diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md
index ea327e380..79fe4b478 100644
--- a/BREAKING-CHANGES.md
+++ b/BREAKING-CHANGES.md
@@ -867,6 +867,8 @@ prime, `17` ([#1450](https://github.com/asc-community/AngouriMath/issues/1450)).
| `"PP intersect [1; 30]".ToEntity().Evaled` | as written | `{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }` |
| `"min(ZZ+)".ToEntity().Evaled` | `ZZ+` | `1` |
| `"max(x, x in PP and x < 14)".ToEntity().Evaled` | as written | `13` |
+| `"prime(25)".ToEntity().Evaled` | `prime * 25` — juxtaposition of a variable `prime` | `97`; `prime(n)` is the `n`-th prime, `NaN` off the positive whole numbers |
+| `"valuation(12, 2)".ToEntity().Evaled` | `UnrecognizedFunctionParseException` | `2`; `valuation(n, p)` is the `p`-adic valuation, `+oo` at `0` and `NaN` off the primes |
### `binomial(n, k)` is a function
diff --git a/Sources/AngouriMath/Convenience/MathS.cs b/Sources/AngouriMath/Convenience/MathS.cs
index 5b3ef1069..2b6e2d01d 100644
--- a/Sources/AngouriMath/Convenience/MathS.cs
+++ b/Sources/AngouriMath/Convenience/MathS.cs
@@ -50,6 +50,40 @@ public static class NumberTheory
///
public static Entity Phi(Entity integer) => new Phif(integer);
+ ///
+ /// The n-th prime, prime(n): prime(1) is 2 and
+ /// prime(25) is 97. Defined on the positive whole numbers, and a
+ /// function rather than an operation on the set PP, which carries no order.
+ /// https://github.com/asc-community/AngouriMath/issues/1450
+ ///
+ ///
+ ///
+ /// Console.WriteLine(MathS.NumberTheory.Prime(25).Evaled);
+ ///
+ /// Prints
+ ///
+ /// 97
+ ///
+ ///
+ public static Entity Prime(Entity index) => new Primef(index);
+
+ ///
+ /// The p-adic valuation of a whole number, valuation(n, p): the exponent
+ /// of the prime p in n. valuation(12, 2) is 2,
+ /// valuation(12, 5) is 0, and at n = 0 it is +oo.
+ /// https://github.com/asc-community/AngouriMath/issues/1450
+ ///
+ ///
+ ///
+ /// Console.WriteLine(MathS.NumberTheory.Valuation(12, 2).Evaled);
+ ///
+ /// Prints
+ ///
+ /// 2
+ ///
+ ///
+ public static Entity Valuation(Entity argument, Entity prime) => new Valuationf(argument, prime);
+
///
/// The statement that divides ,
/// written a divides b: for integers, that b mod a = 0.
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g
index 0ecf6007b..3195045e8 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g
@@ -570,6 +570,8 @@ atom returns[Entity value]
| 'sign(' args = function_arguments ')' { Assert("sign", 1, $args.list.Count); $value = MathS.Signum($args.list[0]); }
| 'abs(' args = function_arguments ')' { Assert("abs", 1, $args.list.Count); $value = MathS.Abs($args.list[0]); }
| '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]); }
| '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)"); }
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
index 7bb6b6c5b..83c42d881 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
@@ -146,6 +146,8 @@ null
'sign('
'abs('
'phi('
+'prime('
+'valuation('
'card('
'powerset('
'union('
@@ -353,6 +355,8 @@ null
null
null
null
+null
+null
NEWLINE
NUMBER
SPECIALSET
@@ -392,4 +396,4 @@ statement
atn:
-[4, 1, 179, 1065, 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, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 60, 8, 0, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 66, 8, 1, 11, 1, 12, 1, 67, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 74, 8, 1, 11, 1, 12, 1, 75, 3, 1, 78, 8, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 85, 8, 2, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 3, 95, 8, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 3, 105, 8, 3, 1, 3, 1, 3, 1, 3, 3, 3, 110, 8, 3, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 3, 4, 120, 8, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 5, 4, 130, 8, 4, 10, 4, 12, 4, 133, 9, 4, 1, 4, 1, 4, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 3, 5, 145, 8, 5, 1, 5, 1, 5, 1, 5, 1, 5, 5, 5, 151, 8, 5, 10, 5, 12, 5, 154, 9, 5, 1, 5, 1, 5, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 5, 6, 168, 8, 6, 10, 6, 12, 6, 171, 9, 6, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 5, 7, 191, 8, 7, 10, 7, 12, 7, 194, 9, 7, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 5, 8, 226, 8, 8, 10, 8, 12, 8, 229, 9, 8, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 3, 9, 247, 8, 9, 1, 9, 1, 9, 1, 9, 5, 9, 252, 8, 9, 10, 9, 12, 9, 255, 9, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 3, 9, 263, 8, 9, 1, 9, 1, 9, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 3, 10, 282, 8, 10, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 5, 11, 294, 8, 11, 10, 11, 12, 11, 297, 9, 11, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 5, 12, 305, 8, 12, 10, 12, 12, 12, 308, 9, 12, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 5, 13, 316, 8, 13, 10, 13, 12, 13, 319, 9, 13, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 5, 14, 331, 8, 14, 10, 14, 12, 14, 334, 9, 14, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 1, 15, 3, 15, 342, 8, 15, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 3, 16, 350, 8, 16, 1, 16, 1, 16, 1, 16, 3, 16, 355, 8, 16, 1, 17, 1, 17, 1, 17, 1, 17, 1, 17, 1, 17, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 3, 18, 369, 8, 18, 1, 19, 1, 19, 1, 19, 1, 19, 1, 19, 1, 19, 5, 19, 377, 8, 19, 10, 19, 12, 19, 380, 9, 19, 1, 19, 1, 19, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 5, 20, 390, 8, 20, 10, 20, 12, 20, 393, 9, 20, 3, 20, 395, 8, 20, 1, 21, 1, 21, 1, 21, 1, 21, 1, 21, 3, 21, 402, 8, 21, 1, 21, 1, 21, 1, 21, 1, 21, 1, 21, 1, 21, 3, 21, 410, 8, 21, 5, 21, 412, 8, 21, 10, 21, 12, 21, 415, 9, 21, 3, 21, 417, 8, 21, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 22, 1, 23, 1, 23, 1, 23, 1, 23, 1, 23, 1, 23, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 24, 1, 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1069, 1, 0, 0, 0, 1063, 1064, 5, 173, 0, 0, 1064, 1065, 3, 40, 20, 0, 1065, 1066, 5, 31, 0, 0, 1066, 1067, 6, 24, -1, 0, 1067, 1069, 1, 0, 0, 0, 1068, 430, 1, 0, 0, 0, 1068, 432, 1, 0, 0, 0, 1068, 434, 1, 0, 0, 0, 1068, 436, 1, 0, 0, 0, 1068, 438, 1, 0, 0, 0, 1068, 440, 1, 0, 0, 0, 1068, 442, 1, 0, 0, 0, 1068, 444, 1, 0, 0, 0, 1068, 449, 1, 0, 0, 0, 1068, 453, 1, 0, 0, 0, 1068, 458, 1, 0, 0, 0, 1068, 463, 1, 0, 0, 0, 1068, 468, 1, 0, 0, 0, 1068, 473, 1, 0, 0, 0, 1068, 478, 1, 0, 0, 0, 1068, 483, 1, 0, 0, 0, 1068, 488, 1, 0, 0, 0, 1068, 493, 1, 0, 0, 0, 1068, 498, 1, 0, 0, 0, 1068, 503, 1, 0, 0, 0, 1068, 508, 1, 0, 0, 0, 1068, 513, 1, 0, 0, 0, 1068, 518, 1, 0, 0, 0, 1068, 523, 1, 0, 0, 0, 1068, 528, 1, 0, 0, 0, 1068, 533, 1, 0, 0, 0, 1068, 538, 1, 0, 0, 0, 1068, 543, 1, 0, 0, 0, 1068, 548, 1, 0, 0, 0, 1068, 553, 1, 0, 0, 0, 1068, 558, 1, 0, 0, 0, 1068, 563, 1, 0, 0, 0, 1068, 568, 1, 0, 0, 0, 1068, 573, 1, 0, 0, 0, 1068, 578, 1, 0, 0, 0, 1068, 583, 1, 0, 0, 0, 1068, 588, 1, 0, 0, 0, 1068, 593, 1, 0, 0, 0, 1068, 598, 1, 0, 0, 0, 1068, 603, 1, 0, 0, 0, 1068, 608, 1, 0, 0, 0, 1068, 613, 1, 0, 0, 0, 1068, 618, 1, 0, 0, 0, 1068, 623, 1, 0, 0, 0, 1068, 628, 1, 0, 0, 0, 1068, 633, 1, 0, 0, 0, 1068, 638, 1, 0, 0, 0, 1068, 643, 1, 0, 0, 0, 1068, 648, 1, 0, 0, 0, 1068, 653, 1, 0, 0, 0, 1068, 658, 1, 0, 0, 0, 1068, 663, 1, 0, 0, 0, 1068, 668, 1, 0, 0, 0, 1068, 673, 1, 0, 0, 0, 1068, 678, 1, 0, 0, 0, 1068, 683, 1, 0, 0, 0, 1068, 688, 1, 0, 0, 0, 1068, 693, 1, 0, 0, 0, 1068, 698, 1, 0, 0, 0, 1068, 703, 1, 0, 0, 0, 1068, 708, 1, 0, 0, 0, 1068, 713, 1, 0, 0, 0, 1068, 718, 1, 0, 0, 0, 1068, 723, 1, 0, 0, 0, 1068, 728, 1, 0, 0, 0, 1068, 733, 1, 0, 0, 0, 1068, 738, 1, 0, 0, 0, 1068, 743, 1, 0, 0, 0, 1068, 748, 1, 0, 0, 0, 1068, 753, 1, 0, 0, 0, 1068, 758, 1, 0, 0, 0, 1068, 763, 1, 0, 0, 0, 1068, 768, 1, 0, 0, 0, 1068, 773, 1, 0, 0, 0, 1068, 778, 1, 0, 0, 0, 1068, 783, 1, 0, 0, 0, 1068, 788, 1, 0, 0, 0, 1068, 793, 1, 0, 0, 0, 1068, 798, 1, 0, 0, 0, 1068, 803, 1, 0, 0, 0, 1068, 808, 1, 0, 0, 0, 1068, 813, 1, 0, 0, 0, 1068, 818, 1, 0, 0, 0, 1068, 823, 1, 0, 0, 0, 1068, 828, 1, 0, 0, 0, 1068, 833, 1, 0, 0, 0, 1068, 838, 1, 0, 0, 0, 1068, 843, 1, 0, 0, 0, 1068, 848, 1, 0, 0, 0, 1068, 853, 1, 0, 0, 0, 1068, 858, 1, 0, 0, 0, 1068, 863, 1, 0, 0, 0, 1068, 868, 1, 0, 0, 0, 1068, 873, 1, 0, 0, 0, 1068, 878, 1, 0, 0, 0, 1068, 883, 1, 0, 0, 0, 1068, 888, 1, 0, 0, 0, 1068, 893, 1, 0, 0, 0, 1068, 898, 1, 0, 0, 0, 1068, 903, 1, 0, 0, 0, 1068, 908, 1, 0, 0, 0, 1068, 913, 1, 0, 0, 0, 1068, 918, 1, 0, 0, 0, 1068, 923, 1, 0, 0, 0, 1068, 928, 1, 0, 0, 0, 1068, 933, 1, 0, 0, 0, 1068, 938, 1, 0, 0, 0, 1068, 943, 1, 0, 0, 0, 1068, 948, 1, 0, 0, 0, 1068, 953, 1, 0, 0, 0, 1068, 958, 1, 0, 0, 0, 1068, 963, 1, 0, 0, 0, 1068, 968, 1, 0, 0, 0, 1068, 973, 1, 0, 0, 0, 1068, 978, 1, 0, 0, 0, 1068, 983, 1, 0, 0, 0, 1068, 988, 1, 0, 0, 0, 1068, 993, 1, 0, 0, 0, 1068, 998, 1, 0, 0, 0, 1068, 1003, 1, 0, 0, 0, 1068, 1008, 1, 0, 0, 0, 1068, 1013, 1, 0, 0, 0, 1068, 1018, 1, 0, 0, 0, 1068, 1023, 1, 0, 0, 0, 1068, 1028, 1, 0, 0, 0, 1068, 1033, 1, 0, 0, 0, 1068, 1038, 1, 0, 0, 0, 1068, 1043, 1, 0, 0, 0, 1068, 1048, 1, 0, 0, 0, 1068, 1053, 1, 0, 0, 0, 1068, 1058, 1, 0, 0, 0, 1068, 1063, 1, 0, 0, 0, 1069, 49, 1, 0, 0, 0, 1070, 1071, 3, 32, 16, 0, 1071, 1072, 5, 0, 0, 1, 1072, 1073, 6, 25, -1, 0, 1073, 51, 1, 0, 0, 0, 42, 59, 67, 75, 77, 84, 94, 104, 109, 119, 129, 131, 144, 150, 152, 167, 169, 190, 192, 225, 227, 246, 253, 262, 281, 293, 295, 306, 317, 330, 332, 341, 349, 354, 368, 378, 391, 394, 401, 409, 413, 416, 1068]
\ No newline at end of file
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
