diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md
index 8a3ed02c4..3ebcc9e6d 100644
--- a/BREAKING-CHANGES.md
+++ b/BREAKING-CHANGES.md
@@ -704,6 +704,23 @@ met piece by piece now ([#1409](https://github.com/asc-community/AngouriMath/iss
| `{ x in RR : x^2 - 3 x + 2 >= 0 } = { y in RR : y <= 1 or y >= 2 }` | left as written | `True` |
| `"({ 2 } \/ (-oo; 1] \/ (2; +oo)) /\ (1; 2)".ToEntity().Evaled` | left as written | `{ }` |
+### The size of an infinite set is an aleph, and sizes compare
+
+`card` of an infinite set is an aleph, `aleph(k)`, or a power of 2 of one: `card(ZZ)`, `card(QQ)`
+and `card(PP)` are `aleph(0)`, and `card(RR)` is `2^aleph(0)`, an aleph but not a named one, since
+which one it is is the continuum hypothesis, which ZFC does not decide: `2^aleph(0) = aleph(1)`
+stays as written. `card(powerset(S))` is `2^card(S)`. A sum or a product of sizes, one of them
+infinite, is the larger, and a difference or a quotient of sizes has no value and is `NaN`, as
+`log(0)` is. Sizes compare by what ZFC proves, and a set is smaller than its power set whatever it
+is ([#1409](https://github.com/asc-community/AngouriMath/issues/1409), Sullivan and Mackey's §7.6).
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `"card(ZZ)".ToEntity().Simplify()` | `#ZZ` | `aleph(0)` |
+| `"card(ZZ) = card(QQ)".ToEntity().Simplify()` | `#ZZ = #QQ` | `True` |
+| `"card(ZZ) < card(RR)".ToEntity().Simplify()` | `#ZZ < #RR` | `True` |
+| `"aleph(0) + 1".ToEntity().Simplify()` | `1` — `aleph(0)` was read as `aleph * 0` | `aleph(0)` |
+
### An integer range is listed, and a family of sets has a union and an intersection
`ZZ /\ [1; 10]` lists its members now — an integer set cut by a numeric interval with at most
diff --git a/Sources/.editorconfig b/Sources/.editorconfig
index d19f61600..9a49be8a2 100644
--- a/Sources/.editorconfig
+++ b/Sources/.editorconfig
@@ -341,6 +341,8 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
[AngouriMath/Core/Entity/Continuous/Entity.Continuous.Iverson.Classes.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+[AngouriMath/Core/Entity/Continuous/Entity.Continuous.Aleph.Classes.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
[Tests/UnitTests/Core/ProofRecordingTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
@@ -396,6 +398,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
[AngouriMath/Core/Entity/Omni/Sets/SetOperators.Subset.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+[AngouriMath/Core/Entity/Omni/Sets/Cardinality.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+
[Tests/UnitTests/Core/Sets/SubsetTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
diff --git a/Sources/AngouriMath/Convenience/MathS.cs b/Sources/AngouriMath/Convenience/MathS.cs
index ae25c136e..4ba860f7d 100644
--- a/Sources/AngouriMath/Convenience/MathS.cs
+++ b/Sources/AngouriMath/Convenience/MathS.cs
@@ -1394,6 +1394,18 @@ public static Entity VectorLength(Matrix v)
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Entity Iverson(Entity statement) => new Iversonf(statement);
+ /// The aleph number aleph(k), the size of an infinite set
+ /// The index, a whole number from zero
+ /// The node
+ ///
+ /// aleph(0) is the size of the whole numbers and of the rationals, and
+ /// card(ZZ) is it. The size of the reals is 2^aleph(0), not a named aleph:
+ /// which one it is, is the continuum hypothesis.
+ /// https://github.com/asc-community/AngouriMath/issues/1409
+ ///
+ [MethodImpl(MethodImplOptions.AggressiveInlining)]
+ public static Entity Aleph(Entity index) => new Alephf(index);
+
/// The error function, erf(z) = 2/sqrt(pi) int_0^z e^(-t^2) dt
/// The argument, any complex number
/// The node
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g
index e32533e01..7842b0091 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g
@@ -599,6 +599,8 @@ atom returns[Entity value]
/* The Iverson bracket, 1 where a statement holds and 0 where it does not: a count written as
a sum. https://github.com/asc-community/AngouriMath/issues/1478 */
| 'iverson(' args = function_arguments ')' { Assert("iverson", 1, $args.list.Count); $value = MathS.Iverson($args.list[0]); }
+ /* The aleph numbers, the sizes of infinite sets. https://github.com/asc-community/AngouriMath/issues/1409 */
+ | 'aleph(' args = function_arguments ')' { Assert("aleph", 1, $args.list.Count); $value = MathS.Aleph($args.list[0]); }
/* The error functions. https://github.com/asc-community/AngouriMath/issues/1501 */
| 'erf(' args = function_arguments ')' { Assert("erf", 1, $args.list.Count); $value = MathS.Erf($args.list[0]); }
| 'erfc(' args = function_arguments ')' { Assert("erfc", 1, $args.list.Count); $value = MathS.Erfc($args.list[0]); }
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
index d85864492..f40dffad3 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp
@@ -167,6 +167,7 @@ null
'lcm('
'binomial('
'iverson('
+'aleph('
'erf('
'erfc('
'erfi('
@@ -375,6 +376,7 @@ null
null
null
null
+null
NEWLINE
NUMBER
SPECIALSET
@@ -414,4 +416,4 @@ statement
atn:
-[4, 1, 190, 1120, 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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926, 5, 31, 0, 0, 926, 927, 6, 24, -1, 0, 927, 1119, 1, 0, 0, 0, 928, 929, 5, 146, 0, 0, 929, 930, 3, 40, 20, 0, 930, 931, 5, 31, 0, 0, 931, 932, 6, 24, -1, 0, 932, 1119, 1, 0, 0, 0, 933, 934, 5, 147, 0, 0, 934, 935, 3, 40, 20, 0, 935, 936, 5, 31, 0, 0, 936, 937, 6, 24, -1, 0, 937, 1119, 1, 0, 0, 0, 938, 939, 5, 148, 0, 0, 939, 940, 3, 40, 20, 0, 940, 941, 5, 31, 0, 0, 941, 942, 6, 24, -1, 0, 942, 1119, 1, 0, 0, 0, 943, 944, 5, 149, 0, 0, 944, 945, 3, 40, 20, 0, 945, 946, 5, 31, 0, 0, 946, 947, 6, 24, -1, 0, 947, 1119, 1, 0, 0, 0, 948, 949, 5, 150, 0, 0, 949, 950, 3, 40, 20, 0, 950, 951, 5, 31, 0, 0, 951, 952, 6, 24, -1, 0, 952, 1119, 1, 0, 0, 0, 953, 954, 5, 151, 0, 0, 954, 955, 3, 40, 20, 0, 955, 956, 5, 31, 0, 0, 956, 957, 6, 24, -1, 0, 957, 1119, 1, 0, 0, 0, 958, 959, 5, 152, 0, 0, 959, 960, 3, 40, 20, 0, 960, 961, 5, 31, 0, 0, 961, 962, 6, 24, -1, 0, 962, 1119, 1, 0, 0, 0, 963, 964, 5, 153, 0, 0, 964, 965, 3, 40, 20, 0, 965, 966, 5, 31, 0, 0, 966, 967, 6, 24, -1, 0, 967, 1119, 1, 0, 0, 0, 968, 969, 5, 154, 0, 0, 969, 970, 3, 40, 20, 0, 970, 971, 5, 31, 0, 0, 971, 972, 6, 24, -1, 0, 972, 1119, 1, 0, 0, 0, 973, 974, 5, 155, 0, 0, 974, 975, 3, 40, 20, 0, 975, 976, 5, 31, 0, 0, 976, 977, 6, 24, -1, 0, 977, 1119, 1, 0, 0, 0, 978, 979, 5, 156, 0, 0, 979, 980, 3, 40, 20, 0, 980, 981, 5, 31, 0, 0, 981, 982, 6, 24, -1, 0, 982, 1119, 1, 0, 0, 0, 983, 984, 5, 157, 0, 0, 984, 985, 3, 40, 20, 0, 985, 986, 5, 31, 0, 0, 986, 987, 6, 24, -1, 0, 987, 1119, 1, 0, 0, 0, 988, 989, 5, 158, 0, 0, 989, 990, 3, 40, 20, 0, 990, 991, 5, 31, 0, 0, 991, 992, 6, 24, -1, 0, 992, 1119, 1, 0, 0, 0, 993, 994, 5, 159, 0, 0, 994, 995, 3, 40, 20, 0, 995, 996, 5, 31, 0, 0, 996, 997, 6, 24, -1, 0, 997, 1119, 1, 0, 0, 0, 998, 999, 5, 160, 0, 0, 999, 1000, 3, 40, 20, 0, 1000, 1001, 5, 31, 0, 0, 1001, 1002, 6, 24, -1, 0, 1002, 1119, 1, 0, 0, 0, 1003, 1004, 5, 161, 0, 0, 1004, 1005, 3, 40, 20, 0, 1005, 1006, 5, 31, 0, 0, 1006, 1007, 6, 24, -1, 0, 1007, 1119, 1, 0, 0, 0, 1008, 1009, 5, 162, 0, 0, 1009, 1010, 3, 40, 20, 0, 1010, 1011, 5, 31, 0, 0, 1011, 1012, 6, 24, -1, 0, 1012, 1119, 1, 0, 0, 0, 1013, 1014, 5, 163, 0, 0, 1014, 1015, 3, 40, 20, 0, 1015, 1016, 5, 31, 0, 0, 1016, 1017, 6, 24, -1, 0, 1017, 1119, 1, 0, 0, 0, 1018, 1019, 5, 164, 0, 0, 1019, 1020, 3, 40, 20, 0, 1020, 1021, 5, 31, 0, 0, 1021, 1022, 6, 24, -1, 0, 1022, 1119, 1, 0, 0, 0, 1023, 1024, 5, 165, 0, 0, 1024, 1025, 3, 40, 20, 0, 1025, 1026, 5, 31, 0, 0, 1026, 1027, 6, 24, -1, 0, 1027, 1119, 1, 0, 0, 0, 1028, 1029, 5, 166, 0, 0, 1029, 1030, 3, 40, 20, 0, 1030, 1031, 5, 31, 0, 0, 1031, 1032, 6, 24, -1, 0, 1032, 1119, 1, 0, 0, 0, 1033, 1034, 5, 167, 0, 0, 1034, 1035, 3, 40, 20, 0, 1035, 1036, 5, 31, 0, 0, 1036, 1037, 6, 24, -1, 0, 1037, 1119, 1, 0, 0, 0, 1038, 1039, 5, 168, 0, 0, 1039, 1040, 3, 40, 20, 0, 1040, 1041, 5, 31, 0, 0, 1041, 1042, 6, 24, -1, 0, 1042, 1119, 1, 0, 0, 0, 1043, 1044, 5, 169, 0, 0, 1044, 1045, 3, 40, 20, 0, 1045, 1046, 5, 31, 0, 0, 1046, 1047, 6, 24, -1, 0, 1047, 1119, 1, 0, 0, 0, 1048, 1049, 5, 170, 0, 0, 1049, 1050, 3, 40, 20, 0, 1050, 1051, 5, 31, 0, 0, 1051, 1052, 6, 24, -1, 0, 1052, 1119, 1, 0, 0, 0, 1053, 1054, 5, 171, 0, 0, 1054, 1055, 3, 40, 20, 0, 1055, 1056, 5, 31, 0, 0, 1056, 1057, 6, 24, -1, 0, 1057, 1119, 1, 0, 0, 0, 1058, 1059, 5, 172, 0, 0, 1059, 1060, 3, 40, 20, 0, 1060, 1061, 5, 31, 0, 0, 1061, 1062, 6, 24, -1, 0, 1062, 1119, 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, 1119, 1, 0, 0, 0, 1068, 1069, 5, 174, 0, 0, 1069, 1070, 3, 40, 20, 0, 1070, 1071, 5, 31, 0, 0, 1071, 1072, 6, 24, -1, 0, 1072, 1119, 1, 0, 0, 0, 1073, 1074, 5, 175, 0, 0, 1074, 1075, 3, 40, 20, 0, 1075, 1076, 5, 31, 0, 0, 1076, 1077, 6, 24, -1, 0, 1077, 1119, 1, 0, 0, 0, 1078, 1079, 5, 176, 0, 0, 1079, 1080, 3, 40, 20, 0, 1080, 1081, 5, 31, 0, 0, 1081, 1082, 6, 24, -1, 0, 1082, 1119, 1, 0, 0, 0, 1083, 1084, 5, 177, 0, 0, 1084, 1085, 3, 40, 20, 0, 1085, 1086, 5, 31, 0, 0, 1086, 1087, 6, 24, -1, 0, 1087, 1119, 1, 0, 0, 0, 1088, 1089, 5, 178, 0, 0, 1089, 1090, 3, 40, 20, 0, 1090, 1091, 5, 31, 0, 0, 1091, 1092, 6, 24, -1, 0, 1092, 1119, 1, 0, 0, 0, 1093, 1094, 5, 179, 0, 0, 1094, 1095, 3, 40, 20, 0, 1095, 1096, 5, 31, 0, 0, 1096, 1097, 6, 24, -1, 0, 1097, 1119, 1, 0, 0, 0, 1098, 1099, 5, 180, 0, 0, 1099, 1100, 3, 40, 20, 0, 1100, 1101, 5, 31, 0, 0, 1101, 1102, 6, 24, -1, 0, 1102, 1119, 1, 0, 0, 0, 1103, 1104, 5, 181, 0, 0, 1104, 1105, 3, 40, 20, 0, 1105, 1106, 5, 31, 0, 0, 1106, 1107, 6, 24, -1, 0, 1107, 1119, 1, 0, 0, 0, 1108, 1109, 5, 182, 0, 0, 1109, 1110, 3, 40, 20, 0, 1110, 1111, 5, 31, 0, 0, 1111, 1112, 6, 24, -1, 0, 1112, 1119, 1, 0, 0, 0, 1113, 1114, 5, 183, 0, 0, 1114, 1115, 3, 40, 20, 0, 1115, 1116, 5, 31, 0, 0, 1116, 1117, 6, 24, -1, 0, 1117, 1119, 1, 0, 0, 0, 1118, 430, 1, 0, 0, 0, 1118, 432, 1, 0, 0, 0, 1118, 434, 1, 0, 0, 0, 1118, 436, 1, 0, 0, 0, 1118, 438, 1, 0, 0, 0, 1118, 440, 1, 0, 0, 0, 1118, 442, 1, 0, 0, 0, 1118, 444, 1, 0, 0, 0, 1118, 449, 1, 0, 0, 0, 1118, 453, 1, 0, 0, 0, 1118, 458, 1, 0, 0, 0, 1118, 463, 1, 0, 0, 0, 1118, 468, 1, 0, 0, 0, 1118, 473, 1, 0, 0, 0, 1118, 478, 1, 0, 0, 0, 1118, 483, 1, 0, 0, 0, 1118, 488, 1, 0, 0, 0, 1118, 493, 1, 0, 0, 0, 1118, 498, 1, 0, 0, 0, 1118, 503, 1, 0, 0, 0, 1118, 508, 1, 0, 0, 0, 1118, 513, 1, 0, 0, 0, 1118, 518, 1, 0, 0, 0, 1118, 523, 1, 0, 0, 0, 1118, 528, 1, 0, 0, 0, 1118, 533, 1, 0, 0, 0, 1118, 538, 1, 0, 0, 0, 1118, 543, 1, 0, 0, 0, 1118, 548, 1, 0, 0, 0, 1118, 553, 1, 0, 0, 0, 1118, 558, 1, 0, 0, 0, 1118, 563, 1, 0, 0, 0, 1118, 568, 1, 0, 0, 0, 1118, 573, 1, 0, 0, 0, 1118, 578, 1, 0, 0, 0, 1118, 583, 1, 0, 0, 0, 1118, 588, 1, 0, 0, 0, 1118, 593, 1, 0, 0, 0, 1118, 598, 1, 0, 0, 0, 1118, 603, 1, 0, 0, 0, 1118, 608, 1, 0, 0, 0, 1118, 613, 1, 0, 0, 0, 1118, 618, 1, 0, 0, 0, 1118, 623, 1, 0, 0, 0, 1118, 628, 1, 0, 0, 0, 1118, 633, 1, 0, 0, 0, 1118, 638, 1, 0, 0, 0, 1118, 643, 1, 0, 0, 0, 1118, 648, 1, 0, 0, 0, 1118, 653, 1, 0, 0, 0, 1118, 658, 1, 0, 0, 0, 1118, 663, 1, 0, 0, 0, 1118, 668, 1, 0, 0, 0, 1118, 673, 1, 0, 0, 0, 1118, 678, 1, 0, 0, 0, 1118, 683, 1, 0, 0, 0, 1118, 688, 1, 0, 0, 0, 1118, 693, 1, 0, 0, 0, 1118, 698, 1, 0, 0, 0, 1118, 703, 1, 0, 0, 0, 1118, 708, 1, 0, 0, 0, 1118, 713, 1, 0, 0, 0, 1118, 718, 1, 0, 0, 