2096,1,0,0,0,2114,2098,1,0,0,0,2114,2100,1,0,0,0,2114,2102,1,0,0,0,2114,
+ 2104,1,0,0,0,2114,2106,1,0,0,0,2114,2109,1,0,0,0,2114,2112,1,0,0,0,2115,
+ 466,1,0,0,0,2116,2117,5,116,0,0,2117,2118,5,114,0,0,2118,2119,5,117,0,
+ 0,2119,2135,5,101,0,0,2120,2121,5,84,0,0,2121,2122,5,114,0,0,2122,2123,
+ 5,117,0,0,2123,2135,5,101,0,0,2124,2125,5,102,0,0,2125,2126,5,97,0,0,2126,
+ 2127,5,108,0,0,2127,2128,5,115,0,0,2128,2135,5,101,0,0,2129,2130,5,70,
+ 0,0,2130,2131,5,97,0,0,2131,2132,5,108,0,0,2132,2133,5,115,0,0,2133,2135,
+ 5,101,0,0,2134,2116,1,0,0,0,2134,2120,1,0,0,0,2134,2124,1,0,0,0,2134,2129,
+ 1,0,0,0,2135,468,1,0,0,0,2136,2137,5,78,0,0,2137,2138,5,97,0,0,2138,2139,
+ 5,78,0,0,2139,470,1,0,0,0,2140,2142,7,2,0,0,2141,2140,1,0,0,0,2142,2143,
+ 1,0,0,0,2143,2141,1,0,0,0,2143,2144,1,0,0,0,2144,2153,1,0,0,0,2145,2147,
+ 5,95,0,0,2146,2148,7,3,0,0,2147,2146,1,0,0,0,2148,2149,1,0,0,0,2149,2147,
+ 1,0,0,0,2149,2150,1,0,0,0,2150,2152,1,0,0,0,2151,2145,1,0,0,0,2152,2155,
+ 1,0,0,0,2153,2151,1,0,0,0,2153,2154,1,0,0,0,2154,472,1,0,0,0,2155,2153,
+ 1,0,0,0,2156,2157,5,47,0,0,2157,2158,5,47,0,0,2158,2162,1,0,0,0,2159,2161,
+ 8,4,0,0,2160,2159,1,0,0,0,2161,2164,1,0,0,0,2162,2160,1,0,0,0,2162,2163,
+ 1,0,0,0,2163,2169,1,0,0,0,2164,2162,1,0,0,0,2165,2167,5,13,0,0,2166,2165,
+ 1,0,0,0,2166,2167,1,0,0,0,2167,2168,1,0,0,0,2168,2170,5,10,0,0,2169,2166,
+ 1,0,0,0,2169,2170,1,0,0,0,2170,2183,1,0,0,0,2171,2172,5,47,0,0,2172,2173,
+ 5,42,0,0,2173,2177,1,0,0,0,2174,2176,9,0,0,0,2175,2174,1,0,0,0,2176,2179,
+ 1,0,0,0,2177,2178,1,0,0,0,2177,2175,1,0,0,0,2178,2180,1,0,0,0,2179,2177,
+ 1,0,0,0,2180,2181,5,42,0,0,2181,2183,5,47,0,0,2182,2156,1,0,0,0,2182,2171,
+ 1,0,0,0,2183,2184,1,0,0,0,2184,2185,6,236,0,0,2185,474,1,0,0,0,2186,2188,
+ 7,5,0,0,2187,2186,1,0,0,0,2188,2189,1,0,0,0,2189,2187,1,0,0,0,2189,2190,
+ 1,0,0,0,2190,2191,1,0,0,0,2191,2192,6,237,0,0,2192,476,1,0,0,0,25,0,2043,
+ 2048,2054,2059,2064,2070,2074,2077,2080,2085,2088,2091,2094,2114,2134,
+ 2143,2149,2153,2162,2166,2169,2177,2182,2189,1,6,0,0
};
public static readonly ATN _ATN =
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
index 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, 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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]
\ 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()