index 574c17dbc..41379e333 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
@@ -169,14 +169,16 @@ T__167=168
T__168=169
T__169=170
T__170=171
-NEWLINE=172
-NUMBER=173
-SPECIALSET=174
-BOOLEAN=175
-NAN=176
-VARIABLE=177
-COMMENT=178
-WS=179
+T__171=172
+T__172=173
+NEWLINE=174
+NUMBER=175
+SPECIALSET=176
+BOOLEAN=177
+NAN=178
+VARIABLE=179
+COMMENT=180
+WS=181
'!'=1
'^'=2
'-'=3
@@ -323,29 +325,31 @@ WS=179
'sign('=144
'abs('=145
'phi('=146
-'card('=147
-'powerset('=148
-'union('=149
-'intersection('=150
-'complement('=151
-'image('=152
-'preimage('=153
-'floor('=154
-'ceil('=155
-'ceiling('=156
-'round('=157
-'min('=158
-'max('=159
-'argmax('=160
-'argmin('=161
-'gcd('=162
-'lcm('=163
-'binomial('=164
-'trunc('=165
-'erf('=166
-'conjugate('=167
-'domain('=168
-'piecewise('=169
-'apply('=170
-'lambda('=171
-'NaN'=176
+'prime('=147
+'valuation('=148
+'card('=149
+'powerset('=150
+'union('=151
+'intersection('=152
+'complement('=153
+'image('=154
+'preimage('=155
+'floor('=156
+'ceil('=157
+'ceiling('=158
+'round('=159
+'min('=160
+'max('=161
+'argmax('=162
+'argmin('=163
+'gcd('=164
+'lcm('=165
+'binomial('=166
+'trunc('=167
+'erf('=168
+'conjugate('=169
+'domain('=170
+'piecewise('=171
+'apply('=172
+'lambda('=173
+'NaN'=178
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
index 6430a2111..f8b780924 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
@@ -59,8 +59,9 @@ public const int
T__149=150, T__150=151, T__151=152, T__152=153, T__153=154, T__154=155,
T__155=156, T__156=157, T__157=158, T__158=159, T__159=160, T__160=161,
T__161=162, T__162=163, T__163=164, T__164=165, T__165=166, T__166=167,
- T__167=168, T__168=169, T__169=170, T__170=171, NEWLINE=172, NUMBER=173,
- SPECIALSET=174, BOOLEAN=175, NAN=176, VARIABLE=177, COMMENT=178, WS=179;
+ T__167=168, T__168=169, T__169=170, T__170=171, T__171=172, T__172=173,
+ NEWLINE=174, NUMBER=175, SPECIALSET=176, BOOLEAN=177, NAN=178, VARIABLE=179,
+ COMMENT=180, WS=181;
public static string[] channelNames = {
"DEFAULT_TOKEN_CHANNEL", "HIDDEN"
};
@@ -92,8 +93,8 @@ public const int
"T__147", "T__148", "T__149", "T__150", "T__151", "T__152", "T__153",
"T__154", "T__155", "T__156", "T__157", "T__158", "T__159", "T__160",
"T__161", "T__162", "T__163", "T__164", "T__165", "T__166", "T__167",
- "T__168", "T__169", "T__170", "NEWLINE", "EXPONENT", "NUMBER", "SPECIALSET",
- "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS"
+ "T__168", "T__169", "T__170", "T__171", "T__172", "NEWLINE", "EXPONENT",
+ "NUMBER", "SPECIALSET", "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS"
};
@@ -135,12 +136,12 @@ 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('", "'card('", "'powerset('", "'union('",
- "'intersection('", "'complement('", "'image('", "'preimage('", "'floor('",
- "'ceil('", "'ceiling('", "'round('", "'min('", "'max('", "'argmax('",
- "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'trunc('", "'erf('",
- "'conjugate('", "'domain('", "'piecewise('", "'apply('", "'lambda('",
- null, null, null, null, "'NaN'"
+ "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'card('",
+ "'powerset('", "'union('", "'intersection('", "'complement('", "'image('",
+ "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('",
+ "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('",
+ "'trunc('", "'erf('", "'conjugate('", "'domain('", "'piecewise('", "'apply('",
+ "'lambda('", null, null, null, null, "'NaN'"
};
private static readonly string[] _SymbolicNames = {
null, null, null, null, null, null, null, null, null, null, null, null,
@@ -157,8 +158,8 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu
null, null, null, null, null, null, null, null, null, null, null, null,
null, null, null, null, null, null, null, null, null, null, null, null,
null, null, null, null, null, null, null, null, null, null, null, null,
- null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN",
- "NAN", "VARIABLE", "COMMENT", "WS"
+ null, null, null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET",
+ "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS"
};
public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames);
@@ -188,7 +189,7 @@ static AngouriMathLexer() {
}
}
private static int[] _serializedATN = {
- 4,0,179,1539,6,-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,
+ 4,0,181,1561,6,-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,
@@ -215,507 +216,515 @@ static AngouriMathLexer() {
7,158,2,159,7,159,2,160,7,160,2,161,7,161,2,162,7,162,2,163,7,163,2,164,
7,164,2,165,7,165,2,166,7,166,2,167,7,167,2,168,7,168,2,169,7,169,2,170,
7,170,2,171,7,171,2,172,7,172,2,173,7,173,2,174,7,174,2,175,7,175,2,176,
- 7,176,2,177,7,177,2,178,7,178,2,179,7,179,1,0,1,0,1,1,1,1,1,2,1,2,1,3,
- 1,3,1,4,1,4,1,5,1,5,1,5,1,5,1,6,1,6,1,7,1,7,1,8,1,8,1,8,1,8,1,9,1,9,1,
- 9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,10,1,10,1,10,1,11,1,11,1,11,1,11,1,11,
- 1,11,1,12,1,12,1,12,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
- 1,13,1,13,1,14,1,14,1,15,1,15,1,15,1,16,1,16,1,16,1,16,1,16,1,16,1,16,
- 1,17,1,17,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,19,1,19,1,20,
- 1,20,1,20,1,20,1,20,1,20,1,20,1,20,1,21,1,21,1,22,1,22,1,22,1,23,1,23,
- 1,23,1,24,1,24,1,25,1,25,1,26,1,26,1,27,1,27,1,27,1,28,1,28,1,29,1,29,
- 1,30,1,30,1,31,1,31,1,31,1,31,1,32,1,32,1,32,1,32,1,33,1,33,1,34,1,34,
- 1,34,1,34,1,35,1,35,1,35,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,37,
- 1,37,1,37,1,38,1,38,1,38,1,38,1,38,1,38,1,38,1,38,1,38,1,39,1,39,1,39,
- 1,40,1,40,1,41,1,41,1,41,1,41,1,41,1,41,1,41,1,42,1,42,1,43,1,43,1,43,
- 1,43,1,43,1,43,1,43,1,43,1,44,1,44,1,44,1,45,1,45,1,45,1,45,1,45,1,45,
- 1,45,1,46,1,46,1,47,1,47,1,48,1,48,1,49,1,49,1,49,1,49,1,50,1,50,1,50,
- 1,50,1,51,1,51,1,51,1,52,1,52,1,52,1,53,1,53,1,54,1,54,1,55,1,55,1,55,
- 1,56,1,56,1,57,1,57,1,58,1,58,1,59,1,59,1,59,1,59,1,59,1,60,1,60,1,60,
- 1,60,1,60,1,60,1,60,1,61,1,61,1,61,1,61,1,61,1,61,1,62,1,62,1,62,1,62,
- 1,62,1,63,1,63,1,63,1,63,1,63,1,63,1,64,1,64,1,64,1,64,1,64,1,64,1,65,
- 1,65,1,65,1,65,1,65,1,66,1,66,1,66,1,66,1,67,1,67,1,67,1,67,1,67,1,68,
- 1,68,1,68,1,68,1,68,1,69,1,69,1,69,1,69,1,69,1,70,1,70,1,70,1,70,1,70,
- 1,71,1,71,1,71,1,71,1,71,1,71,1,71,1,72,1,72,1,72,1,72,1,72,1,73,1,73,
- 1,73,1,73,1,73,1,74,1,74,1,74,1,74,1,74,1,74,1,74,1,75,1,75,1,75,1,75,
- 1,75,1,76,1,76,1,76,1,76,1,76,1,76,1,76,1,76,1,77,1,77,1,77,1,77,1,77,
- 1,77,1,77,1,77,1,78,1,78,1,78,1,78,1,78,1,78,1,78,1,78,1,79,1,79,1,79,
- 1,79,1,79,1,79,1,79,1,79,1,79,1,79,1,80,1,80,1,80,1,80,1,80,1,80,1,80,
- 1,80,1,81,1,81,1,81,1,81,1,81,1,81,1,81,1,81,1,81,1,81,1,82,1,82,1,82,
- 1,82,1,82,1,82,1,82,1,82,1,83,1,83,1,83,1,83,1,83,1,83,1,84,1,84,1,84,
- 1,84,1,84,1,84,1,85,1,85,1,85,1,85,1,85,1,85,1,86,1,86,1,86,1,86,1,86,
- 1,86,1,87,1,87,1,87,1,87,1,87,1,87,1,87,1,87,1,88,1,88,1,88,1,88,1,88,
- 1,88,1,89,1,89,1,89,1,89,1,89,1,89,1,89,1,89,1,90,1,90,1,90,1,90,1,90,
- 1,90,1,91,1,91,1,91,1,91,1,91,1,91,1,91,1,91,1,92,1,92,1,92,1,92,1,92,
- 1,92,1,93,1,93,1,93,1,93,1,94,1,94,1,94,1,94,1,94,1,94,1,95,1,95,1,95,
- 1,95,1,96,1,96,1,96,1,96,1,96,1,96,1,97,1,97,1,97,1,97,1,98,1,98,1,98,
- 1,98,1,98,1,98,1,98,1,98,1,99,1,99,1,99,1,99,1,99,1,99,1,100,1,100,1,100,
- 1,100,1,100,1,101,1,101,1,101,1,101,1,101,1,101,1,102,1,102,1,102,1,102,
- 1,102,1,103,1,103,1,103,1,103,1,103,1,103,1,103,1,103,1,104,1,104,1,104,
- 1,104,1,104,1,104,1,105,1,105,1,105,1,105,1,105,1,105,1,105,1,106,1,106,
- 1,106,1,106,1,106,1,106,1,106,1,106,1,107,1,107,1,107,1,107,1,107,1,107,
- 1,108,1,108,1,108,1,108,1,108,1,108,1,108,1,108,1,108,1,109,1,109,1,109,
- 1,109,1,109,1,109,1,109,1,110,1,110,1,110,1,110,1,110,1,110,1,110,1,110,
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- 1,112,1,112,1,112,1,113,1,113,1,113,1,113,1,113,1,113,1,113,1,114,1,114,
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- 1,120,1,120,1,120,1,120,1,120,1,120,1,120,1,121,1,121,1,121,1,121,1,121,
- 1,121,1,121,1,122,1,122,1,122,1,122,1,122,1,122,1,122,1,122,1,122,1,122,
- 1,122,1,123,1,123,1,123,1,123,1,123,1,123,1,123,1,124,1,124,1,124,1,124,
- 1,124,1,124,1,124,1,124,1,125,1,125,1,125,1,125,1,125,1,125,1,125,1,126,
- 1,126,1,126,1,126,1,126,1,126,1,126,1,126,1,126,1,127,1,127,1,127,1,127,
- 1,127,1,127,1,127,1,127,1,127,1,128,1,128,1,128,1,128,1,128,1,128,1,128,
- 1,128,1,128,1,128,1,129,1,129,1,129,1,129,1,129,1,129,1,129,1,129,1,130,
- 1,130,1,130,1,130,1,130,1,130,1,130,1,130,1,130,1,130,1,130,1,131,1,131,
- 1,131,1,131,1,131,1,131,1,131,1,132,1,132,1,132,1,132,1,132,1,132,1,132,
- 1,132,1,132,1,132,1,132,1,133,1,133,1,133,1,133,1,133,1,133,1,133,1,134,
- 1,134,1,134,1,134,1,134,1,134,1,134,1,134,1,134,1,134,1,134,1,134,1,135,
- 1,135,1,135,1,135,1,135,1,135,1,135,1,135,1,135,1,135,1,136,1,136,1,136,
- 1,136,1,136,1,136,1,136,1,137,1,137,1,137,1,137,1,137,1,137,1,137,1,137,
- 1,137,1,137,1,137,1,138,1,138,1,138,1,138,1,138,1,138,1,138,1,138,1,138,
- 1,138,1,138,1,138,1,139,1,139,1,139,1,139,1,139,1,140,1,140,1,140,1,140,
- 1,140,1,140,1,140,1,140,1,140,1,141,1,141,1,141,1,141,1,141,1,141,1,141,
- 1,141,1,142,1,142,1,142,1,142,1,142,1,143,1,143,1,143,1,143,1,143,1,143,
- 1,144,1,144,1,144,1,144,1,144,1,145,1,145,1,145,1,145,1,145,1,146,1,146,
- 1,146,1,146,1,146,1,146,1,147,1,147,1,147,1,147,1,147,1,147,1,147,1,147,
- 1,147,1,147,1,148,1,148,1,148,1,148,1,148,1,148,1,148,1,149,1,149,1,149,
- 1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,149,1,150,
- 1,150,1,150,1,150,1,150,1,150,1,150,1,150,1,150,1,150,1,150,1,150,1,151,
- 1,151,1,151,1,151,1,151,1,151,1,151,1,152,1,152,1,152,1,152,1,152,1,152,