0, 1118, 723, 1, 0, 0, 0, 1118, 728, 1, 0, 0, 0, 1118, 733, 1, 0, 0, 0, 1118, 738, 1, 0, 0, 0, 1118, 743, 1, 0, 0, 0, 1118, 748, 1, 0, 0, 0, 1118, 753, 1, 0, 0, 0, 1118, 758, 1, 0, 0, 0, 1118, 763, 1, 0, 0, 0, 1118, 768, 1, 0, 0, 0, 1118, 773, 1, 0, 0, 0, 1118, 778, 1, 0, 0, 0, 1118, 783, 1, 0, 0, 0, 1118, 788, 1, 0, 0, 0, 1118, 793, 1, 0, 0, 0, 1118, 798, 1, 0, 0, 0, 1118, 803, 1, 0, 0, 0, 1118, 808, 1, 0, 0, 0, 1118, 813, 1, 0, 0, 0, 1118, 818, 1, 0, 0, 0, 1118, 823, 1, 0, 0, 0, 1118, 828, 1, 0, 0, 0, 1118, 833, 1, 0, 0, 0, 1118, 838, 1, 0, 0, 0, 1118, 843, 1, 0, 0, 0, 1118, 848, 1, 0, 0, 0, 1118, 853, 1, 0, 0, 0, 1118, 858, 1, 0, 0, 0, 1118, 863, 1, 0, 0, 0, 1118, 868, 1, 0, 0, 0, 1118, 873, 1, 0, 0, 0, 1118, 878, 1, 0, 0, 0, 1118, 883, 1, 0, 0, 0, 1118, 888, 1, 0, 0, 0, 1118, 893, 1, 0, 0, 0, 1118, 898, 1, 0, 0, 0, 1118, 903, 1, 0, 0, 0, 1118, 908, 1, 0, 0, 0, 1118, 913, 1, 0, 0, 0, 1118, 918, 1, 0, 0, 0, 1118, 923, 1, 0, 0, 0, 1118, 928, 1, 0, 0, 0, 1118, 933, 1, 0, 0, 0, 1118, 938, 1, 0, 0, 0, 1118, 943, 1, 0, 0, 0, 1118, 948, 1, 0, 0, 0, 1118, 953, 1, 0, 0, 0, 1118, 958, 1, 0, 0, 0, 1118, 963, 1, 0, 0, 0, 1118, 968, 1, 0, 0, 0, 1118, 973, 1, 0, 0, 0, 1118, 978, 1, 0, 0, 0, 1118, 983, 1, 0, 0, 0, 1118, 988, 1, 0, 0, 0, 1118, 993, 1, 0, 0, 0, 1118, 998, 1, 0, 0, 0, 1118, 1003, 1, 0, 0, 0, 1118, 1008, 1, 0, 0, 0, 1118, 1013, 1, 0, 0, 0, 1118, 1018, 1, 0, 0, 0, 1118, 1023, 1, 0, 0, 0, 1118, 1028, 1, 0, 0, 0, 1118, 1033, 1, 0, 0, 0, 1118, 1038, 1, 0, 0, 0, 1118, 1043, 1, 0, 0, 0, 1118, 1048, 1, 0, 0, 0, 1118, 1053, 1, 0, 0, 0, 1118, 1058, 1, 0, 0, 0, 1118, 1063, 1, 0, 0, 0, 1118, 1068, 1, 0, 0, 0, 1118, 1073, 1, 0, 0, 0, 1118, 1078, 1, 0, 0, 0, 1118, 1083, 1, 0, 0, 0, 1118, 1088, 1, 0, 0, 0, 1118, 1093, 1, 0, 0, 0, 1118, 1098, 1, 0, 0, 0, 1118, 1103, 1, 0, 0, 0, 1118, 1108, 1, 0, 0, 0, 1118, 1113, 1, 0, 0, 0, 1119, 49, 1, 0, 0, 0, 1120, 1121, 3, 32, 16, 0, 1121, 1122, 5, 0, 0, 1, 1122, 1123, 6, 25, -1, 0, 1123, 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, 1118]
\ No newline at end of file
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
index 7ab99b888..d3b5bc330 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
@@ -180,14 +180,15 @@ T__178=179
T__179=180
T__180=181
T__181=182
-NEWLINE=183
-NUMBER=184
-SPECIALSET=185
-BOOLEAN=186
-NAN=187
-VARIABLE=188
-COMMENT=189
-WS=190
+T__182=183
+NEWLINE=184
+NUMBER=185
+SPECIALSET=186
+BOOLEAN=187
+NAN=188
+VARIABLE=189
+COMMENT=190
+WS=191
'!'=1
'^'=2
'-'=3
@@ -355,19 +356,20 @@ WS=190
'lcm('=165
'binomial('=166
'iverson('=167
-'erf('=168
-'erfc('=169
-'erfi('=170
-'Ei('=171
-'li('=172
-'Si('=173
-'Ci('=174
-'Shi('=175
-'Chi('=176
-'trunc('=177
-'conjugate('=178
-'domain('=179
-'piecewise('=180
-'apply('=181
-'lambda('=182
-'NaN'=187
+'aleph('=168
+'erf('=169
+'erfc('=170
+'erfi('=171
+'Ei('=172
+'li('=173
+'Si('=174
+'Ci('=175
+'Shi('=176
+'Chi('=177
+'trunc('=178
+'conjugate('=179
+'domain('=180
+'piecewise('=181
+'apply('=182
+'lambda('=183
+'NaN'=188
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
index 37c1f6318..830797aee 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs
@@ -61,8 +61,8 @@ public const int
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, T__171=172, T__172=173,
T__173=174, T__174=175, T__175=176, T__176=177, T__177=178, T__178=179,
- T__179=180, T__180=181, T__181=182, NEWLINE=183, NUMBER=184, SPECIALSET=185,
- BOOLEAN=186, NAN=187, VARIABLE=188, COMMENT=189, WS=190;
+ T__179=180, T__180=181, T__181=182, T__182=183, NEWLINE=184, NUMBER=185,
+ SPECIALSET=186, BOOLEAN=187, NAN=188, VARIABLE=189, COMMENT=190, WS=191;
public static string[] channelNames = {
"DEFAULT_TOKEN_CHANNEL", "HIDDEN"
};
@@ -96,8 +96,8 @@ public const int
"T__161", "T__162", "T__163", "T__164", "T__165", "T__166", "T__167",
"T__168", "T__169", "T__170", "T__171", "T__172", "T__173", "T__174",
"T__175", "T__176", "T__177", "T__178", "T__179", "T__180", "T__181",
- "NEWLINE", "EXPONENT", "NUMBER", "SPECIALSET", "BOOLEAN", "NAN", "VARIABLE",
- "COMMENT", "WS"
+ "T__182", "NEWLINE", "EXPONENT", "NUMBER", "SPECIALSET", "BOOLEAN", "NAN",
+ "VARIABLE", "COMMENT", "WS"
};
@@ -143,8 +143,8 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu
"'powerset('", "'union('", "'intersection('", "'complement('", "'image('",
"'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('",
"'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('",
- "'iverson('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'Si('",
- "'Ci('", "'Shi('", "'Chi('", "'trunc('", "'conjugate('", "'domain('",
+ "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('",
+ "'Si('", "'Ci('", "'Shi('", "'Chi('", "'trunc('", "'conjugate('", "'domain('",
"'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'"
};
private static readonly string[] _SymbolicNames = {
@@ -163,8 +163,8 @@ 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, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN", "NAN",
- "VARIABLE", "COMMENT", "WS"
+ null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN",
+ "NAN", "VARIABLE", "COMMENT", "WS"
};
public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames);
@@ -194,7 +194,7 @@ static AngouriMathLexer() {
}
}
private static int[] _serializedATN = {
- 4,0,190,1626,6,-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,
+ 4,0,191,1635,6,-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,
@@ -223,536 +223,539 @@ static AngouriMathLexer() {
7,170,2,171,7,171,2,172,7,172,2,173,7,173,2,174,7,174,2,175,7,175,2,176,
7,176,2,177,7,177,2,178,7,178,2,179,7,179,2,180,7,180,2,181,7,181,2,182,
7,182,2,183,7,183,2,184,7,184,2,185,7,185,2,186,7,186,2,187,7,187,2,188,
- 7,188,2,189,7,189,2,190,7,190,1,0,1,0,1,1,1,1,1,2,1,2,1,3,1,3,1,4,1,4,
- 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,
- 1,109,1,109,1,110,1,110,1,110,1,110,1,110,1,110,1,110,1,110,1,111,1,111,
- 1,111,1,111,1,111,1,111,1,112,1,112,1,112,1,112,1,112,1,112,1,112,1,112,
- 1,112,1,113,1,113,1,113,1,113,1,113,1,113,1,113,1,114,1,114,1,114,1,114,
- 1,114,1,114,1,114,1,114,1,115,1,115,1,115,1,115,1,115,1,115,1,116,1,116,
- 1,116,1,116,1,116,1,116,1,116,1,116,1,116,1,117,1,117,1,117,1,117,1,117,
- 1,117,1,117,1,118,1,118,1,118,1,118,1,118,1,118,1,118,1,118,1,119,1,119,
- 1,119,1,119,1,119,1,119,1,119,1,119,1,119,1,120,1,120,1,120,1,120,1,120,
- 1,120,1,120,1,120,1,120,1,120,1,121,1,121,1,121,1,121,1,121,1,121,1,121,
- 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,
- 1,146,1,146,1,146,1,147,1,147,1,147,1,147,1,147,1,147,1,147,1,147,1,147,
- 1,147,1,147,1,148,1,148,1,148,1,148,1,148,1,148,1,149,1,149,1,149,1,149,
- 1,149,1,149,1,149,1,149,1,149,1,149,1,150,1,150,1,150,1,150,1,150,1,150,
- 1,150,1,151,1,151,1,151,1,151,1,151,1,151,1,151,1,151,1,151,1,151,1,151,
- 1,151,1,151,1,151,1,152,1,152,1,152,1,152,1,152,1,152,1,152,1,152,1,152,
- 1,152,1,152,1,152,1,153,1,153,1,153,1,153,1,153,1,153,1,153,1,154,1,154,
- 1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,154,1,155,1,155,1,155,1,155,
- 1,155,1,155,1,155,1,156,1,156,1,156,1,156,1,156,1,156,1,157,1,157,1,157,
- 1,157,1,157,1,157,1,157,1,157,1,157,1,158,1,158,1,158,1,158,1,158,1,158,
- 1,158,1,159,1,159,1,159,1,159,1,159,1,160,1,160,1,160,1,160,1,160,1,161,
- 1,161,1,161,1,161,1,161,1,161,1,161,1,161,1,162,1,162,1,162,1,162,1,162,
- 1,162,1,162,1,162,1,163,1,163,1,163,1,163,1,163,1,164,1,164,1,164,1,164,
- 1,164,1,165,1,165,1,165,1,165,1,165,1,165,1,165,1,165,1,165,1,165,1,166,
- 1,166,1,166,1,166,1,166,1,166,1,166,1,166,1,166,1,167,1,167,1,167,1,167,
- 1,167,1,168,1,168,1,168,1,168,1,168,1,168,1,169,1,169,1,169,1,169,1,169,
- 1,169,1,170,1,170,1,170,1,170,1,171,1,171,1,171,1,171,1,172,1,172,1,172,
- 1,172,1,173,1,173,1,173,1,173,1,174,1,174,1,174,1,174,1,174,1,175,1,175,
- 1,175,1,175,1,175,1,176,1,176,1,176,1,176,1,176,1,176,1,176,1,177,1,177,
- 1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,177,1,178,1,178,1,178,
- 1,178,1,178,1,178,1,178,1,178,1,179,1,179,1,179,1,179,1,179,1,179,1,179,
- 1,179,1,179,1,179,1,179,1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,181,
- 1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,182,3,182,1480,8,182,1,182,
- 4,182,1483,8,182,11,182,12,182,1484,1,182,1,182,1,183,1,183,3,183,1491,
- 8,183,1,183,4,183,1494,8,183,11,183,12,183,1495,1,184,4,184,1499,8,184,
- 11,184,12,184,1500,1,184,1,184,5,184,1505,8,184,10,184,12,184,1508,9,184,
- 1,184,3,184,1511,8,184,1,184,3,184,1514,8,184,1,184,3,184,1517,8,184,1,
- 184,4,184,1520,8,184,11,184,12,184,1521,1,184,3,184,1525,8,184,1,184,3,
- 184,1528,8,184,1,184,3,184,1531,8,184,1,185,1,185,1,185,1,185,1,185,1,
- 185,1,185,1,185,1,185,1,185,1,185,1,185,1,185,1,185,1,185,1,185,1,185,
- 1,185,3,185,1551,8,185,1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,
- 1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,1,186,3,186,1571,
- 8,186,1,187,1,187,1,187,1,187,1,188,4,188,1578,8,188,11,188,12,188,1579,
- 1,188,1,188,4,188,1584,8,188,11,188,12,188,1585,3,188,1588,8,188,1,189,
- 1,189,1,189,1,189,5,189,1594,8,189,10,189,12,189,1597,9,189,1,189,3,189,
- 1600,8,189,1,189,3,189,1603,8,189,1,189,1,189,1,189,1,189,5,189,1609,8,
- 189,10,189,12,189,1612,9,189,1,189,1,189,3,189,1616,8,189,1,189,1,189,
- 1,190,4,190,1621,8,190,11,190,12,190,1622,1,190,1,190,1,1610,0,191,1,1,
- 3,2,5,3,7,4,9,5,11,6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,27,14,29,15,
- 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,
- 61,123,62,125,63,127,64,129,65,131,66,133,67,135,68,137,69,139,70,141,
- 71,143,72,145,73,147,74,149,75,151,76,153,77,155,78,157,79,159,80,161,
- 81,163,82,165,83,167,84,169,85,171,86,173,87,175,88,177,89,179,90,181,
- 91,183,92,185,93,187,94,189,95,191,96,193,97,195,98,197,99,199,100,201,
- 101,203,102,205,103,207,104,209,105,211,106,213,107,215,108,217,109,219,
- 110,221,111,223,112,225,113,227,114,229,115,231,116,233,117,235,118,237,
- 119,239,120,241,121,243,122,245,123,247,124,249,125,251,126,253,127,255,
- 128,257,129,259,130,261,131,263,132,265,133,267,134,269,135,271,136,273,
- 137,275,138,277,139,279,140,281,141,283,142,285,143,287,144,289,145,291,
- 146,293,147,295,148,297,149,299,150,301,151,303,152,305,153,307,154,309,
- 155,311,156,313,157,315,158,317,159,319,160,321,161,323,162,325,163,327,
- 164,329,165,331,166,333,167,335,168,337,169,339,170,341,171,343,172,345,
- 173,347,174,349,175,351,176,353,177,355,178,357,179,359,180,361,181,363,
- 182,365,183,367,0,369,184,371,185,373,186,375,187,377,188,379,189,381,
- 190,1,0,6,2,0,69,69,101,101,2,0,43,43,45,45,4,0,65,90,97,122,880,1279,
- 7936,8191,5,0,48,57,65,90,97,122,880,1279,7936,8191,2,0,10,10,13,13,2,
- 0,9,9,32,32,1657,0,1,1,0,0,0,0,3,1,0,0,0,0,5,1,0,0,0,0,7,1,0,0,0,0,9,1,
- 0,0,0,0,11,1,0,0,0,0,13,1,0,0,0,0,15,1,0,0,0,0,17,1,0,0,0,0,19,1,0,0,0,
- 0,21,1,0,0,0,0,23,1,0,0,0,0,25,1,0,0,0,0,27,1,0,0,0,0,29,1,0,0,0,0,31,
- 1,0,0,0,0,33,1,0,0,0,0,35,1,0,0,0,0,37,1,0,0,0,0,39,1,0,0,0,0,41,1,0,0,
- 0,0,43,1,0,0,0,0,45,1,0,0,0,0,47,1,0,0,0,0,49,1,0,0,0,0,51,1,0,0,0,0,53,
- 1,0,0,0,0,55,1,0,0,0,0,57,1,0,0,0,0,59,1,0,0,0,0,61,1,0,0,0,0,63,1,0,0,
- 0,0,65,1,0,0,0,0,67,1,0,0,0,0,69,1,0,0,0,0,71,1,0,0,0,0,73,1,0,0,0,0,75,
- 1,0,0,0,0,77,1,0,0,0,0,79,1,0,0,0,0,81,1,0,0,0,0,83,1,0,0,0,0,85,1,0,0,
- 0,0,87,1,0,0,0,0,89,1,0,0,0,0,91,1,0,0,0,0,93,1,0,0,0,0,95,1,0,0,0,0,97,
- 1,0,0,0,0,99,1,0,0,0,0,101,1,0,0,0,0,103,1,0,0,0,0,105,1,0,0,0,0,107,1,