- 1,152,1,152,1,152,1,152,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,154,
- 1,154,1,154,1,154,1,154,1,154,1,155,1,155,1,155,1,155,1,155,1,155,1,155,
- 1,155,1,155,1,156,1,156,1,156,1,156,1,156,1,156,1,156,1,157,1,157,1,157,
- 1,157,1,157,1,158,1,158,1,158,1,158,1,158,1,159,1,159,1,159,1,159,1,159,
- 1,159,1,159,1,159,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,160,1,161,
- 1,161,1,161,1,161,1,161,1,162,1,162,1,162,1,162,1,162,1,163,1,163,1,163,
- 1,163,1,163,1,163,1,163,1,163,1,163,1,163,1,164,1,164,1,164,1,164,1,164,
- 1,164,1,164,1,165,1,165,1,165,1,165,1,165,1,166,1,166,1,166,1,166,1,166,
- 1,166,1,166,1,166,1,166,1,166,1,166,1,167,1,167,1,167,1,167,1,167,1,167,
- 1,167,1,167,1,168,1,168,1,168,1,168,1,168,1,168,1,168,1,168,1,168,1,168,
- 1,168,1,169,1,169,1,169,1,169,1,169,1,169,1,169,1,170,1,170,1,170,1,170,
- 1,170,1,170,1,170,1,170,1,171,3,171,1393,8,171,1,171,4,171,1396,8,171,
- 11,171,12,171,1397,1,171,1,171,1,172,1,172,3,172,1404,8,172,1,172,4,172,
- 1407,8,172,11,172,12,172,1408,1,173,4,173,1412,8,173,11,173,12,173,1413,
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- 8,173,1,173,3,173,1427,8,173,1,173,3,173,1430,8,173,1,173,4,173,1433,8,
- 173,11,173,12,173,1434,1,173,3,173,1438,8,173,1,173,3,173,1441,8,173,1,
- 173,3,173,1444,8,173,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,
- 174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174,3,174,1464,8,
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- 1,175,1,175,1,175,1,175,1,175,1,175,1,175,3,175,1484,8,175,1,176,1,176,
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- 6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,27,14,29,15,31,16,33,17,35,18,
- 37,19,39,20,41,21,43,22,45,23,47,24,49,25,51,26,53,27,55,28,57,29,59,30,
- 61,31,63,32,65,33,67,34,69,35,71,36,73,37,75,38,77,39,79,40,81,41,83,42,
- 85,43,87,44,89,45,91,46,93,47,95,48,97,49,99,50,101,51,103,52,105,53,107,
- 54,109,55,111,56,113,57,115,58,117,59,119,60,121,61,123,62,125,63,127,
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+ 5,40,0,0,1280,310,1,0,0,0,1281,1282,5,102,0,0,1282,1283,5,108,0,0,1283,
+ 1284,5,111,0,0,1284,1285,5,111,0,0,1285,1286,5,114,0,0,1286,1287,5,40,
+ 0,0,1287,312,1,0,0,0,1288,1289,5,99,0,0,1289,1290,5,101,0,0,1290,1291,
+ 5,105,0,0,1291,1292,5,108,0,0,1292,1293,5,40,0,0,1293,314,1,0,0,0,1294,
+ 1295,5,99,0,0,1295,1296,5,101,0,0,1296,1297,5,105,0,0,1297,1298,5,108,
+ 0,0,1298,1299,5,105,0,0,1299,1300,5,110,0,0,1300,1301,5,103,0,0,1301,1302,
+ 5,40,0,0,1302,316,1,0,0,0,1303,1304,5,114,0,0,1304,1305,5,111,0,0,1305,
+ 1306,5,117,0,0,1306,1307,5,110,0,0,1307,1308,5,100,0,0,1308,1309,5,40,
+ 0,0,1309,318,1,0,0,0,1310,1311,5,109,0,0,1311,1312,5,105,0,0,1312,1313,
+ 5,110,0,0,1313,1314,5,40,0,0,1314,320,1,0,0,0,1315,1316,5,109,0,0,1316,
+ 1317,5,97,0,0,1317,1318,5,120,0,0,1318,1319,5,40,0,0,1319,322,1,0,0,0,
+ 1320,1321,5,97,0,0,1321,1322,5,114,0,0,1322,1323,5,103,0,0,1323,1324,5,
+ 109,0,0,1324,1325,5,97,0,0,1325,1326,5,120,0,0,1326,1327,5,40,0,0,1327,
+ 324,1,0,0,0,1328,1329,5,97,0,0,1329,1330,5,114,0,0,1330,1331,5,103,0,0,
+ 1331,1332,5,109,0,0,1332,1333,5,105,0,0,1333,1334,5,110,0,0,1334,1335,
+ 5,40,0,0,1335,326,1,0,0,0,1336,1337,5,103,0,0,1337,1338,5,99,0,0,1338,
+ 1339,5,100,0,0,1339,1340,5,40,0,0,1340,328,1,0,0,0,1341,1342,5,108,0,0,
+ 1342,1343,5,99,0,0,1343,1344,5,109,0,0,1344,1345,5,40,0,0,1345,330,1,0,
+ 0,0,1346,1347,5,98,0,0,1347,1348,5,105,0,0,1348,1349,5,110,0,0,1349,1350,
+ 5,111,0,0,1350,1351,5,109,0,0,1351,1352,5,105,0,0,1352,1353,5,97,0,0,1353,
+ 1354,5,108,0,0,1354,1355,5,40,0,0,1355,332,1,0,0,0,1356,1357,5,116,0,0,
+ 1357,1358,5,114,0,0,1358,1359,5,117,0,0,1359,1360,5,110,0,0,1360,1361,
+ 5,99,0,0,1361,1362,5,40,0,0,1362,334,1,0,0,0,1363,1364,5,101,0,0,1364,
+ 1365,5,114,0,0,1365,1366,5,102,0,0,1366,1367,5,40,0,0,1367,336,1,0,0,0,
+ 1368,1369,5,99,0,0,1369,1370,5,111,0,0,1370,1371,5,110,0,0,1371,1372,5,
+ 106,0,0,1372,1373,5,117,0,0,1373,1374,5,103,0,0,1374,1375,5,97,0,0,1375,
+ 1376,5,116,0,0,1376,1377,5,101,0,0,1377,1378,5,40,0,0,1378,338,1,0,0,0,
+ 1379,1380,5,100,0,0,1380,1381,5,111,0,0,1381,1382,5,109,0,0,1382,1383,
+ 5,97,0,0,1383,1384,5,105,0,0,1384,1385,5,110,0,0,1385,1386,5,40,0,0,1386,
+ 340,1,0,0,0,1387,1388,5,112,0,0,1388,1389,5,105,0,0,1389,1390,5,101,0,
+ 0,1390,1391,5,99,0,0,1391,1392,5,101,0,0,1392,1393,5,119,0,0,1393,1394,
+ 5,105,0,0,1394,1395,5,115,0,0,1395,1396,5,101,0,0,1396,1397,5,40,0,0,1397,
+ 342,1,0,0,0,1398,1399,5,97,0,0,1399,1400,5,112,0,0,1400,1401,5,112,0,0,
+ 1401,1402,5,108,0,0,1402,1403,5,121,0,0,1403,1404,5,40,0,0,1404,344,1,
+ 0,0,0,1405,1406,5,108,0,0,1406,1407,5,97,0,0,1407,1408,5,109,0,0,1408,
+ 1409,5,98,0,0,1409,1410,5,100,0,0,1410,1411,5,97,0,0,1411,1412,5,40,0,
+ 0,1412,346,1,0,0,0,1413,1415,5,13,0,0,1414,1413,1,0,0,0,1414,1415,1,0,
+ 0,0,1415,1416,1,0,0,0,1416,1418,5,10,0,0,1417,1414,1,0,0,0,1418,1419,1,
+ 0,0,0,1419,1417,1,0,0,0,1419,1420,1,0,0,0,1420,1421,1,0,0,0,1421,1422,
+ 6,173,0,0,1422,348,1,0,0,0,1423,1425,7,0,0,0,1424,1426,7,1,0,0,1425,1424,
+ 1,0,0,0,1425,1426,1,0,0,0,1426,1428,1,0,0,0,1427,1429,2,48,57,0,1428,1427,
+ 1,0,0,0,1429,1430,1,0,0,0,1430,1428,1,0,0,0,1430,1431,1,0,0,0,1431,350,
+ 1,0,0,0,1432,1434,2,48,57,0,1433,1432,1,0,0,0,1434,1435,1,0,0,0,1435,1433,
+ 1,0,0,0,1435,1436,1,0,0,0,1436,1437,1,0,0,0,1437,1441,5,46,0,0,1438,1440,
+ 2,48,57,0,1439,1438,1,0,0,0,1440,1443,1,0,0,0,1441,1439,1,0,0,0,1441,1442,
+ 1,0,0,0,1442,1445,1,0,0,0,1443,1441,1,0,0,0,1444,1446,3,349,174,0,1445,
+ 1444,1,0,0,0,1445,1446,1,0,0,0,1446,1448,1,0,0,0,1447,1449,5,105,0,0,1448,
+ 1447,1,0,0,0,1448,1449,1,0,0,0,1449,1466,1,0,0,0,1450,1452,5,46,0,0,1451,
+ 1450,1,0,0,0,1451,1452,1,0,0,0,1452,1454,1,0,0,0,1453,1455,2,48,57,0,1454,
+ 1453,1,0,0,0,1455,1456,1,0,0,0,1456,1454,1,0,0,0,1456,1457,1,0,0,0,1457,
+ 1459,1,0,0,0,1458,1460,3,349,174,0,1459,1458,1,0,0,0,1459,1460,1,0,0,0,
+ 1460,1462,1,0,0,0,1461,1463,5,105,0,0,1462,1461,1,0,0,0,1462,1463,1,0,
+ 0,0,1463,1466,1,0,0,0,1464,1466,5,105,0,0,1465,1433,1,0,0,0,1465,1451,
+ 1,0,0,0,1465,1464,1,0,0,0,1466,352,1,0,0,0,1467,1468,5,67,0,0,1468,1486,
+ 5,67,0,0,1469,1470,5,82,0,0,1470,1486,5,82,0,0,1471,1472,5,81,0,0,1472,
+ 1486,5,81,0,0,1473,1474,5,90,0,0,1474,1486,5,90,0,0,1475,1476,5,66,0,0,
+ 1476,1486,5,66,0,0,1477,1478,5,90,0,0,1478,1479,5,90,0,0,1479,1486,5,42,
+ 0,0,1480,1481,5,90,0,0,1481,1482,5,90,0,0,1482,1486,5,43,0,0,1483,1484,
+ 5,80,0,0,1484,1486,5,80,0,0,1485,1467,1,0,0,0,1485,1469,1,0,0,0,1485,1471,
+ 1,0,0,0,1485,1473,1,0,0,0,1485,1475,1,0,0,0,1485,1477,1,0,0,0,1485,1480,
+ 1,0,0,0,1485,1483,1,0,0,0,1486,354,1,0,0,0,1487,1488,5,116,0,0,1488,1489,
+ 5,114,0,0,1489,1490,5,117,0,0,1490,1506,5,101,0,0,1491,1492,5,84,0,0,1492,
+ 1493,5,114,0,0,1493,1494,5,117,0,0,1494,1506,5,101,0,0,1495,1496,5,102,
+ 0,0,1496,1497,5,97,0,0,1497,1498,5,108,0,0,1498,1499,5,115,0,0,1499,1506,
+ 5,101,0,0,1500,1501,5,70,0,0,1501,1502,5,97,0,0,1502,1503,5,108,0,0,1503,
+ 1504,5,115,0,0,1504,1506,5,101,0,0,1505,1487,1,0,0,0,1505,1491,1,0,0,0,
+ 1505,1495,1,0,0,0,1505,1500,1,0,0,0,1506,356,1,0,0,0,1507,1508,5,78,0,
+ 0,1508,1509,5,97,0,0,1509,1510,5,78,0,0,1510,358,1,0,0,0,1511,1513,7,2,
+ 0,0,1512,1511,1,0,0,0,1513,1514,1,0,0,0,1514,1512,1,0,0,0,1514,1515,1,
+ 0,0,0,1515,1522,1,0,0,0,1516,1518,5,95,0,0,1517,1519,7,3,0,0,1518,1517,
+ 1,0,0,0,1519,1520,1,0,0,0,1520,1518,1,0,0,0,1520,1521,1,0,0,0,1521,1523,
+ 1,0,0,0,1522,1516,1,0,0,0,1522,1523,1,0,0,0,1523,360,1,0,0,0,1524,1525,
+ 5,47,0,0,1525,1526,5,47,0,0,1526,1530,1,0,0,0,1527,1529,8,4,0,0,1528,1527,
+ 1,0,0,0,1529,1532,1,0,0,0,1530,1528,1,0,0,0,1530,1531,1,0,0,0,1531,1537,
+ 1,0,0,0,1532,1530,1,0,0,0,1533,1535,5,13,0,0,1534,1533,1,0,0,0,1534,1535,
+ 1,0,0,0,1535,1536,1,0,0,0,1536,1538,5,10,0,0,1537,1534,1,0,0,0,1537,1538,
+ 1,0,0,0,1538,1551,1,0,0,0,1539,1540,5,47,0,0,1540,1541,5,42,0,0,1541,1545,
+ 1,0,0,0,1542,1544,9,0,0,0,1543,1542,1,0,0,0,1544,1547,1,0,0,0,1545,1546,
+ 1,0,0,0,1545,1543,1,0,0,0,1546,1548,1,0,0,0,1547,1545,1,0,0,0,1548,1549,
+ 5,42,0,0,1549,1551,5,47,0,0,1550,1524,1,0,0,0,1550,1539,1,0,0,0,1551,1552,
+ 1,0,0,0,1552,1553,6,180,0,0,1553,362,1,0,0,0,1554,1556,7,5,0,0,1555,1554,
+ 1,0,0,0,1556,1557,1,0,0,0,1557,1555,1,0,0,0,1557,1558,1,0,0,0,1558,1559,
+ 1,0,0,0,1559,1560,6,181,0,0,1560,364,1,0,0,0,25,0,1414,1419,1425,1430,
+ 1435,1441,1445,1448,1451,1456,1459,1462,1465,1485,1505,1514,1520,1522,
+ 1530,1534,1537,1545,1550,1557,1,6,0,0
};
public static readonly ATN _ATN =
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
index 3be9d3165..b3111f937 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
@@ -146,6 +146,8 @@ null
'sign('
'abs('
'phi('
+'prime('
+'valuation('
'card('
'powerset('
'union('
@@ -353,6 +355,8 @@ null
null
null
null
+null
+null
NEWLINE
NUMBER
SPECIALSET
@@ -534,6 +538,8 @@ T__167
T__168
T__169
T__170
+T__171
+T__172
NEWLINE
EXPONENT
NUMBER
@@ -552,4 +558,4 @@ mode names:
DEFAULT_MODE
atn:
-[4, 0, 179, 1539, 6, -1, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 2, 6, 7, 6, 2, 7, 7, 7, 2, 8, 7, 8, 2, 9, 7, 9, 2, 10, 7, 10, 2, 11, 7, 11, 2, 12, 7, 12, 2, 13, 7, 13, 2, 14, 7, 14, 2, 15, 7, 15, 2, 16, 7, 16, 2, 17, 7, 17, 2, 18, 7, 18, 2, 19, 7, 19, 2, 20, 7, 20, 2, 21, 7, 21, 2, 22, 7, 22, 2, 23, 7, 23, 2, 24, 7, 24, 2, 25, 7, 25, 2, 26, 7, 26, 2, 27, 7, 27, 2, 28, 7, 28, 2, 29, 7, 29, 2, 30, 7, 30, 2, 31, 7, 31, 2, 32, 7, 32, 2, 33, 7, 33, 2, 34, 7, 34, 2, 35, 7, 35, 2, 36, 7, 36, 2, 37, 7, 37, 2, 38, 7, 38, 2, 39, 7, 39, 2, 40, 7, 40, 2, 41, 7, 41, 2, 42, 7, 42, 2, 43, 7, 43, 2, 44, 7, 44, 2, 45, 7, 45, 2, 46, 7, 46, 2, 47, 7, 47, 2, 48, 7, 48, 2, 49, 7, 49, 2, 50, 7, 50, 2, 51, 7, 51, 2, 52, 7, 52, 2, 53, 7, 53, 2, 54, 7, 54, 2, 55, 7, 55, 2, 56, 7, 56, 2, 57, 7, 57, 2, 58, 7, 58, 2, 59, 7, 59, 2, 60, 7, 60, 2, 61, 7, 61, 2, 62, 7, 62, 2, 63, 7, 63, 2, 64, 7, 64, 2, 65, 7, 65, 2, 66, 7, 66, 2, 67, 7, 67, 2, 68, 7, 68, 2, 69, 7, 69, 2, 70, 7, 70, 2, 71, 7, 71, 2, 72, 7, 72, 2, 73, 7, 73, 2, 74, 7, 74, 2, 75, 7, 75, 2, 76, 7, 76, 2, 77, 7, 77, 2, 78, 7, 78, 2, 79, 7, 79, 2, 80, 7, 80, 2, 81, 7, 81, 2, 82, 7, 82, 2, 83, 7, 83, 2, 84, 7, 84, 2, 85, 7, 85, 2, 86, 7, 86, 2, 87, 7, 87, 2, 88, 7, 88, 2, 89, 7, 89, 2, 90, 7, 90, 2, 91, 7, 91, 2, 92, 7, 92, 2, 93, 7, 93, 2, 94, 7, 94, 2, 95, 7, 95, 2, 96, 7, 96, 2, 97, 7, 97, 2, 98, 7, 98, 2, 99, 7, 99, 2, 100, 7, 100, 2, 101, 7, 101, 2, 102, 7, 102, 2, 103, 7, 103, 2, 104, 7, 104, 2, 105, 7, 105, 2, 106, 7, 106, 2, 107, 7, 107, 2, 108, 7, 108, 2, 109, 7, 109, 2, 110, 7, 110, 2, 111, 7, 111, 2, 112, 7, 112, 2, 113, 7, 113, 2, 114, 7, 114, 2, 115, 7, 115, 2, 116, 7, 116, 2, 117, 7, 117, 2, 118, 7, 118, 2, 119, 7, 119, 2, 120, 7, 120, 2, 121, 7, 121, 2, 122, 7, 122, 2, 123, 7, 123, 2, 124, 7, 124, 2, 125, 7, 125, 2, 126, 7, 126, 2, 127, 7, 127, 2, 128, 7, 128, 2, 129, 7, 129, 2, 130, 7, 130, 2, 131, 7, 131, 2, 132, 7, 132, 2, 133, 7, 133, 2, 134, 7, 134, 2, 135, 7, 135, 2, 136, 7, 136, 2, 137, 7, 137, 2, 138, 7, 138, 2, 139, 7, 139, 2, 140, 7, 140, 2, 141, 7, 141, 2, 142, 7, 142, 2, 143, 7, 143, 2, 144, 7, 144, 2, 145, 7, 145, 2, 146, 7, 146, 2, 147, 7, 147, 2, 148, 7, 148, 2, 149, 7, 149, 2, 150, 7, 150, 2, 151, 7, 151, 2, 152, 7, 152, 2, 153, 7, 153, 2, 154, 7, 154, 2, 155, 7, 155, 2, 156, 7, 156, 2, 157, 7, 157, 2, 158, 7, 158, 2, 159, 7, 159, 2, 160, 7, 160, 2, 161, 7, 161, 2, 162, 7, 162, 2, 163, 7, 163, 2, 164, 7, 164, 2, 165, 7, 165, 2, 166, 7, 166, 2, 167, 7, 167, 2, 168, 7, 168, 2, 169, 7, 169, 2, 170, 7, 170, 2, 171, 7, 171, 2, 172, 7, 172, 2, 173, 7, 173, 2, 174, 7, 174, 2, 175, 7, 175, 2, 176, 7, 176, 2, 177, 7, 177, 2, 178, 7, 178, 2, 179, 7, 179, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 8, 1, 8, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 12, 1, 12, 1, 12, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 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1189, 1190, 5, 115, 0, 0, 1190, 1191, 5, 40, 0, 0, 1191, 290, 1, 0, 0, 0, 1192, 1193, 5, 112, 0, 0, 1193, 1194, 5, 104, 0, 0, 1194, 1195, 5, 105, 0, 0, 1195, 1196, 5, 40, 0, 0, 1196, 292, 1, 0, 0, 0, 1197, 1198, 5, 112, 0, 0, 1198, 1199, 5, 114, 0, 0, 1199, 1200, 5, 105, 0, 0, 1200, 1201, 5, 109, 0, 0, 1201, 1202, 5, 101, 0, 0, 1202, 1203, 5, 40, 0, 0, 1203, 294, 1, 0, 0, 0, 1204, 1205, 5, 118, 0, 0, 1205, 1206, 5, 97, 0, 0, 1206, 1207, 5, 108, 0, 0, 1207, 1208, 5, 117, 0, 0, 1208, 1209, 5, 97, 0, 0, 1209, 1210, 5, 116, 0, 0, 1210, 1211, 5, 105, 0, 0, 1211, 1212, 5, 111, 0, 0, 1212, 1213, 5, 110, 0, 0, 1213, 1214, 5, 40, 0, 0, 1214, 296, 1, 0, 0, 0, 1215, 1216, 5, 99, 0, 0, 1216, 1217, 5, 97, 0, 0, 1217, 1218, 5, 114, 0, 0, 1218, 1219, 5, 100, 0, 0, 1219, 1220, 5, 40, 0, 0, 1220, 298, 1, 0, 0, 0, 1221, 1222, 5, 112, 0, 0, 1222, 1223, 5, 111, 0, 0, 1223, 1224, 5, 119, 0, 0, 1224, 1225, 5, 101, 0, 0, 1225, 1226, 5, 114, 0, 0, 1226, 1227, 5, 115, 0, 0, 1227, 1228, 5, 101, 0, 0, 1228, 1229, 5, 116, 0, 0, 1229, 1230, 5, 40, 0, 0, 1230, 300, 1, 0, 0, 0, 1231, 1232, 5, 117, 0, 0, 1232, 1233, 5, 110, 0, 0, 1233, 1234, 5, 105, 0, 0, 1234, 1235, 5, 111, 0, 0, 1235, 1236, 5, 110, 0, 0, 1236, 1237, 5, 40, 0, 0, 1237, 302, 1, 0, 0, 0, 1238, 1239, 5, 105, 0, 0, 1239, 1240, 5, 110, 0, 0, 1240, 1241, 5, 116, 0, 0, 1241, 1242, 5, 101, 0, 0, 1242, 1243, 5, 114, 0, 0, 1243, 1244, 5, 115, 0, 0, 1244, 1245, 5, 101, 0, 0, 1245, 1246, 5, 99, 0, 0, 1246, 1247, 5, 116, 0, 0, 1247, 1248, 5, 105, 0, 0, 1248, 1249, 5, 111, 0, 0, 1249, 1250, 5, 110, 0, 0, 1250, 1251, 5, 40, 0, 0, 1251, 304, 1, 0, 0, 0, 1252, 1253, 5, 99, 0, 0, 1253, 1254, 5, 111, 0, 0, 1254, 1255, 5, 109, 0, 0, 1255, 1256, 5, 112, 0, 0, 1256, 1257, 5, 108, 0, 0, 1257, 1258, 5, 101, 0, 0, 1258, 1259, 5, 109, 0, 0, 1259, 1260, 5, 101, 0, 0, 1260, 1261, 5, 110, 0, 0, 1261, 1262, 5, 116, 0, 0, 1262, 1263, 5, 40, 0, 0, 1263, 306, 1, 0, 0, 0, 1264, 1265, 5, 105, 0, 0, 1265, 1266, 5, 109, 0, 0, 1266, 1267, 5, 97, 0, 0, 1267, 1268, 5, 103, 0, 0, 1268, 1269, 5, 101, 0, 0, 1269, 1270, 5, 40, 0, 0, 1270, 308, 1, 0, 0, 0, 1271, 1272, 5, 112, 0, 0, 1272, 1273, 5, 114, 0, 0, 1273, 1274, 5, 101, 0, 0, 1274, 1275, 5, 105, 0, 0, 1275, 1276, 5, 109, 0, 0, 1276, 1277, 5, 97, 0, 0, 1277, 1278, 5, 103, 0, 0, 1278, 1279, 5, 101, 0, 0, 1279, 1280, 5, 40, 0, 0, 1280, 310, 1, 0, 0, 0, 1281, 1282, 5, 102, 0, 0, 1282, 1283, 5, 108, 0, 0, 1283, 1284, 5, 111, 0, 0, 1284, 1285, 5, 111, 0, 0, 1285, 1286, 5, 114, 0, 0, 1286, 1287, 5, 40, 0, 0, 1287, 312, 1, 0, 0, 0, 1288, 1289, 5, 99, 0, 0, 1289, 1290, 5, 101, 0, 0, 1290, 1291, 5, 105, 0, 0, 1291, 1292, 5, 108, 0, 0, 1292, 1293, 5, 40, 0, 0, 1293, 314, 1, 0, 0, 0, 1294, 1295, 5, 99, 0, 0, 1295, 1296, 5, 101, 0, 0, 1296, 1297, 5, 105, 0, 0, 1297, 1298, 5, 108, 0, 0, 1298, 1299, 5, 105, 0, 0, 1299, 1300, 5, 110, 0, 0, 1300, 1301, 5, 103, 0, 0, 1301, 1302, 5, 40, 0, 0, 1302, 316, 1, 0, 0, 0, 1303, 1304, 5, 114, 0, 0, 1304, 1305, 5, 111, 0, 0, 1305, 1306, 5, 117, 0, 0, 1306, 1307, 5, 110, 0, 0, 1307, 1308, 5, 100, 0, 0, 1308, 1309, 5, 40, 0, 0, 1309, 318, 1, 0, 0, 0, 1310, 1311, 5, 109, 0, 0, 1311, 1312, 5, 105, 0, 0, 1312, 1313, 5, 110, 0, 0, 1313, 1314, 5, 40, 0, 0, 1314, 320, 1, 0, 0, 0, 1315, 1316, 5, 109, 0, 0, 1316, 1317, 5, 97, 0, 0, 1317, 1318, 5, 120, 0, 0, 1318, 1319, 5, 40, 0, 0, 1319, 322, 1, 0, 0, 0, 1320, 1321, 5, 97, 0, 0, 1321, 1322, 5, 114, 0, 0, 1322, 1323, 5, 103, 0, 0, 1323, 1324, 5, 109, 0, 0, 1324, 1325, 5, 97, 0, 0, 1325, 1326, 5, 120, 0, 0, 1326, 1327, 5, 40, 0, 0, 1327, 324, 1, 0, 0, 0, 1328, 1329, 5, 97, 0, 0, 1329, 1330, 5, 114, 0, 0, 1330, 1331, 5, 103, 0, 0, 1331, 1332, 5, 109, 0, 0, 1332, 1333, 5, 105, 0, 0, 1333, 1334, 5, 110, 0, 0, 1334, 1335, 5, 40, 0, 0, 1335, 326, 1, 0, 0, 0, 1336, 1337, 5, 103, 0, 0, 1337, 1338, 5, 99, 0, 0, 1338, 1339, 5, 100, 0, 0, 1339, 1340, 5, 40, 0, 0, 1340, 328, 1, 0, 0, 0, 1341, 1342, 5, 108, 0, 0, 1342, 1343, 5, 99, 0, 0, 1343, 1344, 5, 109, 0, 0, 1344, 1345, 5, 40, 0, 0, 1345, 330, 1, 0, 0, 0, 1346, 1347, 5, 98, 0, 0, 1347, 1348, 5, 105, 0, 0, 1348, 1349, 5, 110, 0, 0, 1349, 1350, 5, 111, 0, 0, 1350, 1351, 5, 109, 0, 0, 1351, 1352, 5, 105, 0, 0, 1352, 1353, 5, 97, 0, 0, 1353, 1354, 5, 108, 0, 0, 1354, 1355, 5, 40, 0, 0, 1355, 332, 1, 0, 0, 0, 1356, 1357, 5, 116, 0, 0, 1357, 1358, 5, 114, 0, 0, 1358, 1359, 5, 117, 0, 0, 1359, 1360, 5, 110, 0, 0, 1360, 1361, 5, 99, 0, 0, 1361, 1362, 5, 40, 0, 0, 1362, 334, 1, 0, 0, 0, 1363, 1364, 5, 101, 0, 0, 1364, 1365, 5, 114, 0, 0, 1365, 1366, 5, 102, 0, 0, 1366, 1367, 5, 40, 0, 0, 1367, 336, 1, 0, 0, 0, 1368, 1369, 5, 99, 0, 0, 1369, 1370, 5, 111, 0, 0, 1370, 1371, 5, 110, 0, 0, 1371, 1372, 5, 106, 0, 0, 1372, 1373, 5, 117, 0, 0, 1373, 1374, 5, 103, 0, 0, 1374, 1375, 5, 97, 0, 0, 1375, 1376, 5, 116, 0, 0, 1376, 1377, 5, 101, 0, 0, 1377, 1378, 5, 40, 0, 0, 1378, 338, 1, 0, 0, 0, 1379, 1380, 5, 100, 0, 0, 1380, 1381, 5, 111, 0, 0, 1381, 1382, 5, 109, 0, 0, 1382, 1383, 5, 97, 0, 0, 1383, 1384, 5, 105, 0, 0, 1384, 1385, 5, 110, 0, 0, 1385, 1386, 5, 40, 0, 0, 1386, 340, 1, 0, 0, 0, 1387, 1388, 5, 112, 0, 0, 1388, 1389, 5, 105, 0, 0, 1389, 1390, 5, 101, 0, 0, 1390, 1391, 5, 99, 0, 0, 1391, 1392, 5, 101, 0, 0, 1392, 1393, 5, 119, 0, 0, 1393, 1394, 5, 105, 0, 0, 1394, 1395, 5, 115, 0, 0, 1395, 1396, 5, 101, 0, 0, 1396, 1397, 5, 40, 0, 0, 1397, 342, 1, 0, 0, 0, 1398, 1399, 5, 97, 0, 0, 1399, 1400, 5, 112, 0, 0, 1400, 1401, 5, 112, 0, 0, 1401, 1402, 5, 108, 0, 0, 1402, 1403, 5, 121, 0, 0, 1403, 1404, 5, 40, 0, 0, 1404, 344, 1, 0, 0, 0, 1405, 1406, 5, 108, 0, 0, 1406, 1407, 5, 97, 0, 0, 1407, 1408, 5, 109, 0, 0, 1408, 1409, 5, 98, 0, 0, 1409, 1410, 5, 100, 0, 0, 1410, 1411, 5, 97, 0, 0, 1411, 1412, 5, 40, 0, 0, 1412, 346, 1, 0, 0, 0, 1413, 1415, 5, 13, 0, 0, 1414, 1413, 1, 0, 0, 0, 1414, 1415, 1, 0, 0, 0, 1415, 1416, 1, 0, 0, 0, 1416, 1418, 5, 10, 0, 0, 1417, 1414, 1, 0, 0, 0, 1418, 1419, 1, 0, 0, 0, 1419, 1417, 1, 0, 0, 0, 1419, 1420, 1, 0, 0, 0, 1420, 1421, 1, 0, 0, 0, 1421, 1422, 6, 173, 0, 0, 1422, 348, 1, 0, 0, 0, 1423, 1425, 7, 0, 0, 0, 1424, 1426, 7, 1, 0, 0, 1425, 1424, 1, 0, 0, 0, 1425, 1426, 1, 0, 0, 0, 1426, 1428, 1, 0, 0, 0, 1427, 1429, 2, 48, 57, 0, 1428, 1427, 1, 0, 0, 0, 1429, 1430, 1, 0, 0, 0, 1430, 1428, 1, 0, 0, 0, 1430, 1431, 1, 0, 0, 0, 1431, 350, 1, 0, 0, 0, 1432, 1434, 2, 48, 57, 0, 1433, 1432, 1, 0, 0, 0, 1434, 1435, 1, 0, 0, 0, 1435, 1433, 1, 0, 0, 0, 1435, 1436, 1, 0, 0, 0, 1436, 1437, 1, 0, 0, 0, 1437, 1441, 5, 46, 0, 0, 1438, 1440, 2, 48, 57, 0, 1439, 1438, 1, 0, 0, 0, 1440, 1443, 1, 0, 0, 0, 1441, 1439, 1, 0, 0, 0, 1441, 1442, 1, 0, 0, 0, 1442, 1445, 1, 0, 0, 0, 1443, 1441, 1, 0, 0, 0, 1444, 1446, 3, 349, 174, 0, 1445, 1444, 1, 0, 0, 0, 1445, 1446, 1, 0, 0, 0, 1446, 1448, 1, 0, 0, 0, 1447, 1449, 5, 105, 0, 0, 1448, 1447, 1, 0, 0, 0, 1448, 1449, 1, 0, 0, 0, 1449, 1466, 1, 0, 0, 0, 1450, 1452, 5, 46, 0, 0, 1451, 1450, 1, 0, 0, 0, 1451, 1452, 1, 0, 0, 0, 1452, 1454, 1, 0, 0, 0, 1453, 1455, 2, 48, 57, 0, 1454, 1453, 1, 0, 0, 0, 1455, 1456, 1, 0, 0, 0, 1456, 1454, 1, 0, 0, 0, 1456, 1457, 1, 0, 0, 0, 1457, 1459, 1, 0, 0, 0, 1458, 1460, 3, 349, 174, 0, 1459, 1458, 1, 0, 0, 0, 1459, 1460, 1, 0, 0, 0, 1460, 1462, 1, 0, 0, 0, 1461, 1463, 5, 105, 0, 0, 1462, 1461, 1, 0, 0, 0, 1462, 1463, 1, 0, 0, 0, 1463, 1466, 1, 0, 0, 0, 1464, 1466, 5, 105, 0, 0, 1465, 1433, 1, 0, 0, 0, 