- 0,0,0,0,109,1,0,0,0,0,111,1,0,0,0,0,113,1,0,0,0,0,115,1,0,0,0,0,117,1,
- 0,0,0,0,119,1,0,0,0,0,121,1,0,0,0,0,123,1,0,0,0,0,125,1,0,0,0,0,127,1,
- 0,0,0,0,129,1,0,0,0,0,131,1,0,0,0,0,133,1,0,0,0,0,135,1,0,0,0,0,137,1,
- 0,0,0,0,139,1,0,0,0,0,141,1,0,0,0,0,143,1,0,0,0,0,145,1,0,0,0,0,147,1,
- 0,0,0,0,149,1,0,0,0,0,151,1,0,0,0,0,153,1,0,0,0,0,155,1,0,0,0,0,157,1,
- 0,0,0,0,159,1,0,0,0,0,161,1,0,0,0,0,163,1,0,0,0,0,165,1,0,0,0,0,167,1,
- 0,0,0,0,169,1,0,0,0,0,171,1,0,0,0,0,173,1,0,0,0,0,175,1,0,0,0,0,177,1,
- 0,0,0,0,179,1,0,0,0,0,181,1,0,0,0,0,183,1,0,0,0,0,185,1,0,0,0,0,187,1,
- 0,0,0,0,189,1,0,0,0,0,191,1,0,0,0,0,193,1,0,0,0,0,195,1,0,0,0,0,197,1,
- 0,0,0,0,199,1,0,0,0,0,201,1,0,0,0,0,203,1,0,0,0,0,205,1,0,0,0,0,207,1,
- 0,0,0,0,209,1,0,0,0,0,211,1,0,0,0,0,213,1,0,0,0,0,215,1,0,0,0,0,217,1,
- 0,0,0,0,219,1,0,0,0,0,221,1,0,0,0,0,223,1,0,0,0,0,225,1,0,0,0,0,227,1,
- 0,0,0,0,229,1,0,0,0,0,231,1,0,0,0,0,233,1,0,0,0,0,235,1,0,0,0,0,237,1,
- 0,0,0,0,239,1,0,0,0,0,241,1,0,0,0,0,243,1,0,0,0,0,245,1,0,0,0,0,247,1,
- 0,0,0,0,249,1,0,0,0,0,251,1,0,0,0,0,253,1,0,0,0,0,255,1,0,0,0,0,257,1,
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- 5,103,0,0,1355,1356,5,99,0,0,1356,1357,5,100,0,0,1357,1358,5,40,0,0,1358,
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- 0,1377,1378,5,114,0,0,1378,1379,5,115,0,0,1379,1380,5,111,0,0,1380,1381,
- 5,110,0,0,1381,1382,5,40,0,0,1382,334,1,0,0,0,1383,1384,5,101,0,0,1384,
- 1385,5,114,0,0,1385,1386,5,102,0,0,1386,1387,5,40,0,0,1387,336,1,0,0,0,
- 1388,1389,5,101,0,0,1389,1390,5,114,0,0,1390,1391,5,102,0,0,1391,1392,
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- 104,0,0,1418,1419,5,105,0,0,1419,1420,5,40,0,0,1420,350,1,0,0,0,1421,1422,
- 5,67,0,0,1422,1423,5,104,0,0,1423,1424,5,105,0,0,1424,1425,5,40,0,0,1425,
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- 0,1429,1430,5,110,0,0,1430,1431,5,99,0,0,1431,1432,5,40,0,0,1432,354,1,
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- 5,112,0,0,1466,1467,5,108,0,0,1467,1468,5,121,0,0,1468,1469,5,40,0,0,1469,
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- 1473,1474,5,98,0,0,1474,1475,5,100,0,0,1475,1476,5,97,0,0,1476,1477,5,
- 40,0,0,1477,364,1,0,0,0,1478,1480,5,13,0,0,1479,1478,1,0,0,0,1479,1480,
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- 1,0,0,0,1587,1581,1,0,0,0,1587,1588,1,0,0,0,1588,378,1,0,0,0,1589,1590,
- 5,47,0,0,1590,1591,5,47,0,0,1591,1595,1,0,0,0,1592,1594,8,4,0,0,1593,1592,
- 1,0,0,0,1594,1597,1,0,0,0,1595,1593,1,0,0,0,1595,1596,1,0,0,0,1596,1602,
- 1,0,0,0,1597,1595,1,0,0,0,1598,1600,5,13,0,0,1599,1598,1,0,0,0,1599,1600,
- 1,0,0,0,1600,1601,1,0,0,0,1601,1603,5,10,0,0,1602,1599,1,0,0,0,1602,1603,
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- 1,0,0,0,1607,1609,9,0,0,0,1608,1607,1,0,0,0,1609,1612,1,0,0,0,1610,1611,
- 1,0,0,0,1610,1608,1,0,0,0,1611,1613,1,0,0,0,1612,1610,1,0,0,0,1613,1614,
- 5,42,0,0,1614,1616,5,47,0,0,1615,1589,1,0,0,0,1615,1604,1,0,0,0,1616,1617,
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- 1500,1506,1510,1513,1516,1521,1524,1527,1530,1550,1570,1579,1585,1587,
- 1595,1599,1602,1610,1615,1622,1,6,0,0
+ 7,188,2,189,7,189,2,190,7,190,2,191,7,191,1,0,1,0,1,1,1,1,1,2,1,2,1,3,
+ 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,
+ 1,111,1,111,1,111,1,111,1,111,1,111,1,112,1,112,1,112,1,112,1,112,1,112,
+ 1,112,1,112,1,112,1,113,1,113,1,113,1,113,1,113,1,113,1,113,1,114,1,114,
+ 1,114,1,114,1,114,1,114,1,114,1,114,1,115,1,115,1,115,1,115,1,115,1,115,
+ 1,116,1,116,1,116,1,116,1,116,1,116,1,116,1,116,1,116,1,117,1,117,1,117,
+ 1,117,1,117,1,117,1,117,1,118,1,118,1,118,1,118,1,118,1,118,1,118,1,118,
+ 1,119,1,119,1,119,1,119,1,119,1,119,1,119,1,119,1,119,1,120,1,120,1,120,
+ 1,120,1,120,1,120,1,120,1,120,1,120,1,120,1,121,1,121,1,121,1,121,1,121,
+ 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,
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+ 0,0,1524,1526,5,46,0,0,1525,1524,1,0,0,0,1525,1526,1,0,0,0,1526,1528,1,
+ 0,0,0,1527,1529,2,48,57,0,1528,1527,1,0,0,0,1529,1530,1,0,0,0,1530,1528,
+ 1,0,0,0,1530,1531,1,0,0,0,1531,1533,1,0,0,0,1532,1534,3,369,184,0,1533,
+ 1532,1,0,0,0,1533,1534,1,0,0,0,1534,1536,1,0,0,0,1535,1537,5,105,0,0,1536,
+ 1535,1,0,0,0,1536,1537,1,0,0,0,1537,1540,1,0,0,0,1538,1540,5,105,0,0,1539,
+ 1507,1,0,0,0,1539,1525,1,0,0,0,1539,1538,1,0,0,0,1540,372,1,0,0,0,1541,
+ 1542,5,67,0,0,1542,1560,5,67,0,0,1543,1544,5,82,0,0,1544,1560,5,82,0,0,
+ 1545,1546,5,81,0,0,1546,1560,5,81,0,0,1547,1548,5,90,0,0,1548,1560,5,90,
+ 0,0,1549,1550,5,66,0,0,1550,1560,5,66,0,0,1551,1552,5,90,0,0,1552,1553,
+ 5,90,0,0,1553,1560,5,42,0,0,1554,1555,5,90,0,0,1555,1556,5,90,0,0,1556,
+ 1560,5,43,0,0,1557,1558,5,80,0,0,1558,1560,5,80,0,0,1559,1541,1,0,0,0,
+ 1559,1543,1,0,0,0,1559,1545,1,0,0,0,1559,1547,1,0,0,0,1559,1549,1,0,0,
+ 0,1559,1551,1,0,0,0,1559,1554,1,0,0,0,1559,1557,1,0,0,0,1560,374,1,0,0,
+ 0,1561,1562,5,116,0,0,1562,1563,5,114,0,0,1563,1564,5,117,0,0,1564,1580,
+ 5,101,0,0,1565,1566,5,84,0,0,1566,1567,5,114,0,0,1567,1568,5,117,0,0,1568,
+ 1580,5,101,0,0,1569,1570,5,102,0,0,1570,1571,5,97,0,0,1571,1572,5,108,
+ 0,0,1572,1573,5,115,0,0,1573,1580,5,101,0,0,1574,1575,5,70,0,0,1575,1576,
+ 5,97,0,0,1576,1577,5,108,0,0,1577,1578,5,115,0,0,1578,1580,5,101,0,0,1579,
+ 1561,1,0,0,0,1579,1565,1,0,0,0,1579,1569,1,0,0,0,1579,1574,1,0,0,0,1580,
+ 376,1,0,0,0,1581,1582,5,78,0,0,1582,1583,5,97,0,0,1583,1584,5,78,0,0,1584,
+ 378,1,0,0,0,1585,1587,7,2,0,0,1586,1585,1,0,0,0,1587,1588,1,0,0,0,1588,
+ 1586,1,0,0,0,1588,1589,1,0,0,0,1589,1596,1,0,0,0,1590,1592,5,95,0,0,1591,
+ 1593,7,3,0,0,1592,1591,1,0,0,0,1593,1594,1,0,0,0,1594,1592,1,0,0,0,1594,
+ 1595,1,0,0,0,1595,1597,1,0,0,0,1596,1590,1,0,0,0,1596,1597,1,0,0,0,1597,
+ 380,1,0,0,0,1598,1599,5,47,0,0,1599,1600,5,47,0,0,1600,1604,1,0,0,0,1601,
+ 1603,8,4,0,0,1602,1601,1,0,0,0,1603,1606,1,0,0,0,1604,1602,1,0,0,0,1604,
+ 1605,1,0,0,0,1605,1611,1,0,0,0,1606,1604,1,0,0,0,1607,1609,5,13,0,0,1608,
+ 1607,1,0,0,0,1608,1609,1,0,0,0,1609,1610,1,0,0,0,1610,1612,5,10,0,0,1611,
+ 1608,1,0,0,0,1611,1612,1,0,0,0,1612,1625,1,0,0,0,1613,1614,5,47,0,0,1614,
+ 1615,5,42,0,0,1615,1619,1,0,0,0,1616,1618,9,0,0,0,1617,1616,1,0,0,0,1618,
+ 1621,1,0,0,0,1619,1620,1,0,0,0,1619,1617,1,0,0,0,1620,1622,1,0,0,0,1621,
+ 1619,1,0,0,0,1622,1623,5,42,0,0,1623,1625,5,47,0,0,1624,1598,1,0,0,0,1624,
+ 1613,1,0,0,0,1625,1626,1,0,0,0,1626,1627,6,190,0,0,1627,382,1,0,0,0,1628,
+ 1630,7,5,0,0,1629,1628,1,0,0,0,1630,1631,1,0,0,0,1631,1629,1,0,0,0,1631,
+ 1632,1,0,0,0,1632,1633,1,0,0,0,1633,1634,6,191,0,0,1634,384,1,0,0,0,25,
+ 0,1488,1493,1499,1504,1509,1515,1519,1522,1525,1530,1533,1536,1539,1559,
+ 1579,1588,1594,1596,1604,1608,1611,1619,1624,1631,1,6,0,0
};
public static readonly ATN _ATN =
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
index c217b80af..84c6c6012 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp
@@ -167,6 +167,7 @@ null
'lcm('
'binomial('
'iverson('
+'aleph('
'erf('
'erfc('
'erfi('
@@ -375,6 +376,7 @@ null
null
null
null
+null
NEWLINE
NUMBER
SPECIALSET
@@ -567,6 +569,7 @@ T__178
T__179
T__180
T__181
+T__182
NEWLINE
EXPONENT
NUMBER
@@ -585,4 +588,4 @@ mode names:
DEFAULT_MODE
atn:
-[4, 0, 190, 1626, 6, -1, 2, 0, 7, 0, 2, 1, 7, 1, 2, 2, 7, 2, 2, 3, 7, 3, 2, 4, 7, 4, 2, 5, 7, 5, 2, 6, 7, 6, 2, 7, 7, 7, 2, 8, 7, 8, 2, 9, 7, 9, 2, 10, 7, 10, 2, 11, 7, 11, 2, 12, 7, 12, 2, 13, 7, 13, 2, 14, 7, 14, 2, 15, 7, 15, 2, 16, 7, 16, 2, 17, 7, 17, 2, 18, 7, 18, 2, 19, 7, 19, 2, 20, 7, 20, 2, 21, 7, 21, 2, 22, 7, 22, 2, 23, 7, 23, 2, 24, 7, 24, 2, 25, 7, 25, 2, 26, 7, 26, 2, 27, 7, 27, 2, 28, 7, 28, 2, 29, 7, 29, 2, 30, 7, 30, 2, 31, 7, 31, 2, 32, 7, 32, 2, 33, 7, 33, 2, 34, 7, 34, 2, 35, 7, 35, 2, 36, 7, 36, 2, 37, 7, 37, 2, 38, 7, 38, 2, 39, 7, 39, 2, 40, 7, 40, 2, 41, 7, 41, 2, 42, 7, 42, 2, 43, 7, 43, 2, 44, 7, 44, 2, 45, 7, 45, 2, 46, 7, 46, 2, 47, 7, 47, 2, 48, 7, 48, 2, 49, 7, 49, 2, 50, 7, 50, 2, 51, 7, 51, 2, 52, 7, 52, 2, 53, 7, 53, 2, 54, 7, 54, 2, 55, 7, 55, 2, 56, 7, 56, 2, 57, 7, 57, 2, 58, 7, 58, 2, 59, 7, 59, 2, 60, 7, 60, 2, 61, 7, 61, 2, 62, 7, 62, 2, 63, 7, 63, 2, 64, 7, 64, 2, 65, 7, 65, 2, 66, 7, 66, 2, 67, 7, 67, 2, 68, 7, 68, 2, 69, 7, 69, 2, 70, 7, 70, 2, 71, 7, 71, 2, 72, 7, 72, 2, 73, 7, 73, 2, 74, 7, 74, 2, 75, 7, 75, 2, 76, 7, 76, 2, 77, 7, 77, 2, 78, 7, 78, 2, 79, 7, 79, 2, 80, 7, 80, 2, 81, 7, 81, 2, 82, 7, 82, 2, 83, 7, 83, 2, 84, 7, 84, 2, 85, 7, 85, 2, 86, 7, 86, 2, 87, 7, 87, 2, 88, 7, 88, 2, 89, 7, 89, 2, 90, 7, 90, 2, 91, 7, 91, 2, 92, 7, 92, 2, 93, 7, 93, 2, 94, 7, 94, 2, 95, 7, 95, 2, 96, 7, 96, 2, 97, 7, 97, 2, 98, 7, 98, 2, 99, 7, 99, 2, 100, 7, 100, 2, 101, 7, 101, 2, 102, 7, 102, 2, 103, 7, 103, 2, 104, 7, 104, 2, 105, 7, 105, 2, 106, 7, 106, 2, 107, 7, 107, 2, 108, 7, 108, 2, 109, 7, 109, 2, 110, 7, 110, 2, 111, 7, 111, 2, 112, 7, 112, 2, 113, 7, 113, 2, 114, 7, 114, 2, 115, 7, 115, 2, 116, 7, 116, 2, 117, 7, 117, 2, 118, 7, 118, 2, 119, 7, 119, 2, 120, 7, 120, 2, 121, 7, 121, 2, 122, 7, 122, 2, 123, 7, 123, 2, 124, 7, 124, 2, 125, 7, 125, 2, 126, 7, 126, 2, 127, 7, 127, 2, 128, 7, 128, 2, 129, 7, 129, 2, 130, 7, 130, 2, 131, 7, 131, 2, 132, 7, 132, 2, 133, 7, 133, 2, 134, 7, 134, 2, 135, 7, 135, 2, 136, 7, 136, 2, 137, 7, 137, 2, 138, 7, 138, 2, 139, 7, 139, 2, 140, 7, 140, 2, 141, 7, 141, 2, 142, 7, 142, 2, 143, 7, 143, 2, 144, 7, 144, 2, 145, 7, 145, 2, 146, 7, 146, 2, 147, 7, 147, 2, 148, 7, 148, 2, 149, 7, 149, 2, 150, 7, 150, 2, 151, 7, 151, 2, 152, 7, 152, 2, 153, 7, 153, 2, 154, 7, 154, 2, 155, 7, 155, 2, 156, 7, 156, 2, 157, 7, 157, 2, 158, 7, 158, 2, 159, 7, 159, 2, 160, 7, 160, 2, 161, 7, 161, 2, 162, 7, 162, 2, 163, 7, 163, 2, 164, 7, 164, 2, 165, 7, 165, 2, 166, 7, 166, 2, 167, 7, 167, 2, 168, 7, 168, 2, 169, 7, 169, 2, 170, 7, 170, 2, 171, 7, 171, 2, 172, 7, 172, 2, 173, 7, 173, 2, 174, 7, 174, 2, 175, 7, 175, 2, 176, 7, 176, 2, 177, 7, 177, 2, 178, 7, 178, 2, 179, 7, 179, 2, 180, 7, 180, 2, 181, 7, 181, 2, 182, 7, 182, 2, 183, 7, 183, 2, 184, 7, 184, 2, 185, 7, 185, 2, 186, 7, 186, 2, 187, 7, 187, 2, 188, 7, 188, 2, 189, 7, 189, 2, 190, 7, 190, 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, 1, 111, 1, 111, 1, 111, 1, 111, 1, 111, 1, 111, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 112, 1, 113, 1, 113, 1, 113, 1, 113, 1, 113, 1, 113, 1, 113, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 114, 1, 115, 1, 115, 1, 115, 1, 115, 1, 115, 1, 115, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 116, 1, 117, 1, 117, 1, 117, 1, 117, 1, 117, 1, 117, 1, 117, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 118, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 119, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 120, 1, 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, 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0, 1243, 1244, 5, 119, 0, 0, 1244, 1245, 5, 101, 0, 0, 1245, 1246, 5, 114, 0, 0, 1246, 1247, 5, 115, 0, 0, 1247, 1248, 5, 101, 0, 0, 1248, 1249, 5, 116, 0, 0, 1249, 1250, 5, 40, 0, 0, 1250, 300, 1, 0, 0, 0, 1251, 1252, 5, 117, 0, 0, 1252, 1253, 5, 110, 0, 0, 1253, 1254, 5, 105, 0, 0, 1254, 1255, 5, 111, 0, 0, 1255, 1256, 5, 110, 0, 0, 1256, 1257, 5, 40, 0, 0, 1257, 302, 1, 0, 0, 0, 1258, 1259, 5, 105, 0, 0, 1259, 1260, 5, 110, 0, 0, 1260, 1261, 5, 116, 0, 0, 1261, 1262, 5, 101, 0, 0, 1262, 1263, 5, 114, 0, 0, 1263, 1264, 5, 115, 0, 0, 1264, 1265, 5, 101, 0, 0, 1265, 1266, 5, 99, 0, 0, 1266, 1267, 5, 116, 0, 0, 1267, 1268, 5, 105, 0, 0, 