1465, 1451, 1, 0, 0, 0, 1465, 1464, 1, 0, 0, 0, 1466, 352, 1, 0, 0, 0, 1467, 1468, 5, 67, 0, 0, 1468, 1486, 5, 67, 0, 0, 1469, 1470, 5, 82, 0, 0, 1470, 1486, 5, 82, 0, 0, 1471, 1472, 5, 81, 0, 0, 1472, 1486, 5, 81, 0, 0, 1473, 1474, 5, 90, 0, 0, 1474, 1486, 5, 90, 0, 0, 1475, 1476, 5, 66, 0, 0, 1476, 1486, 5, 66, 0, 0, 1477, 1478, 5, 90, 0, 0, 1478, 1479, 5, 90, 0, 0, 1479, 1486, 5, 42, 0, 0, 1480, 1481, 5, 90, 0, 0, 1481, 1482, 5, 90, 0, 0, 1482, 1486, 5, 43, 0, 0, 1483, 1484, 5, 80, 0, 0, 1484, 1486, 5, 80, 0, 0, 1485, 1467, 1, 0, 0, 0, 1485, 1469, 1, 0, 0, 0, 1485, 1471, 1, 0, 0, 0, 1485, 1473, 1, 0, 0, 0, 1485, 1475, 1, 0, 0, 0, 1485, 1477, 1, 0, 0, 0, 1485, 1480, 1, 0, 0, 0, 1485, 1483, 1, 0, 0, 0, 1486, 354, 1, 0, 0, 0, 1487, 1488, 5, 116, 0, 0, 1488, 1489, 5, 114, 0, 0, 1489, 1490, 5, 117, 0, 0, 1490, 1506, 5, 101, 0, 0, 1491, 1492, 5, 84, 0, 0, 1492, 1493, 5, 114, 0, 0, 1493, 1494, 5, 117, 0, 0, 1494, 1506, 5, 101, 0, 0, 1495, 1496, 5, 102, 0, 0, 1496, 1497, 5, 97, 0, 0, 1497, 1498, 5, 108, 0, 0, 1498, 1499, 5, 115, 0, 0, 1499, 1506, 5, 101, 0, 0, 1500, 1501, 5, 70, 0, 0, 1501, 1502, 5, 97, 0, 0, 1502, 1503, 5, 108, 0, 0, 1503, 1504, 5, 115, 0, 0, 1504, 1506, 5, 101, 0, 0, 1505, 1487, 1, 0, 0, 0, 1505, 1491, 1, 0, 0, 0, 1505, 1495, 1, 0, 0, 0, 1505, 1500, 1, 0, 0, 0, 1506, 356, 1, 0, 0, 0, 1507, 1508, 5, 78, 0, 0, 1508, 1509, 5, 97, 0, 0, 1509, 1510, 5, 78, 0, 0, 1510, 358, 1, 0, 0, 0, 1511, 1513, 7, 2, 0, 0, 1512, 1511, 1, 0, 0, 0, 1513, 1514, 1, 0, 0, 0, 1514, 1512, 1, 0, 0, 0, 1514, 1515, 1, 0, 0, 0, 1515, 1522, 1, 0, 0, 0, 1516, 1518, 5, 95, 0, 0, 1517, 1519, 7, 3, 0, 0, 1518, 1517, 1, 0, 0, 0, 1519, 1520, 1, 0, 0, 0, 1520, 1518, 1, 0, 0, 0, 1520, 1521, 1, 0, 0, 0, 1521, 1523, 1, 0, 0, 0, 1522, 1516, 1, 0, 0, 0, 1522, 1523, 1, 0, 0, 0, 1523, 360, 1, 0, 0, 0, 1524, 1525, 5, 47, 0, 0, 1525, 1526, 5, 47, 0, 0, 1526, 1530, 1, 0, 0, 0, 1527, 1529, 8, 4, 0, 0, 1528, 1527, 1, 0, 0, 0, 1529, 1532, 1, 0, 0, 0, 1530, 1528, 1, 0, 0, 0, 1530, 1531, 1, 0, 0, 0, 1531, 1537, 1, 0, 0, 0, 1532, 1530, 1, 0, 0, 0, 1533, 1535, 5, 13, 0, 0, 1534, 1533, 1, 0, 0, 0, 1534, 1535, 1, 0, 0, 0, 1535, 1536, 1, 0, 0, 0, 1536, 1538, 5, 10, 0, 0, 1537, 1534, 1, 0, 0, 0, 1537, 1538, 1, 0, 0, 0, 1538, 1551, 1, 0, 0, 0, 1539, 1540, 5, 47, 0, 0, 1540, 1541, 5, 42, 0, 0, 1541, 1545, 1, 0, 0, 0, 1542, 1544, 9, 0, 0, 0, 1543, 1542, 1, 0, 0, 0, 1544, 1547, 1, 0, 0, 0, 1545, 1546, 1, 0, 0, 0, 1545, 1543, 1, 0, 0, 0, 1546, 1548, 1, 0, 0, 0, 1547, 1545, 1, 0, 0, 0, 1548, 1549, 5, 42, 0, 0, 1549, 1551, 5, 47, 0, 0, 1550, 1524, 1, 0, 0, 0, 1550, 1539, 1, 0, 0, 0, 1551, 1552, 1, 0, 0, 0, 1552, 1553, 6, 180, 0, 0, 1553, 362, 1, 0, 0, 0, 1554, 1556, 7, 5, 0, 0, 1555, 1554, 1, 0, 0, 0, 1556, 1557, 1, 0, 0, 0, 1557, 1555, 1, 0, 0, 0, 1557, 1558, 1, 0, 0, 0, 1558, 1559, 1, 0, 0, 0, 1559, 1560, 6, 181, 0, 0, 1560, 364, 1, 0, 0, 0, 25, 0, 1414, 1419, 1425, 1430, 1435, 1441, 1445, 1448, 1451, 1456, 1459, 1462, 1465, 1485, 1505, 1514, 1520, 1522, 1530, 1534, 1537, 1545, 1550, 1557, 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 574c17dbc..41379e333 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens
@@ -169,14 +169,16 @@ T__167=168
T__168=169
T__169=170
T__170=171
-NEWLINE=172
-NUMBER=173
-SPECIALSET=174
-BOOLEAN=175
-NAN=176
-VARIABLE=177
-COMMENT=178
-WS=179
+T__171=172
+T__172=173
+NEWLINE=174
+NUMBER=175
+SPECIALSET=176
+BOOLEAN=177
+NAN=178
+VARIABLE=179
+COMMENT=180
+WS=181
'!'=1
'^'=2
'-'=3
@@ -323,29 +325,31 @@ WS=179
'sign('=144
'abs('=145
'phi('=146
-'card('=147
-'powerset('=148
-'union('=149
-'intersection('=150
-'complement('=151
-'image('=152
-'preimage('=153
-'floor('=154
-'ceil('=155
-'ceiling('=156
-'round('=157
-'min('=158
-'max('=159
-'argmax('=160
-'argmin('=161
-'gcd('=162
-'lcm('=163
-'binomial('=164
-'trunc('=165
-'erf('=166
-'conjugate('=167
-'domain('=168
-'piecewise('=169
-'apply('=170
-'lambda('=171
-'NaN'=176
+'prime('=147
+'valuation('=148
+'card('=149
+'powerset('=150
+'union('=151
+'intersection('=152
+'complement('=153
+'image('=154
+'preimage('=155
+'floor('=156
+'ceil('=157
+'ceiling('=158
+'round('=159
+'min('=160
+'max('=161
+'argmax('=162
+'argmin('=163
+'gcd('=164
+'lcm('=165
+'binomial('=166
+'trunc('=167
+'erf('=168
+'conjugate('=169
+'domain('=170
+'piecewise('=171
+'apply('=172
+'lambda('=173
+'NaN'=178
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
index ad7bebcc9..1b8430ee8 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
@@ -71,8 +71,9 @@ public const int
T__149=150, T__150=151, T__151=152, T__152=153, T__153=154, T__154=155,
T__155=156, T__156=157, T__157=158, T__158=159, T__159=160, T__160=161,
T__161=162, T__162=163, T__163=164, T__164=165, T__165=166, T__166=167,
- T__167=168, T__168=169, T__169=170, T__170=171, NEWLINE=172, NUMBER=173,
- SPECIALSET=174, BOOLEAN=175, NAN=176, VARIABLE=177, COMMENT=178, WS=179;
+ T__167=168, T__168=169, T__169=170, T__170=171, T__171=172, T__172=173,
+ NEWLINE=174, NUMBER=175, SPECIALSET=176, BOOLEAN=177, NAN=178, VARIABLE=179,
+ COMMENT=180, WS=181;
public const int
RULE_factorial_expression = 0, RULE_power_list = 1, RULE_power_expression = 2,
RULE_unary_expression = 3, RULE_mult_expression = 4, RULE_sum_expression = 5,
@@ -115,12 +116,12 @@ public const int
"'arcsech('", "'acosech('", "'arcosech('", "'arcsch('", "'arccosech('",
"'acsch('", "'factorial('", "'gamma('", "'derivative('", "'integral('",
"'limit('", "'limitleft('", "'limitright('", "'sum('", "'product('", "'signum('",
- "'sgn('", "'sign('", "'abs('", "'phi('", "'card('", "'powerset('", "'union('",
- "'intersection('", "'complement('", "'image('", "'preimage('", "'floor('",
- "'ceil('", "'ceiling('", "'round('", "'min('", "'max('", "'argmax('",
- "'argmin('", "'gcd('", "'lcm('", "'binomial('", "'trunc('", "'erf('",
- "'conjugate('", "'domain('", "'piecewise('", "'apply('", "'lambda('",
- null, null, null, null, "'NaN'"
+ "'sgn('", "'sign('", "'abs('", "'phi('", "'prime('", "'valuation('", "'card('",
+ "'powerset('", "'union('", "'intersection('", "'complement('", "'image('",
+ "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('",
+ "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('",
+ "'trunc('", "'erf('", "'conjugate('", "'domain('", "'piecewise('", "'apply('",
+ "'lambda('", null, null, null, null, "'NaN'"
};
private static readonly string[] _SymbolicNames = {
null, null, null, null, null, null, null, null, null, null, null, null,
@@ -137,8 +138,8 @@ public const int
null, null, null, null, null, null, null, null, null, null, null, null,
null, null, null, null, null, null, null, null, null, null, null, null,
null, null, null, null, null, null, null, null, null, null, null, null,
- null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN",
- "NAN", "VARIABLE", "COMMENT", "WS"
+ null, null, null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET",
+ "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS"
};
public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames);
@@ -735,6 +736,8 @@ public Mult_expressionContext mult_expression() {
case T__168:
case T__169:
case T__170:
+ case T__171:
+ case T__172:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -981,6 +984,8 @@ public Sum_expressionContext sum_expression() {
case T__168:
case T__169:
case T__170:
+ case T__171:
+ case T__172:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2149,6 +2154,8 @@ public ExpressionContext expression() {
case T__168:
case T__169:
case T__170:
+ case T__171:
+ case T__172:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2514,7 +2521,7 @@ public Function_argumentsContext function_arguments() {
State = 394;
ErrorHandler.Sync(this);
_la = TokenStream.LA(1);
- if ((((_la) & ~0x3f) == 0 && ((1L << _la) & -802489551279882216L) != 0) || ((((_la - 64)) & ~0x3f) == 0 && ((1L << (_la - 64)) & -1L) != 0) || ((((_la - 128)) & ~0x3f) == 0 && ((1L << (_la - 128)) & 1108307720798207L) != 0)) {
+ if ((((_la) & ~0x3f) == 0 && ((1L << _la) & -802489551279882216L) != 0) || ((((_la - 64)) & ~0x3f) == 0 && ((1L << (_la - 64)) & -1L) != 0) || ((((_la - 128)) & ~0x3f) == 0 && ((1L << (_la - 128)) & 4433230883192831L) != 0)) {
{
State = 383;
_localctx.e = expression();
@@ -2590,7 +2597,7 @@ public Set_itemsContext set_items() {
State = 416;
ErrorHandler.Sync(this);
_la = TokenStream.LA(1);
- if ((((_la) & ~0x3f) == 0 && ((1L << _la) & -802489551279882024L) != 0) || ((((_la - 64)) & ~0x3f) == 0 && ((1L << (_la - 64)) & -1L) != 0) || ((((_la - 128)) & ~0x3f) == 0 && ((1L << (_la - 128)) & 1108307720798207L) != 0)) {
+ if ((((_la) & ~0x3f) == 0 && ((1L << _la) & -802489551279882024L) != 0) || ((((_la - 64)) & ~0x3f) == 0 && ((1L << (_la - 64)) & -1L) != 0) || ((((_la - 128)) & ~0x3f) == 0 && ((1L << (_la - 128)) & 4433230883192831L) != 0)) {
{
State = 401;
ErrorHandler.Sync(this);
@@ -2723,6 +2730,8 @@ public Set_itemsContext set_items() {
case T__168:
case T__169:
case T__170:
+ case T__171:
+ case T__172:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2891,6 +2900,8 @@ public Set_itemsContext set_items() {
case T__168:
case T__169:
case T__170:
+ case T__171:
+ case T__172:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -3110,7 +3121,7 @@ public AtomContext atom() {
AtomContext _localctx = new AtomContext(Context, State);
EnterRule(_localctx, 48, RULE_atom);
try {
- State = 1058;
+ State = 1068;
ErrorHandler.Sync(this);
switch ( Interpreter.AdaptivePredict(TokenStream,41,Context) ) {
case 1:
@@ -4381,7 +4392,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 935;
Match(T__30);