1268, 1269, 5, 111, 0, 0, 1269, 1270, 5, 110, 0, 0, 1270, 1271, 5, 40, 0, 0, 1271, 304, 1, 0, 0, 0, 1272, 1273, 5, 99, 0, 0, 1273, 1274, 5, 111, 0, 0, 1274, 1275, 5, 109, 0, 0, 1275, 1276, 5, 112, 0, 0, 1276, 1277, 5, 108, 0, 0, 1277, 1278, 5, 101, 0, 0, 1278, 1279, 5, 109, 0, 0, 1279, 1280, 5, 101, 0, 0, 1280, 1281, 5, 110, 0, 0, 1281, 1282, 5, 116, 0, 0, 1282, 1283, 5, 40, 0, 0, 1283, 306, 1, 0, 0, 0, 1284, 1285, 5, 105, 0, 0, 1285, 1286, 5, 109, 0, 0, 1286, 1287, 5, 97, 0, 0, 1287, 1288, 5, 103, 0, 0, 1288, 1289, 5, 101, 0, 0, 1289, 1290, 5, 40, 0, 0, 1290, 308, 1, 0, 0, 0, 1291, 1292, 5, 112, 0, 0, 1292, 1293, 5, 114, 0, 0, 1293, 1294, 5, 101, 0, 0, 1294, 1295, 5, 105, 0, 0, 1295, 1296, 5, 109, 0, 0, 1296, 1297, 5, 97, 0, 0, 1297, 1298, 5, 103, 0, 0, 1298, 1299, 5, 101, 0, 0, 1299, 1300, 5, 40, 0, 0, 1300, 310, 1, 0, 0, 0, 1301, 1302, 5, 102, 0, 0, 1302, 1303, 5, 108, 0, 0, 1303, 1304, 5, 111, 0, 0, 1304, 1305, 5, 111, 0, 0, 1305, 1306, 5, 114, 0, 0, 1306, 1307, 5, 40, 0, 0, 1307, 312, 1, 0, 0, 0, 1308, 1309, 5, 99, 0, 0, 1309, 1310, 5, 101, 0, 0, 1310, 1311, 5, 105, 0, 0, 1311, 1312, 5, 108, 0, 0, 1312, 1313, 5, 40, 0, 0, 1313, 314, 1, 0, 0, 0, 1314, 1315, 5, 99, 0, 0, 1315, 1316, 5, 101, 0, 0, 1316, 1317, 5, 105, 0, 0, 1317, 1318, 5, 108, 0, 0, 1318, 1319, 5, 105, 0, 0, 1319, 1320, 5, 110, 0, 0, 1320, 1321, 5, 103, 0, 0, 1321, 1322, 5, 40, 0, 0, 1322, 316, 1, 0, 0, 0, 1323, 1324, 5, 114, 0, 0, 1324, 1325, 5, 111, 0, 0, 1325, 1326, 5, 117, 0, 0, 1326, 1327, 5, 110, 0, 0, 1327, 1328, 5, 100, 0, 0, 1328, 1329, 5, 40, 0, 0, 1329, 318, 1, 0, 0, 0, 1330, 1331, 5, 109, 0, 0, 1331, 1332, 5, 105, 0, 0, 1332, 1333, 5, 110, 0, 0, 1333, 1334, 5, 40, 0, 0, 1334, 320, 1, 0, 0, 0, 1335, 1336, 5, 109, 0, 0, 1336, 1337, 5, 97, 0, 0, 1337, 1338, 5, 120, 0, 0, 1338, 1339, 5, 40, 0, 0, 1339, 322, 1, 0, 0, 0, 1340, 1341, 5, 97, 0, 0, 1341, 1342, 5, 114, 0, 0, 1342, 1343, 5, 103, 0, 0, 1343, 1344, 5, 109, 0, 0, 1344, 1345, 5, 97, 0, 0, 1345, 1346, 5, 120, 0, 0, 1346, 1347, 5, 40, 0, 0, 1347, 324, 1, 0, 0, 0, 1348, 1349, 5, 97, 0, 0, 1349, 1350, 5, 114, 0, 0, 1350, 1351, 5, 103, 0, 0, 1351, 1352, 5, 109, 0, 0, 1352, 1353, 5, 105, 0, 0, 1353, 1354, 5, 110, 0, 0, 1354, 1355, 5, 40, 0, 0, 1355, 326, 1, 0, 0, 0, 1356, 1357, 5, 103, 0, 0, 1357, 1358, 5, 99, 0, 0, 1358, 1359, 5, 100, 0, 0, 1359, 1360, 5, 40, 0, 0, 1360, 328, 1, 0, 0, 0, 1361, 1362, 5, 108, 0, 0, 1362, 1363, 5, 99, 0, 0, 1363, 1364, 5, 109, 0, 0, 1364, 1365, 5, 40, 0, 0, 1365, 330, 1, 0, 0, 0, 1366, 1367, 5, 98, 0, 0, 1367, 1368, 5, 105, 0, 0, 1368, 1369, 5, 110, 0, 0, 1369, 1370, 5, 111, 0, 0, 1370, 1371, 5, 109, 0, 0, 1371, 1372, 5, 105, 0, 0, 1372, 1373, 5, 97, 0, 0, 1373, 1374, 5, 108, 0, 0, 1374, 1375, 5, 40, 0, 0, 1375, 332, 1, 0, 0, 0, 1376, 1377, 5, 105, 0, 0, 1377, 1378, 5, 118, 0, 0, 1378, 1379, 5, 101, 0, 0, 1379, 1380, 5, 114, 0, 0, 1380, 1381, 5, 115, 0, 0, 1381, 1382, 5, 111, 0, 0, 1382, 1383, 5, 110, 0, 0, 1383, 1384, 5, 40, 0, 0, 1384, 334, 1, 0, 0, 0, 1385, 1386, 5, 97, 0, 0, 1386, 1387, 5, 108, 0, 0, 1387, 1388, 5, 101, 0, 0, 1388, 1389, 5, 112, 0, 0, 1389, 1390, 5, 104, 0, 0, 1390, 1391, 5, 40, 0, 0, 1391, 336, 1, 0, 0, 0, 1392, 1393, 5, 101, 0, 0, 1393, 1394, 5, 114, 0, 0, 1394, 1395, 5, 102, 0, 0, 1395, 1396, 5, 40, 0, 0, 1396, 338, 1, 0, 0, 0, 1397, 1398, 5, 101, 0, 0, 1398, 1399, 5, 114, 0, 0, 1399, 1400, 5, 102, 0, 0, 1400, 1401, 5, 99, 0, 0, 1401, 1402, 5, 40, 0, 0, 1402, 340, 1, 0, 0, 0, 1403, 1404, 5, 101, 0, 0, 1404, 1405, 5, 114, 0, 0, 1405, 1406, 5, 102, 0, 0, 1406, 1407, 5, 105, 0, 0, 1407, 1408, 5, 40, 0, 0, 1408, 342, 1, 0, 0, 0, 1409, 1410, 5, 69, 0, 0, 1410, 1411, 5, 105, 0, 0, 1411, 1412, 5, 40, 0, 0, 1412, 344, 1, 0, 0, 0, 1413, 1414, 5, 108, 0, 0, 1414, 1415, 5, 105, 0, 0, 1415, 1416, 5, 40, 0, 0, 1416, 346, 1, 0, 0, 0, 1417, 1418, 5, 83, 0, 0, 1418, 1419, 5, 105, 0, 0, 1419, 1420, 5, 40, 0, 0, 1420, 348, 1, 0, 0, 0, 1421, 1422, 5, 67, 0, 0, 1422, 1423, 5, 105, 0, 0, 1423, 1424, 5, 40, 0, 0, 1424, 350, 1, 0, 0, 0, 1425, 1426, 5, 83, 0, 0, 1426, 1427, 5, 104, 0, 0, 1427, 1428, 5, 105, 0, 0, 1428, 1429, 5, 40, 0, 0, 1429, 352, 1, 0, 0, 0, 1430, 1431, 5, 67, 0, 0, 1431, 1432, 5, 104, 0, 0, 1432, 1433, 5, 105, 0, 0, 1433, 1434, 5, 40, 0, 0, 1434, 354, 1, 0, 0, 0, 1435, 1436, 5, 116, 0, 0, 1436, 1437, 5, 114, 0, 0, 1437, 1438, 5, 117, 0, 0, 1438, 1439, 5, 110, 0, 0, 1439, 1440, 5, 99, 0, 0, 1440, 1441, 5, 40, 0, 0, 1441, 356, 1, 0, 0, 0, 1442, 1443, 5, 99, 0, 0, 1443, 1444, 5, 111, 0, 0, 1444, 1445, 5, 110, 0, 0, 1445, 1446, 5, 106, 0, 0, 1446, 1447, 5, 117, 0, 0, 1447, 1448, 5, 103, 0, 0, 1448, 1449, 5, 97, 0, 0, 1449, 1450, 5, 116, 0, 0, 1450, 1451, 5, 101, 0, 0, 1451, 1452, 5, 40, 0, 0, 1452, 358, 1, 0, 0, 0, 1453, 1454, 5, 100, 0, 0, 1454, 1455, 5, 111, 0, 0, 1455, 1456, 5, 109, 0, 0, 1456, 1457, 5, 97, 0, 0, 1457, 1458, 5, 105, 0, 0, 1458, 1459, 5, 110, 0, 0, 1459, 1460, 5, 40, 0, 0, 1460, 360, 1, 0, 0, 0, 1461, 1462, 5, 112, 0, 0, 1462, 1463, 5, 105, 0, 0, 1463, 1464, 5, 101, 0, 0, 1464, 1465, 5, 99, 0, 0, 1465, 1466, 5, 101, 0, 0, 1466, 1467, 5, 119, 0, 0, 1467, 1468, 5, 105, 0, 0, 1468, 1469, 5, 115, 0, 0, 1469, 1470, 5, 101, 0, 0, 1470, 1471, 5, 40, 0, 0, 1471, 362, 1, 0, 0, 0, 1472, 1473, 5, 97, 0, 0, 1473, 1474, 5, 112, 0, 0, 1474, 1475, 5, 112, 0, 0, 1475, 1476, 5, 108, 0, 0, 1476, 1477, 5, 121, 0, 0, 1477, 1478, 5, 40, 0, 0, 1478, 364, 1, 0, 0, 0, 1479, 1480, 5, 108, 0, 0, 1480, 1481, 5, 97, 0, 0, 1481, 1482, 5, 109, 0, 0, 1482, 1483, 5, 98, 0, 0, 1483, 1484, 5, 100, 0, 0, 1484, 1485, 5, 97, 0, 0, 1485, 1486, 5, 40, 0, 0, 1486, 366, 1, 0, 0, 0, 1487, 1489, 5, 13, 0, 0, 1488, 1487, 1, 0, 0, 0, 1488, 1489, 1, 0, 0, 0, 1489, 1490, 1, 0, 0, 0, 1490, 1492, 5, 10, 0, 0, 1491, 1488, 1, 0, 0, 0, 1492, 1493, 1, 0, 0, 0, 1493, 1491, 1, 0, 0, 0, 1493, 1494, 1, 0, 0, 0, 1494, 1495, 1, 0, 0, 0, 1495, 1496, 6, 183, 0, 0, 1496, 368, 1, 0, 0, 0, 1497, 1499, 7, 0, 0, 0, 1498, 1500, 7, 1, 0, 0, 1499, 1498, 1, 0, 0, 0, 1499, 1500, 1, 0, 0, 0, 1500, 1502, 1, 0, 0, 0, 1501, 1503, 2, 48, 57, 0, 1502, 1501, 1, 0, 0, 0, 1503, 1504, 1, 0, 0, 0, 1504, 1502, 1, 0, 0, 0, 1504, 1505, 1, 0, 0, 0, 1505, 370, 1, 0, 0, 0, 1506, 1508, 2, 48, 57, 0, 1507, 1506, 1, 0, 0, 0, 1508, 1509, 1, 0, 0, 0, 1509, 1507, 1, 0, 0, 0, 1509, 1510, 1, 0, 0, 0, 1510, 1511, 1, 0, 0, 0, 1511, 1515, 5, 46, 0, 0, 1512, 1514, 2, 48, 57, 0, 1513, 1512, 1, 0, 0, 0, 1514, 1517, 1, 0, 0, 0, 1515, 1513, 1, 0, 0, 0, 1515, 1516, 1, 0, 0, 0, 1516, 1519, 1, 0, 0, 0, 1517, 1515, 1, 0, 0, 0, 1518, 1520, 3, 369, 184, 0, 1519, 1518, 1, 0, 0, 0, 1519, 1520, 1, 0, 0, 0, 1520, 1522, 1, 0, 0, 0, 1521, 1523, 5, 105, 0, 0, 1522, 1521, 1, 0, 0, 0, 1522, 1523, 1, 0, 0, 0, 1523, 1540, 1, 0, 0, 0, 1524, 1526, 5, 46, 0, 0, 1525, 1524, 1, 0, 0, 0, 1525, 1526, 1, 0, 0, 0, 1526, 1528, 1, 0, 0, 0, 1527, 1529, 2, 48, 57, 0, 1528, 1527, 1, 0, 0, 0, 1529, 1530, 1, 0, 0, 0, 1530, 1528, 1, 0, 0, 0, 1530, 1531, 1, 0, 0, 0, 1531, 1533, 1, 0, 0, 0, 1532, 1534, 3, 369, 184, 0, 1533, 1532, 1, 0, 0, 0, 1533, 1534, 1, 0, 0, 0, 1534, 1536, 1, 0, 0, 0, 1535, 1537, 5, 105, 0, 0, 1536, 1535, 1, 0, 0, 0, 1536, 1537, 1, 0, 0, 0, 1537, 1540, 1, 0, 0, 0, 1538, 1540, 5, 105, 0, 0, 1539, 1507, 1, 0, 0, 0, 1539, 1525, 1, 0, 0, 0, 1539, 1538, 1, 0, 0, 0, 1540, 372, 1, 0, 0, 0, 1541, 1542, 5, 67, 0, 0, 1542, 1560, 5, 67, 0, 0, 1543, 1544, 5, 82, 0, 0, 1544, 1560, 5, 82, 0, 0, 1545, 1546, 5, 81, 0, 0, 1546, 1560, 5, 81, 0, 0, 1547, 1548, 5, 90, 0, 0, 1548, 1560, 5, 90, 0, 0, 1549, 1550, 5, 66, 0, 0, 1550, 1560, 5, 66, 0, 0, 1551, 1552, 5, 90, 0, 0, 1552, 1553, 5, 90, 0, 0, 1553, 1560, 5, 42, 0, 0, 1554, 1555, 5, 90, 0, 0, 1555, 1556, 5, 90, 0, 0, 1556, 1560, 5, 43, 0, 0, 1557, 1558, 5, 80, 0, 0, 1558, 1560, 5, 80, 0, 0, 1559, 1541, 1, 0, 0, 0, 1559, 1543, 1, 0, 0, 0, 1559, 1545, 1, 0, 0, 0, 1559, 1547, 1, 0, 0, 0, 1559, 1549, 1, 0, 0, 0, 1559, 1551, 1, 0, 0, 0, 1559, 1554, 1, 0, 0, 0, 1559, 1557, 1, 0, 0, 0, 1560, 374, 1, 0, 0, 0, 1561, 1562, 5, 116, 0, 0, 1562, 1563, 5, 114, 0, 0, 1563, 1564, 5, 117, 0, 0, 1564, 1580, 5, 101, 0, 0, 1565, 1566, 5, 84, 0, 0, 1566, 1567, 5, 114, 0, 0, 1567, 1568, 5, 117, 0, 0, 1568, 1580, 5, 101, 0, 0, 1569, 1570, 5, 102, 0, 0, 1570, 1571, 5, 97, 0, 0, 1571, 1572, 5, 108, 0, 0, 1572, 1573, 5, 115, 0, 0, 1573, 1580, 5, 101, 0, 0, 1574, 1575, 5, 70, 0, 0, 1575, 1576, 5, 97, 0, 0, 1576, 1577, 5, 108, 0, 0, 1577, 1578, 5, 115, 0, 0, 1578, 1580, 5, 101, 0, 0, 1579, 1561, 1, 0, 0, 0, 1579, 1565, 1, 0, 0, 0, 1579, 1569, 1, 0, 0, 0, 1579, 1574, 1, 0, 0, 0, 1580, 376, 1, 0, 0, 0, 1581, 1582, 5, 78, 0, 0, 1582, 1583, 5, 97, 0, 0, 1583, 1584, 5, 78, 0, 0, 1584, 378, 1, 0, 0, 0, 1585, 1587, 7, 2, 0, 0, 1586, 1585, 1, 0, 0, 0, 1587, 1588, 1, 0, 0, 0, 1588, 1586, 1, 0, 0, 0, 1588, 1589, 1, 0, 0, 0, 1589, 1596, 1, 0, 0, 0, 1590, 1592, 5, 95, 0, 0, 1591, 1593, 7, 3, 0, 0, 1592, 1591, 1, 0, 0, 0, 1593, 1594, 1, 0, 0, 0, 1594, 1592, 1, 0, 0, 0, 1594, 1595, 1, 0, 0, 0, 1595, 1597, 1, 0, 0, 0, 1596, 1590, 1, 0, 0, 0, 1596, 1597, 1, 0, 0, 0, 1597, 380, 1, 0, 0, 0, 1598, 1599, 5, 47, 0, 0, 1599, 1600, 5, 47, 0, 0, 1600, 1604, 1, 0, 0, 0, 1601, 1603, 8, 4, 0, 0, 1602, 1601, 1, 0, 0, 0, 1603, 1606, 1, 0, 0, 0, 1604, 1602, 1, 0, 0, 0, 1604, 1605, 1, 0, 0, 0, 1605, 1611, 1, 0, 0, 0, 1606, 1604, 1, 0, 0, 0, 1607, 1609, 5, 13, 0, 0, 1608, 1607, 1, 0, 0, 0, 1608, 1609, 1, 0, 0, 0, 1609, 1610, 1, 0, 0, 0, 1610, 1612, 5, 10, 0, 0, 1611, 1608, 1, 0, 0, 0, 1611, 1612, 1, 0, 0, 0, 1612, 1625, 1, 0, 0, 0, 1613, 1614, 5, 47, 0, 0, 1614, 1615, 5, 42, 0, 0, 1615, 1619, 1, 0, 0, 0, 1616, 1618, 9, 0, 0, 0, 1617, 1616, 1, 0, 0, 0, 1618, 1621, 1, 0, 0, 0, 1619, 1620, 1, 0, 0, 0, 1619, 1617, 1, 0, 0, 0, 1620, 1622, 1, 0, 0, 0, 1621, 1619, 1, 0, 0, 0, 1622, 1623, 5, 42, 0, 0, 1623, 1625, 5, 47, 0, 0, 1624, 1598, 1, 0, 0, 0, 1624, 1613, 1, 0, 0, 0, 1625, 1626, 1, 0, 0, 0, 1626, 1627, 6, 190, 0, 0, 1627, 382, 1, 0, 0, 0, 1628, 1630, 7, 5, 0, 0, 1629, 1628, 1, 0, 0, 0, 1630, 1631, 1, 0, 0, 0, 1631, 1629, 1, 0, 0, 0, 1631, 1632, 1, 0, 0, 0, 1632, 1633, 1, 0, 0, 0, 1633, 1634, 6, 191, 0, 0, 1634, 384, 1, 0, 0, 0, 25, 0, 1488, 1493, 1499, 1504, 1509, 1515, 1519, 1522, 1525, 1530, 1533, 1536, 1539, 1559, 1579, 1588, 1594, 1596, 1604, 1608, 1611, 1619, 1624, 1631, 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 7ab99b888..d3b5bc330 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens
@@ -180,14 +180,15 @@ T__178=179
T__179=180
T__180=181
T__181=182
-NEWLINE=183
-NUMBER=184
-SPECIALSET=185
-BOOLEAN=186
-NAN=187
-VARIABLE=188
-COMMENT=189
-WS=190
+T__182=183
+NEWLINE=184
+NUMBER=185
+SPECIALSET=186
+BOOLEAN=187
+NAN=188
+VARIABLE=189
+COMMENT=190
+WS=191
'!'=1
'^'=2
'-'=3
@@ -355,19 +356,20 @@ WS=190
'lcm('=165
'binomial('=166
'iverson('=167
-'erf('=168
-'erfc('=169
-'erfi('=170
-'Ei('=171
-'li('=172
-'Si('=173
-'Ci('=174
-'Shi('=175
-'Chi('=176
-'trunc('=177
-'conjugate('=178
-'domain('=179
-'piecewise('=180
-'apply('=181
-'lambda('=182
-'NaN'=187
+'aleph('=168
+'erf('=169
+'erfc('=170
+'erfi('=171
+'Ei('=172
+'li('=173
+'Si('=174
+'Ci('=175
+'Shi('=176
+'Chi('=177
+'trunc('=178
+'conjugate('=179
+'domain('=180
+'piecewise('=181
+'apply('=182
+'lambda('=183
+'NaN'=188
diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
index 391f0d6b6..615d7ea1a 100644
--- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
+++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs
@@ -73,8 +73,8 @@ public const int
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, T__171=172, T__172=173,
T__173=174, T__174=175, T__175=176, T__176=177, T__177=178, T__178=179,
- T__179=180, T__180=181, T__181=182, NEWLINE=183, NUMBER=184, SPECIALSET=185,
- BOOLEAN=186, NAN=187, VARIABLE=188, COMMENT=189, WS=190;
+ T__179=180, T__180=181, T__181=182, T__182=183, NEWLINE=184, NUMBER=185,
+ SPECIALSET=186, BOOLEAN=187, NAN=188, VARIABLE=189, COMMENT=190, WS=191;
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,
@@ -121,8 +121,8 @@ public const int
"'powerset('", "'union('", "'intersection('", "'complement('", "'image('",
"'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('",
"'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('",
- "'iverson('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'Si('",
- "'Ci('", "'Shi('", "'Chi('", "'trunc('", "'conjugate('", "'domain('",
+ "'iverson('", "'aleph('", "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('",
+ "'Si('", "'Ci('", "'Shi('", "'Chi('", "'trunc('", "'conjugate('", "'domain('",
"'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'"
};
private static readonly string[] _SymbolicNames = {
@@ -141,8 +141,8 @@ 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, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN", "NAN",
- "VARIABLE", "COMMENT", "WS"
+ null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", "BOOLEAN",
+ "NAN", "VARIABLE", "COMMENT", "WS"
};
public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames);
@@ -750,6 +750,7 @@ public Mult_expressionContext mult_expression() {
case T__179:
case T__180:
case T__181:
+ case T__182:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -1007,6 +1008,7 @@ public Sum_expressionContext sum_expression() {
case T__179:
case T__180:
case T__181:
+ case T__182:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2186,6 +2188,7 @@ public ExpressionContext expression() {
case T__179:
case T__180:
case T__181:
+ case T__182:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2551,7 +2554,7 @@ 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)) & 2269814212194729983L) != 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)) & 4539628424389459967L) != 0)) {
{
State = 383;
_localctx.e = expression();
@@ -2627,7 +2630,7 @@ 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)) & 2269814212194729983L) != 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)) & 4539628424389459967L) != 0)) {
{
State = 401;
ErrorHandler.Sync(this);
@@ -2771,6 +2774,7 @@ public Set_itemsContext set_items() {
case T__179:
case T__180:
case T__181:
+ case T__182:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -2950,6 +2954,7 @@ public Set_itemsContext set_items() {
case T__179:
case T__180:
case T__181:
+ case T__182:
case NUMBER:
case SPECIALSET:
case BOOLEAN:
@@ -3169,7 +3174,7 @@ public AtomContext atom() {
AtomContext _localctx = new AtomContext(Context, State);
EnterRule(_localctx, 48, RULE_atom);
try {
- State = 1113;
+ State = 1118;
ErrorHandler.Sync(this);
switch ( Interpreter.AdaptivePredict(TokenStream,41,Context) ) {
case 1:
@@ -4692,7 +4697,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1040;
Match(T__30);
- Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]);
+ Assert("aleph", 1, _localctx.args.list.Count); _localctx.value = MathS.Aleph(_localctx.args.list[0]);
}
break;
case 128:
@@ -4704,7 +4709,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1045;
Match(T__30);
- Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]);
+ Assert("erf", 1, _localctx.args.list.Count); _localctx.value = MathS.Erf(_localctx.args.list[0]);
}
break;
case 129:
@@ -4716,7 +4721,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1050;
Match(T__30);
- Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]);
+ Assert("erfc", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfc(_localctx.args.list[0]);
}
break;
case 130:
@@ -4728,7 +4733,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1055;
Match(T__30);
- Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]);
+ Assert("erfi", 1, _localctx.args.list.Count); _localctx.value = MathS.Erfi(_localctx.args.list[0]);
}
break;
case 131:
@@ -4740,7 +4745,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1060;
Match(T__30);
- Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]);
+ Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]);
}
break;
case 132:
@@ -4752,7 +4757,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1065;
Match(T__30);
- Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]);
+ Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]);
}
break;
case 133:
@@ -4764,7 +4769,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1070;
Match(T__30);
- Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]);
+ Assert("Si", 1, _localctx.args.list.Count); _localctx.value = MathS.Si(_localctx.args.list[0]);
}
break;
case 134:
@@ -4776,7 +4781,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1075;
Match(T__30);
- Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]);
+ Assert("Ci", 1, _localctx.args.list.Count); _localctx.value = MathS.Ci(_localctx.args.list[0]);
}
break;
case 135:
@@ -4788,7 +4793,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1080;
Match(T__30);
- Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]);
+ Assert("Shi", 1, _localctx.args.list.Count); _localctx.value = MathS.Shi(_localctx.args.list[0]);
}
break;
case 136:
@@ -4800,7 +4805,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1085;
Match(T__30);
- _localctx.value = NotImplementedFunction("trunc", "rounding functions");
+ Assert("Chi", 1, _localctx.args.list.Count); _localctx.value = MathS.Chi(_localctx.args.list[0]);
}
break;
case 137:
@@ -4812,7 +4817,7 @@ public AtomContext atom() {
_localctx.args = function_arguments();
State = 1090;
Match(T__30);
- _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function");
+ _localctx.value = NotImplementedFunction("trunc", "rounding functions");
}
break;
case 138:
@@ -4823,6 +4828,18 @@ public AtomContext atom() {
State = 1094;
_localctx.args = function_arguments();
State = 1095;
+ Match(T__30);
+ _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function");
+ }
+ break;
+ case 139:
+ EnterOuterAlt(_localctx, 139);
+ {
+ State = 1098;
+ Match(T__179);
+ State = 1099;
+ _localctx.args = function_arguments();
+ State = 1100;
Match(T__30);
Assert("domain", 2, _localctx.args.list.Count);
@@ -4849,14 +4866,14 @@ public AtomContext atom() {
}
break;
- case 139:
- EnterOuterAlt(_localctx, 139);
+ case 140:
+ EnterOuterAlt(_localctx, 140);
{
- State = 1098;
- Match(T__179);
- State = 1099;
+ State = 1103;
+ Match(T__180);
+ State = 1104;
_localctx.args = function_arguments();
- State = 1100;
+ State = 1105;
Match(T__30);
var cases = new List();
@@ -4869,14 +4886,14 @@ public AtomContext atom() {
}
break;
- case 140:
- EnterOuterAlt(_localctx, 140);
+ case 141:
+ EnterOuterAlt(_localctx, 141);
{
- State = 1103;
- Match(T__180);
- State = 1104;
+ State = 1108;
+ Match(T__181);
+ State = 1109;
_localctx.args = function_arguments();
- State = 1105;
+ State = 1110;
Match(T__30);
if (_localctx.args.list.Count < 2)
@@ -4885,14 +4902,14 @@ public AtomContext atom() {
}
break;
- case 141:
- EnterOuterAlt(_localctx, 141);
+ case 142:
+ EnterOuterAlt(_localctx, 142);
{
- State = 1108;
- Match(T__181);
- State = 1109;
+ State = 1113;
+ Match(T__182);
+ State = 1114;
_localctx.args = function_arguments();
- State = 1110;
+ State = 1115;
Match(T__30);
if (_localctx.args.list.Count < 2)
@@ -4955,9 +4972,9 @@ public StatementContext statement() {
try {
EnterOuterAlt(_localctx, 1);
{
- State = 1115;
+ State = 1120;
_localctx._expression = expression();
- State = 1116;
+ State = 1121;
Match(Eof);
Result = _localctx._expression.value;
}
@@ -4974,7 +4991,7 @@ public StatementContext statement() {
}
private static int[] _serializedATN = {
- 4,1,190,1120,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2,
+ 4,1,191,1125,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2,
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,
@@ -5053,324 +5070,326 @@ 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,
- 1,24,1,24,1,24,3,24,1114,8,24,1,25,1,25,1,25,1,25,1,25,0,0,26,0,2,4,6,
- 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,
- 0,6,7,1,0,42,43,1,0,44,45,1,0,46,47,1291,0,59,1,0,0,0,2,77,1,0,0,0,4,79,
- 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,
- 0,0,0,44,418,1,0,0,0,46,424,1,0,0,0,48,1113,1,0,0,0,50,1115,1,0,0,0,52,
- 53,3,48,24,0,53,54,5,1,0,0,54,55,6,0,-1,0,55,60,1,0,0,0,56,57,3,48,24,
- 0,57,58,6,0,-1,0,58,60,1,0,0,0,59,52,1,0,0,0,59,56,1,0,0,0,60,1,1,0,0,
- 0,61,62,5,2,0,0,62,63,3,0,0,0,63,64,6,1,-1,0,64,66,1,0,0,0,65,61,1,0,0,
- 0,66,67,1,0,0,0,67,65,1,0,0,0,67,68,1,0,0,0,68,78,1,0,0,0,69,70,5,2,0,
- 0,70,71,3,6,3,0,71,72,6,1,-1,0,72,74,1,0,0,0,73,69,1,0,0,0,74,75,1,0,0,
- 0,75,73,1,0,0,0,75,76,1,0,0,0,76,78,1,0,0,0,77,65,1,0,0,0,77,73,1,0,0,
- 0,78,3,1,0,0,0,79,80,3,0,0,0,80,84,6,2,-1,0,81,82,3,2,1,0,82,83,6,2,-1,
- 0,83,85,1,0,0,0,84,81,1,0,0,0,84,85,1,0,0,0,85,5,1,0,0,0,86,87,5,3,0,0,
- 87,88,3,4,2,0,88,89,6,3,-1,0,89,95,1,0,0,0,90,91,5,4,0,0,91,92,3,4,2,0,
- 92,93,6,3,-1,0,93,95,1,0,0,0,94,86,1,0,0,0,94,90,1,0,0,0,95,110,1,0,0,
- 0,96,97,5,3,0,0,97,98,3,6,3,0,98,99,6,3,-1,0,99,105,1,0,0,0,100,101,5,
- 4,0,0,101,102,3,6,3,0,102,103,6,3,-1,0,103,105,1,0,0,0,104,96,1,0,0,0,
- 104,100,1,0,0,0,105,110,1,0,0,0,106,107,3,4,2,0,107,108,6,3,-1,0,108,110,
- 1,0,0,0,109,94,1,0,0,0,109,104,1,0,0,0,109,106,1,0,0,0,110,7,1,0,0,0,111,
- 112,3,6,3,0,112,131,6,4,-1,0,113,119,5,5,0,0,114,115,7,0,0,0,115,120,6,
- 4,-1,0,116,117,3,6,3,0,117,118,6,4,-1,0,118,120,1,0,0,0,119,114,1,0,0,
- 0,119,116,1,0,0,0,120,130,1,0,0,0,121,122,5,8,0,0,122,123,3,6,3,0,123,
- 124,6,4,-1,0,124,130,1,0,0,0,125,126,5,9,0,0,126,127,3,6,3,0,127,128,6,
- 4,-1,0,128,130,1,0,0,0,129,113,1,0,0,0,129,121,1,0,0,0,129,125,1,0,0,0,
- 130,133,1,0,0,0,131,129,1,0,0,0,131,132,1,0,0,0,132,134,1,0,0,0,133,131,
- 1,0,0,0,134,135,6,4,-1,0,135,9,1,0,0,0,136,137,3,8,4,0,137,152,6,5,-1,
- 0,138,144,5,4,0,0,139,140,7,0,0,0,140,145,6,5,-1,0,141,142,3,8,4,0,142,
- 143,6,5,-1,0,143,145,1,0,0,0,144,139,1,0,0,0,144,141,1,0,0,0,145,151,1,
- 0,0,0,146,147,5,3,0,0,147,148,3,8,4,0,148,149,6,5,-1,0,149,151,1,0,0,0,
- 150,138,1,0,0,0,150,146,1,0,0,0,151,154,1,0,0,0,152,150,1,0,0,0,152,153,
- 1,0,0,0,153,155,1,0,0,0,154,152,1,0,0,0,155,156,6,5,-1,0,156,11,1,0,0,
- 0,157,158,3,10,5,0,158,169,6,6,-1,0,159,160,5,10,0,0,160,161,3,10,5,0,
- 161,162,6,6,-1,0,162,168,1,0,0,0,163,164,5,11,0,0,164,165,3,10,5,0,165,
- 166,6,6,-1,0,166,168,1,0,0,0,167,159,1,0,0,0,167,163,1,0,0,0,168,171,1,
- 0,0,0,169,167,1,0,0,0,169,170,1,0,0,0,170,13,1,0,0,0,171,169,1,0,0,0,172,
- 173,3,12,6,0,173,192,6,7,-1,0,174,175,5,12,0,0,175,176,3,12,6,0,176,177,
- 6,7,-1,0,177,191,1,0,0,0,178,179,5,13,0,0,179,180,3,12,6,0,180,181,6,7,
- -1,0,181,191,1,0,0,0,182,183,5,14,0,0,183,184,3,12,6,0,184,185,6,7,-1,
- 0,185,191,1,0,0,0,186,187,5,15,0,0,187,188,3,12,6,0,188,189,6,7,-1,0,189,
- 191,1,0,0,0,190,174,1,0,0,0,190,178,1,0,0,0,190,182,1,0,0,0,190,186,1,
- 0,0,0,191,194,1,0,0,0,192,190,1,0,0,0,192,193,1,0,0,0,193,15,1,0,0,0,194,
- 192,1,0,0,0,195,196,3,14,7,0,196,227,6,8,-1,0,197,198,5,16,0,0,198,199,
- 3,14,7,0,199,200,6,8,-1,0,200,226,1,0,0,0,201,202,5,17,0,0,202,203,3,14,
- 7,0,203,204,6,8,-1,0,204,226,1,0,0,0,205,206,5,18,0,0,206,207,3,14,7,0,