- Assert("card", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.Card(_localctx.args.list[0]);
+ Assert("prime", 1, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.Prime(_localctx.args.list[0]);
}
break;
case 107:
@@ -4393,7 +4404,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 940;
Match(T__30);
- Assert("powerset", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.PowerSet(_localctx.args.list[0]);
+ Assert("valuation", 2, _localctx.args.list.Count); _localctx.value = MathS.NumberTheory.Valuation(_localctx.args.list[0], _localctx.args.list[1]);
}
break;
case 108:
@@ -4405,7 +4416,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 945;
Match(T__30);
- 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("card", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.Card(_localctx.args.list[0]);
}
break;
case 109:
@@ -4417,7 +4428,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 950;
Match(T__30);
- 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("powerset", 1, _localctx.args.list.Count); _localctx.value = MathS.Sets.PowerSet(_localctx.args.list[0]);
}
break;
case 110:
@@ -4429,7 +4440,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 955;
Match(T__30);
- Assert("complement", 2, _localctx.args.list.Count); _localctx.value = MathS.Sets.Complement(_localctx.args.list[0], _localctx.args.list[1]);
+ 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 111:
@@ -4441,7 +4452,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 960;
Match(T__30);
- 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("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 112:
@@ -4453,7 +4464,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 965;
Match(T__30);
- 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("complement", 2, _localctx.args.list.Count); _localctx.value = MathS.Sets.Complement(_localctx.args.list[0], _localctx.args.list[1]);
}
break;
case 113:
@@ -4465,7 +4476,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 970;
Match(T__30);
- Assert("floor", 1, _localctx.args.list.Count); _localctx.value = MathS.Floor(_localctx.args.list[0]);
+ 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 114:
@@ -4477,7 +4488,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 975;
Match(T__30);
- Assert("ceil", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]);
+ 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 115:
@@ -4489,7 +4500,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 980;
Match(T__30);
- Assert("ceiling", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]);
+ Assert("floor", 1, _localctx.args.list.Count); _localctx.value = MathS.Floor(_localctx.args.list[0]);
}
break;
case 116:
@@ -4501,7 +4512,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 985;
Match(T__30);
- Assert("round", 1, _localctx.args.list.Count); _localctx.value = MathS.Round(_localctx.args.list[0]);
+ Assert("ceil", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]);
}
break;
case 117:
@@ -4513,7 +4524,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 990;
Match(T__30);
- 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("ceiling", 1, _localctx.args.list.Count); _localctx.value = MathS.Ceil(_localctx.args.list[0]);
}
break;
case 118:
@@ -4525,7 +4536,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 995;
Match(T__30);
- 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("round", 1, _localctx.args.list.Count); _localctx.value = MathS.Round(_localctx.args.list[0]);
}
break;
case 119:
@@ -4537,7 +4548,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1000;
Match(T__30);
- 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)");
+ 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 120:
@@ -4549,7 +4560,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1005;
Match(T__30);
- 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)");
+ 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 121:
@@ -4561,7 +4572,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1010;
Match(T__30);
- AssertAtLeast("gcd", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Gcd(a, b));
+ 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 122:
@@ -4573,7 +4584,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1015;
Match(T__30);
- AssertAtLeast("lcm", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Lcm(a, b));
+ 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 123:
@@ -4585,7 +4596,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1020;
Match(T__30);
- Assert("binomial", 2, _localctx.args.list.Count); _localctx.value = MathS.Binomial(_localctx.args.list[0], _localctx.args.list[1]);
+ AssertAtLeast("gcd", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Gcd(a, b));
}
break;
case 124:
@@ -4597,7 +4608,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1025;
Match(T__30);
- _localctx.value = NotImplementedFunction("trunc", "rounding functions");
+ AssertAtLeast("lcm", 1, _localctx.args.list.Count); _localctx.value = _localctx.args.list.Aggregate((a, b) => MathS.Lcm(a, b));
}
break;
case 125:
@@ -4609,7 +4620,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1030;
Match(T__30);
- _localctx.value = NotImplementedFunction("erf", "error function");
+ Assert("binomial", 2, _localctx.args.list.Count); _localctx.value = MathS.Binomial(_localctx.args.list[0], _localctx.args.list[1]);
}
break;
case 126:
@@ -4621,7 +4632,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1035;
Match(T__30);
- _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function");
+ _localctx.value = NotImplementedFunction("trunc", "rounding functions");
}
break;
case 127:
@@ -4632,6 +4643,30 @@ public AtomContext atom() {
State = 1039;
_localctx.args = function_arguments();
State = 1040;
+ Match(T__30);
+ _localctx.value = NotImplementedFunction("erf", "error function");
+ }
+ break;
+ case 128:
+ EnterOuterAlt(_localctx, 128);
+ {
+ State = 1043;
+ Match(T__168);
+ State = 1044;
+ _localctx.args = function_arguments();
+ State = 1045;
+ Match(T__30);
+ _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function");
+ }
+ break;
+ case 129:
+ EnterOuterAlt(_localctx, 129);
+ {
+ State = 1048;
+ Match(T__169);
+ State = 1049;
+ _localctx.args = function_arguments();
+ State = 1050;
Match(T__30);
Assert("domain", 2, _localctx.args.list.Count);
@@ -4658,14 +4693,14 @@ public AtomContext atom() {
}
break;
- case 128:
- EnterOuterAlt(_localctx, 128);
+ case 130:
+ EnterOuterAlt(_localctx, 130);
{
- State = 1043;
- Match(T__168);
- State = 1044;
+ State = 1053;
+ Match(T__170);
+ State = 1054;
_localctx.args = function_arguments();
- State = 1045;
+ State = 1055;
Match(T__30);
var cases = new List();
@@ -4678,14 +4713,14 @@ public AtomContext atom() {
}
break;
- case 129:
- EnterOuterAlt(_localctx, 129);
+ case 131:
+ EnterOuterAlt(_localctx, 131);
{
- State = 1048;
- Match(T__169);
- State = 1049;
+ State = 1058;
+ Match(T__171);
+ State = 1059;
_localctx.args = function_arguments();
- State = 1050;
+ State = 1060;
Match(T__30);
if (_localctx.args.list.Count < 2)
@@ -4694,14 +4729,14 @@ public AtomContext atom() {
}
break;
- case 130:
- EnterOuterAlt(_localctx, 130);
+ case 132:
+ EnterOuterAlt(_localctx, 132);
{
- State = 1053;
- Match(T__170);
- State = 1054;
+ State = 1063;
+ Match(T__172);
+ State = 1064;
_localctx.args = function_arguments();
- State = 1055;
+ State = 1065;
Match(T__30);
if (_localctx.args.list.Count < 2)
@@ -4764,9 +4799,9 @@ public StatementContext statement() {
try {
EnterOuterAlt(_localctx, 1);
{
- State = 1060;
+ State = 1070;
_localctx._expression = expression();
- State = 1061;
+ State = 1071;
Match(Eof);
Result = _localctx._expression.value;
}
@@ -4783,7 +4818,7 @@ public StatementContext statement() {
}
private static int[] _serializedATN = {
- 4,1,179,1065,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2,
+ 4,1,181,1075,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2,
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,
2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,1,0,1,0,1,0,1,0,1,0,1,0,1,0,3,
@@ -4858,306 +4893,310 @@ public StatementContext statement() {
1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,
1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,
1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,
- 1,24,1,24,1,24,1,24,3,24,1059,8,24,1,25,1,25,1,25,1,25,1,25,0,0,26,0,2,
- 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,0,
- 4,1,0,6,7,1,0,42,43,1,0,44,45,1,0,46,47,1225,0,59,1,0,0,0,2,77,1,0,0,0,
- 4,79,1,0,0,0,6,109,1,0,0,0,8,111,1,0,0,0,10,136,1,0,0,0,12,157,1,0,0,0,
- 14,172,1,0,0,0,16,195,1,0,0,0,18,230,1,0,0,0,20,281,1,0,0,0,22,283,1,0,
- 0,0,24,298,1,0,0,0,26,309,1,0,0,0,28,320,1,0,0,0,30,335,1,0,0,0,32,354,
- 1,0,0,0,34,356,1,0,0,0,36,368,1,0,0,0,38,370,1,0,0,0,40,394,1,0,0,0,42,
- 416,1,0,0,0,44,418,1,0,0,0,46,424,1,0,0,0,48,1058,1,0,0,0,50,1060,1,0,
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- 293,295,306,317,330,332,341,349,354,368,378,391,394,401,409,413,416,1058
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+ 0,0,1068,918,1,0,0,0,1068,923,1,0,0,0,1068,928,1,0,0,0,1068,933,1,0,0,
+ 0,1068,938,1,0,0,0,1068,943,1,0,0,0,1068,948,1,0,0,0,1068,953,1,0,0,0,
+ 1068,958,1,0,0,0,1068,963,1,0,0,0,1068,968,1,0,0,0,1068,973,1,0,0,0,1068,
+ 978,1,0,0,0,1068,983,1,0,0,0,1068,988,1,0,0,0,1068,993,1,0,0,0,1068,998,
+ 1,0,0,0,1068,1003,1,0,0,0,1068,1008,1,0,0,0,1068,1013,1,0,0,0,1068,1018,
+ 1,0,0,0,1068,1023,1,0,0,0,1068,1028,1,0,0,0,1068,1033,1,0,0,0,1068,1038,
+ 1,0,0,0,1068,1043,1,0,0,0,1068,1048,1,0,0,0,1068,1053,1,0,0,0,1068,1058,