- 207,208,6,8,-1,0,208,226,1,0,0,0,209,210,5,19,0,0,210,211,3,14,7,0,211,
- 212,6,8,-1,0,212,226,1,0,0,0,213,214,5,20,0,0,214,215,3,14,7,0,215,216,
- 6,8,-1,0,216,226,1,0,0,0,217,218,5,21,0,0,218,219,3,14,7,0,219,220,6,8,
- -1,0,220,226,1,0,0,0,221,222,5,22,0,0,222,223,3,14,7,0,223,224,6,8,-1,
- 0,224,226,1,0,0,0,225,197,1,0,0,0,225,201,1,0,0,0,225,205,1,0,0,0,225,
- 209,1,0,0,0,225,213,1,0,0,0,225,217,1,0,0,0,225,221,1,0,0,0,226,229,1,
- 0,0,0,227,225,1,0,0,0,227,228,1,0,0,0,228,17,1,0,0,0,229,227,1,0,0,0,230,
- 231,3,16,8,0,231,253,6,9,-1,0,232,233,5,23,0,0,233,247,6,9,-1,0,234,235,
- 5,24,0,0,235,247,6,9,-1,0,236,237,5,25,0,0,237,247,6,9,-1,0,238,239,5,
- 26,0,0,239,247,6,9,-1,0,240,241,5,27,0,0,241,247,6,9,-1,0,242,243,5,28,
- 0,0,243,247,6,9,-1,0,244,245,5,29,0,0,245,247,6,9,-1,0,246,232,1,0,0,0,
- 246,234,1,0,0,0,246,236,1,0,0,0,246,238,1,0,0,0,246,240,1,0,0,0,246,242,
- 1,0,0,0,246,244,1,0,0,0,247,248,1,0,0,0,248,249,3,16,8,0,249,250,6,9,-1,
- 0,250,252,1,0,0,0,251,246,1,0,0,0,252,255,1,0,0,0,253,251,1,0,0,0,253,
- 254,1,0,0,0,254,262,1,0,0,0,255,253,1,0,0,0,256,257,5,30,0,0,257,258,5,
- 9,0,0,258,259,3,16,8,0,259,260,5,31,0,0,260,261,6,9,-1,0,261,263,1,0,0,
- 0,262,256,1,0,0,0,262,263,1,0,0,0,263,264,1,0,0,0,264,265,6,9,-1,0,265,
- 19,1,0,0,0,266,267,5,32,0,0,267,268,3,18,9,0,268,269,6,10,-1,0,269,282,
- 1,0,0,0,270,271,5,32,0,0,271,272,3,20,10,0,272,273,6,10,-1,0,273,282,1,
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+ 0,769,770,3,40,20,0,770,771,5,31,0,0,771,772,6,24,-1,0,772,1119,1,0,0,
+ 0,773,774,5,115,0,0,774,775,3,40,20,0,775,776,5,31,0,0,776,777,6,24,-1,
+ 0,777,1119,1,0,0,0,778,779,5,116,0,0,779,780,3,40,20,0,780,781,5,31,0,
+ 0,781,782,6,24,-1,0,782,1119,1,0,0,0,783,784,5,117,0,0,784,785,3,40,20,
+ 0,785,786,5,31,0,0,786,787,6,24,-1,0,787,1119,1,0,0,0,788,789,5,118,0,
+ 0,789,790,3,40,20,0,790,791,5,31,0,0,791,792,6,24,-1,0,792,1119,1,0,0,
+ 0,793,794,5,119,0,0,794,795,3,40,20,0,795,796,5,31,0,0,796,797,6,24,-1,
+ 0,797,1119,1,0,0,0,798,799,5,120,0,0,799,800,3,40,20,0,800,801,5,31,0,
+ 0,801,802,6,24,-1,0,802,1119,1,0,0,0,803,804,5,121,0,0,804,805,3,40,20,
+ 0,805,806,5,31,0,0,806,807,6,24,-1,0,807,1119,1,0,0,0,808,809,5,122,0,
+ 0,809,810,3,40,20,0,810,811,5,31,0,0,811,812,6,24,-1,0,812,1119,1,0,0,
+ 0,813,814,5,123,0,0,814,815,3,40,20,0,815,816,5,31,0,0,816,817,6,24,-1,
+ 0,817,1119,1,0,0,0,818,819,5,124,0,0,819,820,3,40,20,0,820,821,5,31,0,
+ 0,821,822,6,24,-1,0,822,1119,1,0,0,0,823,824,5,125,0,0,824,825,3,40,20,
+ 0,825,826,5,31,0,0,826,827,6,24,-1,0,827,1119,1,0,0,0,828,829,5,126,0,
+ 0,829,830,3,40,20,0,830,831,5,31,0,0,831,832,6,24,-1,0,832,1119,1,0,0,
+ 0,833,834,5,127,0,0,834,835,3,40,20,0,835,836,5,31,0,0,836,837,6,24,-1,
+ 0,837,1119,1,0,0,0,838,839,5,128,0,0,839,840,3,40,20,0,840,841,5,31,0,
+ 0,841,842,6,24,-1,0,842,1119,1,0,0,0,843,844,5,129,0,0,844,845,3,40,20,
+ 0,845,846,5,31,0,0,846,847,6,24,-1,0,847,1119,1,0,0,0,848,849,5,130,0,
+ 0,849,850,3,40,20,0,850,851,5,31,0,0,851,852,6,24,-1,0,852,1119,1,0,0,
+ 0,853,854,5,131,0,0,854,855,3,40,20,0,855,856,5,31,0,0,856,857,6,24,-1,
+ 0,857,1119,1,0,0,0,858,859,5,132,0,0,859,860,3,40,20,0,860,861,5,31,0,
+ 0,861,862,6,24,-1,0,862,1119,1,0,0,0,863,864,5,133,0,0,864,865,3,40,20,
+ 0,865,866,5,31,0,0,866,867,6,24,-1,0,867,1119,1,0,0,0,868,869,5,134,0,
+ 0,869,870,3,40,20,0,870,871,5,31,0,0,871,872,6,24,-1,0,872,1119,1,0,0,
+ 0,873,874,5,135,0,0,874,875,3,40,20,0,875,876,5,31,0,0,876,877,6,24,-1,
+ 0,877,1119,1,0,0,0,878,879,5,136,0,0,879,880,3,40,20,0,880,881,5,31,0,
+ 0,881,882,6,24,-1,0,882,1119,1,0,0,0,883,884,5,137,0,0,884,885,3,40,20,
+ 0,885,886,5,31,0,0,886,887,6,24,-1,0,887,1119,1,0,0,0,888,889,5,138,0,
+ 0,889,890,3,40,20,0,890,891,5,31,0,0,891,892,6,24,-1,0,892,1119,1,0,0,
+ 0,893,894,5,139,0,0,894,895,3,40,20,0,895,896,5,31,0,0,896,897,6,24,-1,
+ 0,897,1119,1,0,0,0,898,899,5,140,0,0,899,900,3,40,20,0,900,901,5,31,0,
+ 0,901,902,6,24,-1,0,902,1119,1,0,0,0,903,904,5,141,0,0,904,905,3,40,20,
+ 0,905,906,5,31,0,0,906,907,6,24,-1,0,907,1119,1,0,0,0,908,909,5,142,0,
+ 0,909,910,3,40,20,0,910,911,5,31,0,0,911,912,6,24,-1,0,912,1119,1,0,0,
+ 0,913,914,5,143,0,0,914,915,3,40,20,0,915,916,5,31,0,0,916,917,6,24,-1,
+ 0,917,1119,1,0,0,0,918,919,5,144,0,0,919,920,3,40,20,0,920,921,5,31,0,
+ 0,921,922,6,24,-1,0,922,1119,1,0,0,0,923,924,5,145,0,0,924,925,3,40,20,
+ 0,925,926,5,31,0,0,926,927,6,24,-1,0,927,1119,1,0,0,0,928,929,5,146,0,
+ 0,929,930,3,40,20,0,930,931,5,31,0,0,931,932,6,24,-1,0,932,1119,1,0,0,
+ 0,933,934,5,147,0,0,934,935,3,40,20,0,935,936,5,31,0,0,936,937,6,24,-1,
+ 0,937,1119,1,0,0,0,938,939,5,148,0,0,939,940,3,40,20,0,940,941,5,31,0,
+ 0,941,942,6,24,-1,0,942,1119,1,0,0,0,943,944,5,149,0,0,944,945,3,40,20,
+ 0,945,946,5,31,0,0,946,947,6,24,-1,0,947,1119,1,0,0,0,948,949,5,150,0,
+ 0,949,950,3,40,20,0,950,951,5,31,0,0,951,952,6,24,-1,0,952,1119,1,0,0,
+ 0,953,954,5,151,0,0,954,955,3,40,20,0,955,956,5,31,0,0,956,957,6,24,-1,
+ 0,957,1119,1,0,0,0,958,959,5,152,0,0,959,960,3,40,20,0,960,961,5,31,0,
+ 0,961,962,6,24,-1,0,962,1119,1,0,0,0,963,964,5,153,0,0,964,965,3,40,20,
+ 0,965,966,5,31,0,0,966,967,6,24,-1,0,967,1119,1,0,0,0,968,969,5,154,0,
+ 0,969,970,3,40,20,0,970,971,5,31,0,0,971,972,6,24,-1,0,972,1119,1,0,0,
+ 0,973,974,5,155,0,0,974,975,3,40,20,0,975,976,5,31,0,0,976,977,6,24,-1,
+ 0,977,1119,1,0,0,0,978,979,5,156,0,0,979,980,3,40,20,0,980,981,5,31,0,
+ 0,981,982,6,24,-1,0,982,1119,1,0,0,0,983,984,5,157,0,0,984,985,3,40,20,
+ 0,985,986,5,31,0,0,986,987,6,24,-1,0,987,1119,1,0,0,0,988,989,5,158,0,
+ 0,989,990,3,40,20,0,990,991,5,31,0,0,991,992,6,24,-1,0,992,1119,1,0,0,
+ 0,993,994,5,159,0,0,994,995,3,40,20,0,995,996,5,31,0,0,996,997,6,24,-1,
+ 0,997,1119,1,0,0,0,998,999,5,160,0,0,999,1000,3,40,20,0,1000,1001,5,31,
+ 0,0,1001,1002,6,24,-1,0,1002,1119,1,0,0,0,1003,1004,5,161,0,0,1004,1005,
+ 3,40,20,0,1005,1006,5,31,0,0,1006,1007,6,24,-1,0,1007,1119,1,0,0,0,1008,
+ 1009,5,162,0,0,1009,1010,3,40,20,0,1010,1011,5,31,0,0,1011,1012,6,24,-1,
+ 0,1012,1119,1,0,0,0,1013,1014,5,163,0,0,1014,1015,3,40,20,0,1015,1016,
+ 5,31,0,0,1016,1017,6,24,-1,0,1017,1119,1,0,0,0,1018,1019,5,164,0,0,1019,
+ 1020,3,40,20,0,1020,1021,5,31,0,0,1021,1022,6,24,-1,0,1022,1119,1,0,0,
+ 0,1023,1024,5,165,0,0,1024,1025,3,40,20,0,1025,1026,5,31,0,0,1026,1027,
+ 6,24,-1,0,1027,1119,1,0,0,0,1028,1029,5,166,0,0,1029,1030,3,40,20,0,1030,
+ 1031,5,31,0,0,1031,1032,6,24,-1,0,1032,1119,1,0,0,0,1033,1034,5,167,0,
+ 0,1034,1035,3,40,20,0,1035,1036,5,31,0,0,1036,1037,6,24,-1,0,1037,1119,
+ 1,0,0,0,1038,1039,5,168,0,0,1039,1040,3,40,20,0,1040,1041,5,31,0,0,1041,
+ 1042,6,24,-1,0,1042,1119,1,0,0,0,1043,1044,5,169,0,0,1044,1045,3,40,20,
+ 0,1045,1046,5,31,0,0,1046,1047,6,24,-1,0,1047,1119,1,0,0,0,1048,1049,5,
+ 170,0,0,1049,1050,3,40,20,0,1050,1051,5,31,0,0,1051,1052,6,24,-1,0,1052,
+ 1119,1,0,0,0,1053,1054,5,171,0,0,1054,1055,3,40,20,0,1055,1056,5,31,0,
+ 0,1056,1057,6,24,-1,0,1057,1119,1,0,0,0,1058,1059,5,172,0,0,1059,1060,
+ 3,40,20,0,1060,1061,5,31,0,0,1061,1062,6,24,-1,0,1062,1119,1,0,0,0,1063,
+ 1064,5,173,0,0,1064,1065,3,40,20,0,1065,1066,5,31,0,0,1066,1067,6,24,-1,
+ 0,1067,1119,1,0,0,0,1068,1069,5,174,0,0,1069,1070,3,40,20,0,1070,1071,
+ 5,31,0,0,1071,1072,6,24,-1,0,1072,1119,1,0,0,0,1073,1074,5,175,0,0,1074,
+ 1075,3,40,20,0,1075,1076,5,31,0,0,1076,1077,6,24,-1,0,1077,1119,1,0,0,
+ 0,1078,1079,5,176,0,0,1079,1080,3,40,20,0,1080,1081,5,31,0,0,1081,1082,
+ 6,24,-1,0,1082,1119,1,0,0,0,1083,1084,5,177,0,0,1084,1085,3,40,20,0,1085,
+ 1086,5,31,0,0,1086,1087,6,24,-1,0,1087,1119,1,0,0,0,1088,1089,5,178,0,
+ 0,1089,1090,3,40,20,0,1090,1091,5,31,0,0,1091,1092,6,24,-1,0,1092,1119,
+ 1,0,0,0,1093,1094,5,179,0,0,1094,1095,3,40,20,0,1095,1096,5,31,0,0,1096,
+ 1097,6,24,-1,0,1097,1119,1,0,0,0,1098,1099,5,180,0,0,1099,1100,3,40,20,
+ 0,1100,1101,5,31,0,0,1101,1102,6,24,-1,0,1102,1119,1,0,0,0,1103,1104,5,
+ 181,0,0,1104,1105,3,40,20,0,1105,1106,5,31,0,0,1106,1107,6,24,-1,0,1107,
+ 1119,1,0,0,0,1108,1109,5,182,0,0,1109,1110,3,40,20,0,1110,1111,5,31,0,
+ 0,1111,1112,6,24,-1,0,1112,1119,1,0,0,0,1113,1114,5,183,0,0,1114,1115,
+ 3,40,20,0,1115,1116,5,31,0,0,1116,1117,6,24,-1,0,1117,1119,1,0,0,0,1118,
+ 430,1,0,0,0,1118,432,1,0,0,0,1118,434,1,0,0,0,1118,436,1,0,0,0,1118,438,
+ 1,0,0,0,1118,440,1,0,0,0,1118,442,1,0,0,0,1118,444,1,0,0,0,1118,449,1,
+ 0,0,0,1118,453,1,0,0,0,1118,458,1,0,0,0,1118,463,1,0,0,0,1118,468,1,0,
+ 0,0,1118,473,1,0,0,0,1118,478,1,0,0,0,1118,483,1,0,0,0,1118,488,1,0,0,
+ 0,1118,493,1,0,0,0,1118,498,1,0,0,0,1118,503,1,0,0,0,1118,508,1,0,0,0,
+ 1118,513,1,0,0,0,1118,518,1,0,0,0,1118,523,1,0,0,0,1118,528,1,0,0,0,1118,
+ 533,1,0,0,0,1118,538,1,0,0,0,1118,543,1,0,0,0,1118,548,1,0,0,0,1118,553,
+ 1,0,0,0,1118,558,1,0,0,0,1118,563,1,0,0,0,1118,568,1,0,0,0,1118,573,1,
+ 0,0,0,1118,578,1,0,0,0,1118,583,1,0,0,0,1118,588,1,0,0,0,1118,593,1,0,
+ 0,0,1118,598,1,0,0,0,1118,603,1,0,0,0,1118,608,1,0,0,0,1118,613,1,0,0,
+ 0,1118,618,1,0,0,0,1118,623,1,0,0,0,1118,628,1,0,0,0,1118,633,1,0,0,0,
+ 1118,638,1,0,0,0,1118,643,1,0,0,0,1118,648,1,0,0,0,1118,653,1,0,0,0,1118,
+ 658,1,0,0,0,1118,663,1,0,0,0,1118,668,1,0,0,0,1118,673,1,0,0,0,1118,678,
+ 1,0,0,0,1118,683,1,0,0,0,1118,688,1,0,0,0,1118,693,1,0,0,0,1118,698,1,
+ 0,0,0,1118,703,1,0,0,0,1118,708,1,0,0,0,1118,713,1,0,0,0,1118,718,1,0,
+ 0,0,1118,723,1,0,0,0,1118,728,1,0,0,0,1118,733,1,0,0,0,1118,738,1,0,0,
+ 0,1118,743,1,0,0,0,1118,748,1,0,0,0,1118,753,1,0,0,0,1118,758,1,0,0,0,
+ 1118,763,1,0,0,0,1118,768,1,0,0,0,1118,773,1,0,0,0,1118,778,1,0,0,0,1118,
+ 783,1,0,0,0,1118,788,1,0,0,0,1118,793,1,0,0,0,1118,798,1,0,0,0,1118,803,
+ 1,0,0,0,1118,808,1,0,0,0,1118,813,1,0,0,0,1118,818,1,0,0,0,1118,823,1,
+ 0,0,0,1118,828,1,0,0,0,1118,833,1,0,0,0,1118,838,1,0,0,0,1118,843,1,0,
+ 0,0,1118,848,1,0,0,0,1118,853,1,0,0,0,1118,858,1,0,0,0,1118,863,1,0,0,
+ 0,1118,868,1,0,0,0,1118,873,1,0,0,0,1118,878,1,0,0,0,1118,883,1,0,0,0,
+ 1118,888,1,0,0,0,1118,893,1,0,0,0,1118,898,1,0,0,0,1118,903,1,0,0,0,1118,
+ 908,1,0,0,0,1118,913,1,0,0,0,1118,918,1,0,0,0,1118,923,1,0,0,0,1118,928,
+ 1,0,0,0,1118,933,1,0,0,0,1118,938,1,0,0,0,1118,943,1,0,0,0,1118,948,1,
+ 0,0,0,1118,953,1,0,0,0,1118,958,1,0,0,0,1118,963,1,0,0,0,1118,968,1,0,
+ 0,0,1118,973,1,0,0,0,1118,978,1,0,0,0,1118,983,1,0,0,0,1118,988,1,0,0,
+ 0,1118,993,1,0,0,0,1118,998,1,0,0,0,1118,1003,1,0,0,0,1118,1008,1,0,0,
+ 0,1118,1013,1,0,0,0,1118,1018,1,0,0,0,1118,1023,1,0,0,0,1118,1028,1,0,
+ 0,0,1118,1033,1,0,0,0,1118,1038,1,0,0,0,1118,1043,1,0,0,0,1118,1048,1,
+ 0,0,0,1118,1053,1,0,0,0,1118,1058,1,0,0,0,1118,1063,1,0,0,0,1118,1068,
+ 1,0,0,0,1118,1073,1,0,0,0,1118,1078,1,0,0,0,1118,1083,1,0,0,0,1118,1088,
+ 1,0,0,0,1118,1093,1,0,0,0,1118,1098,1,0,0,0,1118,1103,1,0,0,0,1118,1108,
+ 1,0,0,0,1118,1113,1,0,0,0,1119,49,1,0,0,0,1120,1121,3,32,16,0,1121,1122,
+ 5,0,0,1,1122,1123,6,25,-1,0,1123,51,1,0,0,0,42,59,67,75,77,84,94,104,109,
+ 119,129,131,144,150,152,167,169,190,192,225,227,246,253,262,281,293,295,
+ 306,317,330,332,341,349,354,368,378,391,394,401,409,413,416,1118
};
public static readonly ATN _ATN =
diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs
index 6f81f0efc..adc24a380 100644
--- a/Sources/AngouriMath/Core/Domains.Classes.cs
+++ b/Sources/AngouriMath/Core/Domains.Classes.cs
@@ -239,6 +239,15 @@ partial record Iversonf
internal override Domain DefaultCodomain => Domain.Real;
}
+ partial record Alephf
+ {
+ // A size of an infinite set, which is no number.