+ 1,0,0,0,1068,1063,1,0,0,0,1069,49,1,0,0,0,1070,1071,3,32,16,0,1071,1072,
+ 5,0,0,1,1072,1073,6,25,-1,0,1073,51,1,0,0,0,42,59,67,75,77,84,94,104,109,
+ 119,129,131,144,150,152,167,169,190,192,225,227,246,253,262,281,293,295,
+ 306,317,330,332,341,349,354,368,378,391,394,401,409,413,416,1068
};
public static readonly ATN _ATN =
diff --git a/Sources/AngouriMath/Core/CostModel.cs b/Sources/AngouriMath/Core/CostModel.cs
index c21790550..86c924ba3 100644
--- a/Sources/AngouriMath/Core/CostModel.cs
+++ b/Sources/AngouriMath/Core/CostModel.cs
@@ -176,6 +176,8 @@ 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
+ Primef => ExtraHeavyWeight + ChildrenCost(expr),
+ Valuationf => ExtraHeavyWeight + ChildrenCost(expr),
Real { IsNegative: true } => MajorWeight + ChildrenCost(expr), // Number of negative reals
ComparisonSign when expr.DirectChildren[0] == 0 => Weight + ChildrenCost(expr), // 0 < x is bad. x > 0 is good.
Notf(Equalsf eq) => -Weight + eq.DefaultCostCached, // (not x = 0) is equally complex as (x = 0)
diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs
index a68235a43..fc5f6a79b 100644
--- a/Sources/AngouriMath/Core/Domains.Classes.cs
+++ b/Sources/AngouriMath/Core/Domains.Classes.cs
@@ -589,6 +589,24 @@ partial record Cardf
internal override Domain DefaultCodomain => Domain.Integer;
}
+ partial record Valuationf
+ {
+ // A whole number wherever the argument is not zero, and +oo there, which no
+ // domain of whole numbers admits: the reals, so that the convention is kept.
+ ///
+ public override Domain Codomain { get; protected init; } = Domain.Real;
+ ///
+ internal override Domain DefaultCodomain => Domain.Real;
+ }
+
+ partial record Primef
+ {
+ ///
+ public override Domain Codomain { get; protected init; } = Domain.Prime;
+ ///
+ internal override Domain DefaultCodomain => Domain.Prime;
+ }
+
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 b98e38abb..2d5250982 100644
--- a/Sources/AngouriMath/Core/Entity/Discrete/Entity.Discrete.Classes.cs
+++ b/Sources/AngouriMath/Core/Entity/Discrete/Entity.Discrete.Classes.cs
@@ -385,6 +385,54 @@ public override Entity Replace(Func func)
#endregion
#region Number theory
+ ///
+ /// The n-th prime, prime(n): prime(1) is 2, prime(25)
+ /// is 97. An enumeration of PP in its order, which a set does not carry, so
+ /// a function of its own -- SymPy's prime(n). Defined on the positive whole numbers.
+ /// https://github.com/asc-community/AngouriMath/issues/1450
+ ///
+ public sealed partial record Primef(Entity Argument) : Function, IUnaryNode
+ {
+ ///
+ public Entity NodeChild => Argument;
+
+ internal Primef 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 p-adic valuation, valuation(n, p): the exponent of the prime
+ /// p in n, so valuation(12, 2) is 2 and valuation(12, 5)
+ /// is 0; +oo at n = 0, by the convention every text uses. Sullivan and
+ /// Mackey's Ex 5.5.1 writes n = 2^m (2 l + 1) with m the 2-adic valuation, and
+ /// n = product(p^valuation(n, p), p in PP) is what a factorisation says.
+ /// https://github.com/asc-community/AngouriMath/issues/1450
+ ///
+ public sealed partial record Valuationf(Entity Argument, Entity Prime) : Function, IBinaryNode
+ {
+ ///
+ public Entity NodeFirstChild => Argument;
+
+ ///
+ public Entity NodeSecondChild => Prime;
+
+ internal Valuationf New(Entity argument, Entity prime)
+ => ReferenceEquals(Argument, argument) && ReferenceEquals(Prime, prime) ? this : new(argument, prime) { Codomain = Codomain };
+
+ ///
+ public override Entity Replace(Func func)
+ => func(New(Argument.Replace(func), Prime.Replace(func)));
+
+ ///
+ protected override Entity[] InitDirectChildren() => new[] { Argument, Prime };
+ }
+
///
/// This node represents the Euler totient function (phi)
///
diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
index 3c3302234..588a57261 100644
--- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
+++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
@@ -77,6 +77,8 @@ [EntityJsonConverter] partial record Number
}
[EntityJsonConverter] partial record Orf;
[EntityJsonConverter] partial record Phif;
+ [EntityJsonConverter] partial record Primef;
+ [EntityJsonConverter] partial record Valuationf;
[EntityJsonConverter] partial record Dividesf;
[EntityJsonConverter] partial record Congruentf;
[EntityJsonConverter] partial record Quantifier;
diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
index 8f8ad4b55..59382d087 100644
--- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
+++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
@@ -476,6 +476,8 @@ 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.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])),
[typeof(Entity.Notf)] = (1, static c => new Entity.Notf(c[0])),
// Arithmetic.
diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md
index 4b30172d2..e6c55450c 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 **48** such types.
+pattern used as a **replacement** must be one the library can construct: there are **50** 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 5029b4889..6febcda2a 100644
--- a/Sources/AngouriMath/Docs/Usage/Syntax.md
+++ b/Sources/AngouriMath/Docs/Usage/Syntax.md
@@ -242,7 +242,11 @@ which is `e ^ x`.
**Powers and logarithms** — `sqrt` `cbrt` `sqr` `pow(a, b)` `exp` `ln` `log(base, x)`. `log` with
one argument is base 10, so `log(100)` is 2; `log10` and `log2` say it in the name.
-**Other** — `abs` `signum` `sgn` `sign` `phi` `gamma` `factorial` (or postfix `!`); `#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)`).
+**Other** — `abs` `signum` `sgn` `sign` `phi` `gamma` `factorial` (or postfix `!`); `prime(n)`
+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)`).
**Rounding** — `floor` `ceil` (`ceiling` is accepted on the way in and prints as `ceil`) `round`.
All three round a complex argument componentwise. `floor` and `ceil` go toward the infinities
diff --git a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
index 9bbc13f87..e6a3b6094 100644
--- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
+++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
@@ -672,6 +672,22 @@ private protected override IEnumerable InvertNode(Entity value, Entity x
}
}
+ partial record Valuationf
+ {
+ // valuation(n, p) = k has every multiple of p^k prime to p for a solution, a set the
+ // inverter cannot hand back.
+ private protected override IEnumerable InvertNode(Entity value, Entity x)
+ => Enumerable.Empty();
+ }
+
+ partial record Primef
+ {
+ // prime(n) = p has the one solution n = pi(p) where p is prime and none otherwise,
+ // and pi is not a node here; declined the way Phif is.
+ private protected override IEnumerable InvertNode(Entity value, Entity x)
+ => Enumerable.Empty();
+ }
+
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 903177c55..23c841e0e 100644
--- a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs
+++ b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs
@@ -537,6 +537,61 @@ private static bool Countable(Entity element)
=> element is Number || element is FiniteSet listed && listed.All(Countable);
}
+ partial record Valuationf
+ {
+ // Defined for a whole n and a prime p; the sign of n does not enter.
+ private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.Z) & Prime.In(MathS.Sets.Primes);
+
+ ///
+ protected override Entity InnerSimplify(bool isExact)
+ => ExpandOnTwoArguments(Argument, Prime,
+ (n, p) => (n, p) switch
+ {
+ (Integer whole, Integer prime) when Functions.Primes.IsPrime(prime.EInteger) is { } isPrime
+ => !isPrime ? MathS.NaN
+ : whole.EInteger.IsZero ? Real.PositiveInfinity
+ : Integer.Create(Multiplicity(whole.EInteger.Abs(), prime.EInteger)),
+ (Number, Number) => MathS.NaN,
+ _ => null
+ },
+ (@this, n, p) => ((Valuationf)@this).New(n, p), isExact);
+
+ private static EInteger Multiplicity(EInteger n, EInteger p)
+ {
+ var count = EInteger.Zero;
+ while (n.Remainder(p).IsZero)
+ {
+ n = n.Divide(p);
+ count += 1;
+ }
+ return count;
+ }
+ }
+
+ partial record Primef
+ {
+ // The n-th prime is defined for a positive whole n; nothing else indexes the primes.
+ private protected override Entity IntrinsicCondition => Argument.In(MathS.Sets.PositiveIntegers);
+
+ ///
+ protected override Entity InnerSimplify(bool isExact)
+ => ExpandOnOneArgument(Argument,
+ a => a switch
+ {
+ // The table of primes is built as far as it is asked for, and a very
+ // large index is left as written rather than built towards.
+ Integer { EInteger.Sign: > 0 } index when index.EInteger.CompareTo(EInteger.FromInt32(LargestIndex)) <= 0
+ => Functions.Primes.GetPrime(index.EInteger.ToInt32Checked() - 1),
+ Integer { EInteger.Sign: > 0 } => null,
+ Number => MathS.NaN,
+ _ => null
+ },
+ (@this, a) => ((Primef)@this).New(a), isExact);
+
+ /// How far the table of primes is built for an index.
+ private const int LargestIndex = 1000000;
+ }
+
partial record Phif
{
// Euler's totient function is defined for all integers in this library.
diff --git a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
index e1313dde7..4283e89f9 100644
--- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
@@ -223,6 +223,19 @@ private protected override string LatexizeNode()
=> $@"\binom{{{Upper.Latexize()}}}{{{Lower.Latexize()}}}";
}
+ partial record Primef
+ {
+ ///
+ private protected override string LatexizeNode() => $@"\operatorname{{prime}}\left({Argument.Latexize()}\right)";
+ }
+
+ partial record Valuationf
+ {
+ ///
+ // The textbook's v_p(n), the prime as a subscript.