+ ///
+ public override Domain Codomain { get; protected init; } = Domain.Any;
+ ///
+ internal override Domain DefaultCodomain => Domain.Any;
+ }
+
partial record Derivativef
{
///
diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Aleph.Classes.cs b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Aleph.Classes.cs
new file mode 100644
index 000000000..07e8ee0b6
--- /dev/null
+++ b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.Aleph.Classes.cs
@@ -0,0 +1,40 @@
+//
+// Copyright (c) 2019-2026 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using System;
+
+namespace AngouriMath
+{
+ partial record Entity
+ {
+ ///
+ /// The aleph number aleph(k), the size of an infinite set: aleph(0) is the
+ /// size of the whole numbers, and aleph(k + 1) the least size after
+ /// aleph(k).
+ ///
+ ///
+ /// card of an infinite set is one of these, or a power of 2 of one:
+ /// card(ZZ) is aleph(0) and card(RR) is 2^aleph(0), which is an
+ /// aleph but not a named one -- that it is aleph(1) is the continuum hypothesis,
+ /// which ZFC does not decide. A sum or a product of sizes is the larger of them, and the
+ /// sizes compare.
+ /// https://github.com/asc-community/AngouriMath/issues/1409
+ ///
+ public sealed partial record Alephf(Entity Index) : Function, IUnaryNode
+ {
+ ///
+ public Entity NodeChild => Index;
+
+ private Alephf New(Entity index) =>
+ ReferenceEquals(Index, index) ? this : new(index) { Codomain = Codomain };
+ ///
+ public override Entity Replace(Func func) => func(New(Index.Replace(func)));
+ ///
+ protected override Entity[] InitDirectChildren() => new[] { Index };
+ }
+ }
+}
diff --git a/Sources/AngouriMath/Core/Entity/Omni/Sets/Cardinality.cs b/Sources/AngouriMath/Core/Entity/Omni/Sets/Cardinality.cs
new file mode 100644
index 000000000..ef0d6c246
--- /dev/null
+++ b/Sources/AngouriMath/Core/Entity/Omni/Sets/Cardinality.cs
@@ -0,0 +1,269 @@
+//
+// Copyright (c) 2019-2026 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using System;
+using PeterO.Numbers;
+using static AngouriMath.Entity;
+using static AngouriMath.Entity.Number;
+using static AngouriMath.Entity.Set;
+
+namespace AngouriMath.Core.Sets
+{
+ ///
+ /// Sizes of sets, Sullivan and Mackey's §7.6: card of an infinite set is an aleph or a
+ /// power of 2 of one, sums and products of sizes are the larger, and sizes compare.
+ ///
+ ///
+ ///
+ /// PP, ZZ+, ZZ*, ZZ and QQ are aleph(0) in size.
+ /// RR, CC and every interval with two distinct ends are 2^aleph(0), the size
+ /// of the power set of ZZ+. That is an aleph too, but which one is the continuum
+ /// hypothesis, which ZFC does not decide, so it is not written as aleph(1). A power set
+ /// is 2^card(S); a union with an infinite side is its larger side; and an infinite
+ /// A less a smaller B keeps the size of A, so the irrationals are the size
+ /// of RR.
+ ///
+ ///
+ /// A size read here is a finite count, or a tower 2^(...^(2^aleph(k))) of height
+ /// t, t = 0 being aleph(k) itself. Only what ZFC proves is used:
+ /// aleph(j) < aleph(k) for j < k; s < 2^s for every size, Cantor's
+ /// theorem; 2^s >= aleph(k + 1) for s >= aleph(k), so a tower of height
+ /// t over aleph(k) is at least aleph(k + t); and 2^s <= 2^u for
+ /// s <= u. What these leave open stays written: 2^aleph(0) = aleph(1) is
+ /// consistent with ZFC and so is its negation. A subset is no larger than its superset, which
+ /// settles one side of a comparison between two sizes that are not read.
+ ///
+ /// https://github.com/asc-community/AngouriMath/issues/1409
+ ///
+ internal static class Cardinality
+ {
+ // A finite power set is counted as 2^n up to this n; past it, only that it is finite.
+ private const int MaxCountedExponent = 4096;
+
+ [ConstantField] private static readonly EInteger Two = EInteger.FromInt32(2);
+
+ ///
+ /// A size: finite, with where it is known, or infinite, a tower of
+ /// height over aleph().
+ ///
+ private readonly record struct Size(bool Infinite, EInteger? Count, int Aleph, int Tower)
+ {
+ internal static Size Finite(EInteger? count) => new(false, count, 0, 0);
+ internal static Size Of(int aleph, int tower) => new(true, null, aleph, tower);
+ }
+
+ ///
+ /// The size of the set a card is taken of, as an aleph or a power of one, where the
+ /// set is infinite and its size read, or .
+ ///
+ internal static Entity? Of(Entity set, bool isExact)
+ {
+ switch (set)
+ {
+ case SpecialSet special:
+ return special.ToDomain() switch
+ {
+ Domain.Boolean => Integer.Create(2),
+ Domain.Prime or Domain.PositiveInteger or Domain.NonNegativeInteger or Domain.Integer or Domain.Rational => MathS.Aleph(0),
+ Domain.Real or Domain.Complex => MathS.Pow(2, MathS.Aleph(0)),
+ _ => null,
+ };
+ case Interval { Left: Real left, Right: Real right } when left.EDecimal.CompareTo(right.EDecimal) < 0:
+ return MathS.Pow(2, MathS.Aleph(0));
+ // |P(S)| = 2^|S|, whatever S is.
+ case Powersetf(var of):
+ return MathS.Pow(2, MathS.Sets.Card(of).InnerSimplified(isExact)).InnerSimplified(isExact);
+ // |A u B| = max(|A|, |B|) where one side is infinite.
+ case Unionf(var either, var other):
+ return Absorbed(MathS.Sets.Card(either).InnerSimplified(isExact), MathS.Sets.Card(other).InnerSimplified(isExact));
+ // An infinite A less a smaller B keeps A's size: were A \ B smaller too, A, their
+ // union with A /\ B, would be smaller than itself.
+ case SetMinusf(var whole, var removed):
+ var wholeSize = MathS.Sets.Card(whole).InnerSimplified(isExact);
+ return SizeOf(wholeSize, false) is { Infinite: true } wholeRead
+ && SizeOf(MathS.Sets.Card(removed).InnerSimplified(isExact), false) is { } removedRead
+ && Signs(removedRead, wholeRead) == (true, false, false)
+ ? wholeSize
+ : null;
+ // RR \ QQ arrives as { x in RR : not x in QQ }, and is read as the difference.
+ case ConditionalSet builder when builder.DeclaredMembership is (var declared, var rest) && builder.Var is Variable member
+ && rest is Notf(Inf(var element, var excluded)) && element == member && !excluded.ContainsNode(member):
+ return Of(new SetMinusf(declared, excluded), isExact);
+ default:
+ return null;
+ }
+ }
+
+ ///
+ /// The sum or, neither being zero, the product of two sizes one of which is infinite: the
+ /// larger, or NaN where the other is a number that is not a size -- a whole number
+ /// from zero -- since a size less one, or a half of one, has no value.
+ /// where no side is an infinite size, or the two do not compare.
+ ///
+ ///
+ /// No value is NaN, as for log(0), which is how Happypig375 asked for it on
+ /// https://github.com/asc-community/AngouriMath/issues/1409.
+ ///
+ internal static Entity? Absorbed(Entity a, Entity b)
+ {
+ if (!IsInfinite(a) && !IsInfinite(b))
+ return null;
+ if (a is Number { IsNaN: false } && SizeOf(a, false) is null || b is Number { IsNaN: false } && SizeOf(b, false) is null)
+ return MathS.NaN;
+ if (SizeOf(a, false) is not { } sizeA || SizeOf(b, false) is not { } sizeB)
+ return null;
+ return Signs(sizeA, sizeB) switch
+ {
+ (true, false, false) => b,
+ (false, true, false) or (false, false, true) => a,
+ _ => null,
+ };
+ }
+
+ ///
+ /// Whether a difference or a quotient with these two sides has no value: one of them is an
+ /// infinite size, and sizes are not subtracted or divided -- taking the even numbers from
+ /// the whole numbers leaves aleph(0) of them and taking all of them none.
+ ///
+ internal static bool HasNoValue(Entity a, Entity b)
+ => IsInfinite(a) || IsInfinite(b);
+
+ ///
+ /// Whether an expression stands for a size: a card, an aleph, or a power of
+ /// 2 of a size.
+ ///
+ internal static bool IsSize(Entity expression)
+ => expression is Cardf or Alephf
+ || expression is Powf(Integer { EInteger: var two }, var exponent) && two.Equals(Two) && IsSize(exponent);
+
+ private static bool IsInfinite(Entity expression)
+ => expression is Alephf
+ || expression is Powf(Integer { EInteger: var two }, var exponent) && two.Equals(Two) && IsInfinite(exponent);
+
+ ///
+ /// The comparison of two sizes, against ,
+ /// as a truth value where every sign the two can have agrees on it, or
+ /// : says whether the statement holds for
+ /// the sign of left - right.
+ ///
+ internal static Entity? Compare(Entity left, Entity right, Func holds, bool isExact)
+ {
+ var (less, equal, greater) = PossibleSigns(left, right, isExact);
+ if (!less && !equal && !greater)
+ return null;
+ var any = (less && holds(-1)) || (equal && holds(0)) || (greater && holds(1));
+ var all = (!less || holds(-1)) && (!equal || holds(0)) && (!greater || holds(1));
+ return all ? Entity.Boolean.True : !any ? Entity.Boolean.False : null;
+ }
+
+ ///
+ /// Which signs left - right can have; none of the three where nothing is known.
+ ///
+ private static (bool Less, bool Equal, bool Greater) PossibleSigns(Entity left, Entity right, bool isExact)
+ {
+ if (left == right)
+ return (false, true, false);
+ // Cantor's theorem: s < 2^s, whatever the size s is.
+ if (IsSize(left) && right is Powf(Integer { EInteger: var twoRight }, var rightExponent) && twoRight.Equals(Two) && rightExponent == left)
+ return (true, false, false);
+ if (IsSize(right) && left is Powf(Integer { EInteger: var twoLeft }, var leftExponent) && twoLeft.Equals(Two) && leftExponent == right)
+ return (false, false, true);
+ if (SizeOf(left, true) is { } leftSize && SizeOf(right, true) is { } rightSize)
+ return Signs(leftSize, rightSize);
+ // A subset is no larger than its superset.
+ if (left is Cardf(var subCandidate) && right is Cardf(var superCandidate))
+ {
+ if (SetOperators.Subset(subCandidate, superCandidate, isExact) == Entity.Boolean.True)
+ return (true, true, false);
+ if (SetOperators.Subset(superCandidate, subCandidate, isExact) == Entity.Boolean.True)
+ return (false, true, true);
+ }
+ return (false, false, false);
+ }
+
+ ///
+ /// Which signs left - right can have for two sizes read, by what ZFC proves of
+ /// alephs and powers of two; all three where it proves nothing.
+ ///
+ private static (bool Less, bool Equal, bool Greater) Signs(Size left, Size right)
+ {
+ const bool y = true, n = false;
+ switch (left.Infinite, right.Infinite)
+ {
+ case (false, false):
+ if (left.Count is { } a && right.Count is { } b)
+ return a.CompareTo(b) switch { < 0 => (y, n, n), 0 => (n, y, n), _ => (n, n, y) };
+ return (y, y, y);
+ case (false, true):
+ return (y, n, n);
+ case (true, false):
+ return (n, n, y);
+ }
+ if (left.Tower == 0 && right.Tower == 0)
+ return left.Aleph.CompareTo(right.Aleph) switch { < 0 => (y, n, n), 0 => (n, y, n), _ => (n, n, y) };
+ if (left.Tower == 0)
+ return AlephAgainstTower(left.Aleph, right.Aleph, right.Tower);
+ if (right.Tower == 0)
+ {
+ var (less, equal, greater) = AlephAgainstTower(right.Aleph, left.Aleph, left.Tower);
+ return (greater, equal, less);
+ }
+ // Two towers: over one aleph, the higher is larger, by Cantor's theorem each step;
+ // over a smaller aleph and no higher, it is no larger, since 2^s is monotone in s.
+ if (left.Aleph == right.Aleph)
+ return left.Tower.CompareTo(right.Tower) switch { < 0 => (y, n, n), 0 => (n, y, n), _ => (n, n, y) };
+ if (left.Aleph < right.Aleph && left.Tower <= right.Tower)
+ return left.Tower < right.Tower ? (y, n, n) : (y, y, n);
+ if (left.Aleph > right.Aleph && left.Tower >= right.Tower)
+ return left.Tower > right.Tower ? (n, n, y) : (n, y, y);
+ return (y, y, y);
+ }
+
+ ///
+ /// aleph(j) against a tower of height over
+ /// aleph(k), which is at least aleph(k + tower): smaller below that,
+ /// no larger at it, and anything above it.
+ ///
+ private static (bool Less, bool Equal, bool Greater) AlephAgainstTower(int j, int k, int tower)
+ => ((long)j).CompareTo((long)k + tower) switch
+ {
+ < 0 => (true, false, false),
+ 0 => (true, true, false),
+ _ => (true, true, true),
+ };
+
+ ///
+ /// The size an expression stands for, or : a whole number from zero,
+ /// any finite real where allows it, an aleph, a power of two
+ /// of a size, or card of a listed set.