+ private protected override string LatexizeNode() => $@"v_{{{Prime.Latexize()}}}\left({Argument.Latexize()}\right)";
+ }
+
partial record Phif
{
///
diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
index ecb2190a0..9d65df4a6 100644
--- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
@@ -97,6 +97,22 @@ partial record Phif
public override string ToString() => Stringize();
}
+ partial record Primef
+ {
+ ///
+ private protected override string StringizeNode() => $@"prime({Argument.Stringize()})";
+ ///
+ public override string ToString() => Stringize();
+ }
+
+ partial record Valuationf
+ {
+ ///
+ private protected override string StringizeNode() => $@"valuation({Argument.Stringize()}, {Prime.Stringize()})";
+ ///
+ public override string ToString() => Stringize();
+ }
+
partial record Cardf
{
///
diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
index 4bc6abd66..baf654b89 100644
--- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
@@ -160,6 +160,16 @@ public partial record Phif
internal override string ToSymPy() => $"sympy.totient({Argument.ToSymPy()})";
}
+ public partial record Primef
+ {
+ internal override string ToSymPy() => $"sympy.prime({Argument.ToSymPy()})";
+ }
+
+ public partial record Valuationf
+ {
+ internal override string ToSymPy() => $"sympy.multiplicity({Prime.ToSymPy()}, {Argument.ToSymPy()})";
+ }
+
public partial record Cardf
{
// SymPy has no cardinality function; a finite set answers len, and an infinite one
diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs
index 2d9bcf028..81445ab2c 100644
--- a/Sources/AngouriMath/Functions/Substitute.cs
+++ b/Sources/AngouriMath/Functions/Substitute.cs
@@ -407,6 +407,20 @@ public override Entity Substitute(Entity x, Entity value)
=> this == x ? value : New(Argument.Substitute(x, value));
}
+ partial record Primef
+ {
+ ///
+ public override Entity Substitute(Entity x, Entity value)
+ => this == x ? value : New(Argument.Substitute(x, value));
+ }
+
+ partial record Valuationf
+ {
+ ///
+ public override Entity Substitute(Entity x, Entity value)
+ => this == x ? value : New(Argument.Substitute(x, value), Prime.Substitute(x, value));
+ }
+
partial record Dividesf
{
///
diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
index 20be5d52d..367ffe10b 100644
--- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
+++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
@@ -445,6 +445,16 @@ partial record Phif
private protected override string SortHashName(SortLevel level) => "phi_";
}
+ partial record Primef
+ {
+ private protected override string SortHashName(SortLevel level) => "prime_";
+ }
+
+ partial record Valuationf
+ {
+ private protected override string SortHashName(SortLevel level) => "valuation_";
+ }
+
partial record Dividesf
{
private protected override string SortHashName(SortLevel level)
diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt
index 4005d3ef2..922b85b52 100644
--- a/Sources/Tests/UnitTests/Common/PublicApi.txt
+++ b/Sources/Tests/UnitTests/Common/PublicApi.txt
@@ -1815,6 +1815,25 @@ 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+Primef.$() : AngouriMath.Entity+Primef
+AngouriMath.Entity+Primef.Argument { } : AngouriMath.Entity
+AngouriMath.Entity+Primef.Codomain { } : AngouriMath.Core.Domain
+AngouriMath.Entity+Primef.Deconstruct(AngouriMath.Entity&) : System.Void
+AngouriMath.Entity+Primef.EqualityContract { } : System.Type
+AngouriMath.Entity+Primef.Equals(AngouriMath.Entity+Function) : System.Boolean
+AngouriMath.Entity+Primef.Equals(AngouriMath.Entity+Primef) : System.Boolean
+AngouriMath.Entity+Primef.Equals(System.Object) : System.Boolean
+AngouriMath.Entity+Primef.GetHashCode() : System.Int32
+AngouriMath.Entity+Primef.InitDirectChildren() : AngouriMath.Entity[]
+AngouriMath.Entity+Primef.InnerSimplify(System.Boolean) : AngouriMath.Entity
+AngouriMath.Entity+Primef.NodeChild { } : AngouriMath.Entity
+AngouriMath.Entity+Primef.PrintMembers(System.Text.StringBuilder) : System.Boolean
+AngouriMath.Entity+Primef.Replace(System.Func) : AngouriMath.Entity
+AngouriMath.Entity+Primef.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity
+AngouriMath.Entity+Primef.ToString() : System.String
+AngouriMath.Entity+Primef.ctor(AngouriMath.Entity)
+AngouriMath.Entity+Primef.op_Equality(AngouriMath.Entity+Primef, AngouriMath.Entity+Primef) : System.Boolean
+AngouriMath.Entity+Primef.op_Inequality(AngouriMath.Entity+Primef, AngouriMath.Entity+Primef) : System.Boolean
AngouriMath.Entity+Productf.$() : AngouriMath.Entity+Productf
AngouriMath.Entity+Productf.Codomain { } : AngouriMath.Core.Domain
AngouriMath.Entity+Productf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&, AngouriMath.Entity&, AngouriMath.Entity&) : System.Void
@@ -2445,6 +2464,27 @@ AngouriMath.Entity+TrigonometricFunction.ctor()
AngouriMath.Entity+TrigonometricFunction.ctor(AngouriMath.Entity+TrigonometricFunction)
AngouriMath.Entity+TrigonometricFunction.op_Equality(AngouriMath.Entity+TrigonometricFunction, AngouriMath.Entity+TrigonometricFunction) : System.Boolean
AngouriMath.Entity+TrigonometricFunction.op_Inequality(AngouriMath.Entity+TrigonometricFunction, AngouriMath.Entity+TrigonometricFunction) : System.Boolean
+AngouriMath.Entity+Valuationf.$() : AngouriMath.Entity+Valuationf
+AngouriMath.Entity+Valuationf.Argument { } : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.Codomain { } : AngouriMath.Core.Domain
+AngouriMath.Entity+Valuationf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void
+AngouriMath.Entity+Valuationf.EqualityContract { } : System.Type
+AngouriMath.Entity+Valuationf.Equals(AngouriMath.Entity+Function) : System.Boolean
+AngouriMath.Entity+Valuationf.Equals(AngouriMath.Entity+Valuationf) : System.Boolean
+AngouriMath.Entity+Valuationf.Equals(System.Object) : System.Boolean
+AngouriMath.Entity+Valuationf.GetHashCode() : System.Int32
+AngouriMath.Entity+Valuationf.InitDirectChildren() : AngouriMath.Entity[]
+AngouriMath.Entity+Valuationf.InnerSimplify(System.Boolean) : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.NodeFirstChild { } : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.NodeSecondChild { } : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.Prime { } : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.PrintMembers(System.Text.StringBuilder) : System.Boolean
+AngouriMath.Entity+Valuationf.Replace(System.Func) : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity
+AngouriMath.Entity+Valuationf.ToString() : System.String
+AngouriMath.Entity+Valuationf.ctor(AngouriMath.Entity, AngouriMath.Entity)
+AngouriMath.Entity+Valuationf.op_Equality(AngouriMath.Entity+Valuationf, AngouriMath.Entity+Valuationf) : System.Boolean
+AngouriMath.Entity+Valuationf.op_Inequality(AngouriMath.Entity+Valuationf, AngouriMath.Entity+Valuationf) : System.Boolean
AngouriMath.Entity+Variable.$() : AngouriMath.Entity+Variable
AngouriMath.Entity+Variable.Codomain { } : AngouriMath.Core.Domain
AngouriMath.Entity+Variable.Deconstruct(System.String&) : System.Void
@@ -2782,6 +2822,8 @@ AngouriMath.MathS+NumberTheory.Factorize(AngouriMath.Entity+Number+Integer) : Sy
AngouriMath.MathS+NumberTheory.GreatestCommonDivisor(AngouriMath.Entity+Number+Integer, AngouriMath.Entity+Number+Integer) : AngouriMath.Entity+Number+Integer
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.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
AngouriMath.MathS+Numbers.Create(PeterO.Numbers.EInteger) : AngouriMath.Entity+Number+Integer
@@ -3083,6 +3125,7 @@ class AngouriMath.Entity+Orf
class AngouriMath.Entity+Phif
class AngouriMath.Entity+Piecewise
class AngouriMath.Entity+Powf
+class AngouriMath.Entity+Primef
class AngouriMath.Entity+Productf
class AngouriMath.Entity+Providedf
class AngouriMath.Entity+Quantifier
@@ -3117,6 +3160,7 @@ class AngouriMath.Entity+Sumf
class AngouriMath.Entity+Summationf
class AngouriMath.Entity+Tanf
class AngouriMath.Entity+TrigonometricFunction
+class AngouriMath.Entity+Valuationf
class AngouriMath.Entity+Variable
class AngouriMath.Entity+Xorf
class AngouriMath.Extensions.AngouriMathExtensions
diff --git a/Sources/Tests/UnitTests/Core/Sets/PrimeSetTest.cs b/Sources/Tests/UnitTests/Core/Sets/PrimeSetTest.cs
index 50775e0d5..b4debf3a0 100644
--- a/Sources/Tests/UnitTests/Core/Sets/PrimeSetTest.cs
+++ b/Sources/Tests/UnitTests/Core/Sets/PrimeSetTest.cs
@@ -81,6 +81,25 @@ public sealed class PrimeSetTest
[InlineData("forall p in PP : 2 divides p", "False")]
[InlineData("exists p in PP : p = 4", "False")]
[InlineData("exists p in PP : p > 100", "True")]
+ // The n-th prime, a function of its own: PP carries no order.
+ [InlineData("prime(1)", "2")]
+ [InlineData("prime(25)", "97")]
+ [InlineData("prime(1000)", "7919")]
+ [InlineData("prime(prime(2))", "5")]
+ [InlineData("prime(2) + prime(3)", "8")]
+ [InlineData("prime(0)", "NaN")]
+ [InlineData("prime(-1)", "NaN")]
+ [InlineData("prime(1/2)", "NaN")]
+ // The p-adic valuation (Sullivan and Mackey's Ex 5.5.1: n = 2^m (2 l + 1), m its 2-adic one).
+ [InlineData("valuation(12, 2)", "2")]
+ [InlineData("valuation(12, 3)", "1")]
+ [InlineData("valuation(12, 5)", "0")]
+ [InlineData("valuation(-40, 2)", "3")]
+ [InlineData("valuation(2^100 * 3, 2)", "100")]
+ [InlineData("valuation(0, 3)", "+oo")]
+ [InlineData("valuation(12, 4)", "NaN")]
+ [InlineData("valuation(1/2, 2)", "NaN")]
+ [InlineData("2^valuation(12, 2) * 3^valuation(12, 3)", "12")]
public void Decided(string input, string expected)
=> Assert.Equal(expected.ToEntity(), input.ToEntity().Evaled);
@@ -95,6 +114,10 @@ public void Decided(string input, string expected)
[InlineData("max(x, x in ZZ+ and x < 1)", typeof(Maximumf))]
[InlineData("min(x, x in PP and x > 14 and x < 16)", typeof(Minimumf))]
[InlineData("PP intersect [1; 10^7]", typeof(Set.Intersectionf))]
+ [InlineData("prime(n)", typeof(Primef))]
+ [InlineData("prime(10^9)", typeof(Primef))]
+ [InlineData("valuation(n, 2)", typeof(Valuationf))]
+ [InlineData("valuation(12, p)", typeof(Valuationf))]
public void LeftAsWritten(string input, System.Type node)
=> Assert.IsType(node, input.ToEntity().Evaled);
@@ -109,6 +132,15 @@ public void PrintsAndReadsBack()
Assert.Equal(@"\min \mathbb{P}", "min(PP)".ToEntity().Latexize());
Assert.Equal("min({ x in PP : x > 14 })", "min(x, x in PP and x > 14)".ToEntity().ToString());
Assert.Equal(AngouriMath.Core.Domain.Prime, "domain(x, PP)".ToEntity().Codomain);
+ Assert.Equal(AngouriMath.Core.Domain.Prime, "prime(n)".ToEntity().Codomain);
+ Assert.Equal("prime(n)", MathS.NumberTheory.Prime("n").ToString());
+ Assert.Equal(@"\operatorname{prime}\left(n\right)", "prime(n)".ToEntity().Latexize());
+ Assert.Contains("sympy.prime(n)", MathS.ToSympyCode("prime(n)".ToEntity()));
+ Assert.Equal("prime(n)".ToEntity(), "prime(n)".ToEntity().ToString().ToEntity());
+ Assert.Equal("valuation(n, p)", MathS.NumberTheory.Valuation("n", "p").ToString());
+ Assert.Equal(@"v_{p}\left(n\right)", "valuation(n, p)".ToEntity().Latexize());
+ Assert.Contains("sympy.multiplicity(p, n)", MathS.ToSympyCode("valuation(n, p)".ToEntity()));
+ Assert.Equal("valuation(n, p)".ToEntity(), "valuation(n, p)".ToEntity().ToString().ToEntity());
}
[Theory]
diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs
index 61f57eeae..f5b7dfa6e 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(48, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types");
+ => Stated(50, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types");
[Fact]
public void ReplacementAPatternOrCode()