+ ///
+ private static Size? SizeOf(Entity expression, bool numbers)
+ {
+ switch (expression)
+ {
+ case Integer { EInteger: var count } when count.Sign >= 0:
+ return Size.Finite(count);
+ case Real { IsFinite: true, IsNaN: false } when numbers:
+ return Size.Finite(null);
+ case Alephf(Integer { EInteger: var index }) when index.Sign >= 0 && index.CanFitInInt32():
+ return Size.Of(index.ToInt32Checked(), 0);
+ case Powf(Integer { EInteger: var two }, var exponent) when two.Equals(Two):
+ if (SizeOf(exponent, false) is not { } power)
+ return null;
+ if (power.Infinite)
+ return Size.Of(power.Aleph, power.Tower + 1);
+ return Size.Finite(power.Count is { } counted && counted.CanFitInInt32() && counted.ToInt32Checked() <= MaxCountedExponent
+ ? EInteger.One.ShiftLeft(counted.ToInt32Checked())
+ : null);
+ case Cardf(FiniteSet listed):
+ return Size.Finite(MathS.Sets.Card(listed).InnerSimplified is Integer { EInteger: var listedCount } ? listedCount : null);
+ default:
+ return null;
+ }
+ }
+ }
+}
diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
index 200411fa8..6cbef6aa1 100644
--- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
+++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs
@@ -121,6 +121,7 @@ [EntityJsonConverter] partial record SpecialSet
[EntityJsonConverter] partial record Signumf;
[EntityJsonConverter] partial record Erff;
[EntityJsonConverter] partial record Iversonf;
+ [EntityJsonConverter] partial record Alephf;
[EntityJsonConverter] partial record Erfcf;
[EntityJsonConverter] partial record Erfif;
[EntityJsonConverter] partial record Eif;
diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
index 34794b86e..4ad91784d 100644
--- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
+++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs
@@ -473,6 +473,7 @@ internal abstract bool ETryBuild(
[typeof(Entity.Signumf)] = (1, static c => new Entity.Signumf(c[0])),
[typeof(Entity.Erff)] = (1, static c => new Entity.Erff(c[0])),
[typeof(Entity.Iversonf)] = (1, static c => new Entity.Iversonf(c[0])),
+ [typeof(Entity.Alephf)] = (1, static c => new Entity.Alephf(c[0])),
[typeof(Entity.Erfcf)] = (1, static c => new Entity.Erfcf(c[0])),
[typeof(Entity.Erfif)] = (1, static c => new Entity.Erfif(c[0])),
[typeof(Entity.Eif)] = (1, static c => new Entity.Eif(c[0])),
diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md
index 8c689c6f6..8589f2dff 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 **60** such types.
+pattern used as a **replacement** must be one the library can construct: there are **61** 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 3441dcc2a..401c737f7 100644
--- a/Sources/AngouriMath/Docs/Usage/Syntax.md
+++ b/Sources/AngouriMath/Docs/Usage/Syntax.md
@@ -191,7 +191,14 @@ value on a side it is `NaN`. **Two sets are equal exactly when each is a subset
and that is how `=` between sets is decided: `{ x in ZZ : x >= 1 } = ZZ+` is `True` and
`[0; 1] = [0; 2]` is `False`; a pair the subset decision leaves open stays written. `card(S)` counts
a listed set whose members are numbers or listed sets of them (`card({1, {}})` is `2`), and
-`card(powerset(S))` is `2^card(S)`.
+`card(powerset(S))` is `2^card(S)`. The size of an infinite set is an aleph, `aleph(k)` (LaTeX
+`\aleph_k`), or a power of 2 of one: `card(ZZ)`, `card(QQ)` and `card(PP)` are `aleph(0)`, and
+`card(RR)` is `2^aleph(0)` — an aleph too, but which one is the continuum hypothesis, which ZFC does
+not decide, so `2^aleph(0) = aleph(1)` stays as written. A sum or a product of sizes, one of them
+infinite, is the larger (`aleph(0) + 1` is `aleph(0)`), and sizes compare by what ZFC proves:
+`card(ZZ) < card(RR)` and `2^aleph(0) >= aleph(1)` are `True`, and a set is smaller than its power
+set whatever it is, so `card(S) < card(powerset(S))` is `True`. A subset is no larger than its
+superset. `card(ZZ) = +oo` stays as written: an infinity is not a size.
There is **no universal set** and no literal for one. A set that constrains nothing is the
conditional set `{ x : True }`, which prints, reads back, compares and answers membership like any
diff --git a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
index c2c8534d7..3b1a9a60d 100644
--- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
+++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs
@@ -302,6 +302,13 @@ partial record Iversonf
null;
}
+ partial record Alephf
+ {
+ // A size is no number an equation between numbers could be solved for.
+ private protected override IEnumerable? InvertNode(Entity value, Entity x) =>
+ null;
+ }
+
partial record Derivativef
{
private protected override IEnumerable? InvertNode(Entity value, Entity x) =>
diff --git a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs
index 7b19d98e8..1fa881448 100644
--- a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Continuous/Evaluation.Continuous.Arithmetics.Classes.cs
@@ -90,6 +90,9 @@ protected override Entity InnerSimplify(bool isExact) =>
(Complex a, Complex b) when !isExact => a + b,
(var n1, Integer(0)) => n1,
(Integer(0), var n2) => n2,
+ // A sum of sizes, one of them infinite, is the larger: aleph(0) + 1 is
+ // aleph(0), the Hilbert hotel. https://github.com/asc-community/AngouriMath/issues/1409
+ _ when Core.Sets.Cardinality.Absorbed(augend, addend) is { } larger => larger,
(Interval inter, var n2) when n2 is not Set => inter.New((inter.Left + n2).InnerSimplified(isExact), (inter.Right + n2).InnerSimplified(isExact)),
(var n2, Interval inter) when n2 is not Set => inter.New((n2 + inter.Left).InnerSimplified(isExact), (n2 + inter.Right).InnerSimplified(isExact)),
_ => null
@@ -108,6 +111,9 @@ protected override Entity InnerSimplify(bool isExact) =>
(Complex a, Complex b) when !isExact => a - b,
(var n1, Integer(0)) => n1,
(Integer(0), var n2) => -n2,
+ // Sizes are not subtracted: aleph(0) - aleph(0) has no value.
+ // https://github.com/asc-community/AngouriMath/issues/1409
+ _ when Core.Sets.Cardinality.HasNoValue(augend, addend) => MathS.NaN,
(Interval inter, var n2) when n2 is not Set => inter.New((inter.Left - n2).InnerSimplified(isExact), (inter.Right - n2).InnerSimplified(isExact)),
// Subtracting an interval turns it round, so the ends swap and their
// openness swaps with them. `5 - (0; 1]` is `[4; 5)`: the excluded 1
@@ -140,6 +146,9 @@ protected override Entity InnerSimplify(bool isExact) =>
(Integer(0), { DomainCondition: var condition }) => Integer.Zero.Provided(condition),
(var n1, Integer(1)) => n1,
(Integer(1), var n2) => n2,
+ // A product of sizes, one of them infinite and neither zero, is the
+ // larger. https://github.com/asc-community/AngouriMath/issues/1409
+ _ when Core.Sets.Cardinality.Absorbed(a, b) is { } larger => larger,
(var n1, var n2) when n1 == n2 => new Powf(n1, 2).InnerSimplified(isExact),
// After the zero arms above, which answer a multiplication by zero for
// every Entity and not only for an interval.
@@ -167,6 +176,9 @@ n0.Evaled is Complex c
(_, Integer(0)) => Real.NaN,
(Complex n1, Complex n2) when !isExact => n1 / n2,
(var n1, Integer(1)) => n1,
+ // Sizes are not divided: aleph(0) / 2 has no value.
+ // https://github.com/asc-community/AngouriMath/issues/1409
+ _ when Core.Sets.Cardinality.HasNoValue(a, b) => MathS.NaN,
// A quotient by minus one is the negation, and a negation of a negation is
// the thing itself: the solver of `b - x = 0` answered `-b / (-1)` and the
// README printed it so.
@@ -444,6 +456,23 @@ protected override Entity InnerSimplify(bool isExact)
(@this, a) => ((Iversonf)@this).New(a), isExact);
}
+ public partial record Alephf
+ {
+ // Indexed by the whole numbers from zero: there is no aleph(-1) and no aleph(1/2).
+ private protected override Entity IntrinsicCondition => Index.In(MathS.Sets.NonNegativeIntegers);
+
+ ///
+ protected override Entity InnerSimplify(bool isExact)
+ => ExpandOnOneArgument(Index,
+ a => a switch
+ {
+ Integer { EInteger.Sign: >= 0 } => null,
+ Number => MathS.NaN,
+ _ => null
+ },
+ (@this, a) => ((Alephf)@this).New(a), isExact);
+ }
+
public partial record Erff
{
// Entire, so defined for every argument. https://github.com/asc-community/AngouriMath/issues/1501
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 e0bed1fae..0fc2e7b4c 100644
--- a/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs
+++ b/Sources/AngouriMath/Functions/Evaluation/Evaluation.Discrete/Evaluation.Discrete.Classes.cs
@@ -268,6 +268,19 @@ private static bool ConstantsAreEqual(Entity left, Entity right)
|| (left - right).Evaled is Number.Complex difference
&& Number.IsZero(difference);
+ ///
+ /// Whether a size that is not a number is inside a constant, which is then not compared
+ /// as a number: the difference of the two sides of sin(aleph(0)) = 0 is no
+ /// number to test for zero, and reading it as a nonzero one would answer False.
+ ///
+ private static bool HasAnUnreadSize(Entity side)
+ {
+ foreach (var node in side.Nodes)
+ if (node is Cardf or Alephf)
+ return true;
+ return false;
+ }
+
///
/// Two sets are equal exactly when each is a subset of the other -- the double
/// containment that defines set equality -- so a pair of sets that are not the same
@@ -289,7 +302,10 @@ private static bool ConstantsAreEqual(Entity left, Entity right)
protected override Entity InnerSimplify(bool isExact)
=> ExpandOnTwoArguments(Left, Right,
(left, right) => left == right ? true
- : left.IsConstant && right.IsConstant ? ConstantsAreEqual(left, right)
+ // A size that is not a number is compared as a size, never by the difference
+ // of two expressions: card(ZZ) - card(QQ) is not zero, and the two are equal.
+ : AngouriMath.Core.Sets.Cardinality.IsSize(left) || AngouriMath.Core.Sets.Cardinality.IsSize(right) ? AngouriMath.Core.Sets.Cardinality.Compare(left, right, static sign => sign == 0, isExact)
+ : left.IsConstant && right.IsConstant ? (HasAnUnreadSize(left) || HasAnUnreadSize(right) ? null : ConstantsAreEqual(left, right))
: left is Set setLeft && right is Set setRight ? SetsAreEqual(setLeft, setRight, isExact)
: null,
(@this, a, b) => ((Equalsf)@this).New(a, b), isExact,
@@ -325,6 +341,7 @@ protected override Entity InnerSimplify(bool isExact)
{
(Number numLeft, Number numRight) when AsAReal(numLeft) is { } reLeft && AsAReal(numRight) is { } reRight => reLeft > reRight,
(Number numLeft, Number numRight) => MathS.NaN,
+ _ when AngouriMath.Core.Sets.Cardinality.IsSize(a) || AngouriMath.Core.Sets.Cardinality.IsSize(b) => AngouriMath.Core.Sets.Cardinality.Compare(a, b, static sign => sign > 0, isExact),
_ => null
},
(@this, a, b) => ((Greaterf)@this).New(a, b), isExact);
@@ -344,6 +361,7 @@ protected override Entity InnerSimplify(bool isExact)
{
(Number numLeft, Number numRight) when AsAReal(numLeft) is { } reLeft && AsAReal(numRight) is { } reRight => reLeft >= reRight,
(Number numLeft, Number numRight) => MathS.NaN,
+ _ when AngouriMath.Core.Sets.Cardinality.IsSize(a) || AngouriMath.Core.Sets.Cardinality.IsSize(b) => AngouriMath.Core.Sets.Cardinality.Compare(a, b, static sign => sign >= 0, isExact),
_ => null
},
(@this, a, b) => ((GreaterOrEqualf)@this).New(a, b), isExact);
@@ -363,6 +381,7 @@ protected override Entity InnerSimplify(bool isExact)
{
(Number numLeft, Number numRight) when AsAReal(numLeft) is { } reLeft && AsAReal(numRight) is { } reRight => reLeft < reRight,
(Number numLeft, Number numRight) => MathS.NaN,
+ _ when AngouriMath.Core.Sets.Cardinality.IsSize(a) || AngouriMath.Core.Sets.Cardinality.IsSize(b) => AngouriMath.Core.Sets.Cardinality.Compare(a, b, static sign => sign < 0, isExact),
_ => null
},
(@this, a, b) => ((Lessf)@this).New(a, b), isExact);
@@ -381,6 +400,7 @@ protected override Entity InnerSimplify(bool isExact)
{
(Number numLeft, Number numRight) when AsAReal(numLeft) is { } reLeft && AsAReal(numRight) is { } reRight => reLeft <= reRight,
(Number numLeft, Number numRight) => MathS.NaN,
+ _ when AngouriMath.Core.Sets.Cardinality.IsSize(a) || AngouriMath.Core.Sets.Cardinality.IsSize(b) => AngouriMath.Core.Sets.Cardinality.Compare(a, b, static sign => sign <= 0, isExact),
_ => null
},
(@this, a, b) => ((LessOrEqualf)@this).New(a, b), isExact);
@@ -572,8 +592,12 @@ FiniteSet finite when finite.All(Countable)
Powersetf(var of) when MathS.Sets.Card(of).InnerSimplified(isExact) is Integer { EInteger: var counted }
&& counted.Sign >= 0 && counted.CanFitInInt32()
=> Integer.Create(EInteger.One.ShiftLeft(counted.ToInt32Checked())),
- // An interval with numeric ends: one point, or none, is countable; a
- // proper interval is not, and there is no number for it here.
+ // An infinite set's size is an aleph, or a power of 2 of one: card(ZZ) is
+ // aleph(0) and card(RR) is 2^aleph(0), Sullivan and Mackey's §7.6.
+ // https://github.com/asc-community/AngouriMath/issues/1409
+ _ when AngouriMath.Core.Sets.Cardinality.Of(a, isExact) is { } size => size,
+ // An interval with numeric ends: one point, or none; a proper interval is
+ // the size of the reals, above.
Interval { Left: Real left, Right: Real right } interval => left.EDecimal.CompareTo(right.EDecimal) switch
{
> 0 => Integer.Zero,
diff --git a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
index a01976f10..c33346f69 100644
--- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs
@@ -176,6 +176,13 @@ private protected override string LatexizeNode()
=> $@"[\![{Argument.Latexize()}]\!]";
}
+ partial record Alephf
+ {
+ ///
+ private protected override string LatexizeNode()
+ => $@"\aleph_{{{Index.Latexize()}}}";
+ }
+
partial record Erfcf
{
///
diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
index 9d4fd061f..58b18a185 100644
--- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs
@@ -148,6 +148,14 @@ public partial record Iversonf
public override string ToString() => Stringize();
}
+ public partial record Alephf
+ {
+ ///
+ private protected override string StringizeNode() => $"aleph({Index.Stringize()})";
+ ///
+ public override string ToString() => Stringize();
+ }
+
public partial record Erfcf
{
///
diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
index 469663ddc..50dfc4060 100644
--- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
+++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs
@@ -94,6 +94,13 @@ internal override string ToSymPy()
=> $@"sympy.Piecewise((1, {Argument.ToSymPy()}), (0, True))";
}
+ // SymPy has no sizes of sets, so an aleph goes as a symbol of its own.
+ public partial record Alephf
+ {
+ internal override string ToSymPy()
+ => $"sympy.Symbol(\"aleph_{Index.Stringize()}\")";
+ }
+
public partial record Erfcf
{
internal override string ToSymPy()
diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs
index 849d3e41e..a77cf72d5 100644
--- a/Sources/AngouriMath/Functions/Substitute.cs
+++ b/Sources/AngouriMath/Functions/Substitute.cs
@@ -195,6 +195,13 @@ public override Entity Substitute(Entity x, Entity value)
=> this == x ? value : New(Argument.Substitute(x, value));
}
+ partial record Alephf
+ {
+ ///
+ public override Entity Substitute(Entity x, Entity value)
+ => this == x ? value : New(Index.Substitute(x, value));
+ }
+
partial record Erfcf
{
///
diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
index 862437d99..a8c5f4c5d 100644
--- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
+++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs
@@ -244,6 +244,12 @@ private protected override string SortHashName(SortLevel level)
=> Choice(level, "iverson_", "iverson_", "iverson_");
}
+ public partial record Alephf
+ {
+ private protected override string SortHashName(SortLevel level)
+ => Choice(level, "aleph_", "aleph_", "aleph_");
+ }
+
public partial record Erfcf
{
private protected override string SortHashName(SortLevel level)
diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt
index bf16aa988..0284d33c0 100644
--- a/Sources/Tests/UnitTests/Common/PublicApi.txt
+++ b/Sources/Tests/UnitTests/Common/PublicApi.txt
@@ -406,6 +406,25 @@ AngouriMath.Entity+Absf.ToString() : System.String
AngouriMath.Entity+Absf.ctor(AngouriMath.Entity)
AngouriMath.Entity+Absf.op_Equality(AngouriMath.Entity+Absf, AngouriMath.Entity+Absf) : System.Boolean
AngouriMath.Entity+Absf.op_Inequality(AngouriMath.Entity+Absf, AngouriMath.Entity+Absf) : System.Boolean
+AngouriMath.Entity+Alephf.$() : AngouriMath.Entity+Alephf
+AngouriMath.Entity+Alephf.Codomain { } : AngouriMath.Core.Domain
+AngouriMath.Entity+Alephf.Deconstruct(AngouriMath.Entity&) : System.Void
+AngouriMath.Entity+Alephf.EqualityContract { } : System.Type
+AngouriMath.Entity+Alephf.Equals(AngouriMath.Entity+Alephf) : System.Boolean
+AngouriMath.Entity+Alephf.Equals(AngouriMath.Entity+Function) : System.Boolean
+AngouriMath.Entity+Alephf.Equals(System.Object) : System.Boolean
+AngouriMath.Entity+Alephf.GetHashCode() : System.Int32
+AngouriMath.Entity+Alephf.Index { } : AngouriMath.Entity
+AngouriMath.Entity+Alephf.InitDirectChildren() : AngouriMath.Entity[]
+AngouriMath.Entity+Alephf.InnerSimplify(System.Boolean) : AngouriMath.Entity
+AngouriMath.Entity+Alephf.NodeChild { } : AngouriMath.Entity
+AngouriMath.Entity+Alephf.PrintMembers(System.Text.StringBuilder) : System.Boolean
+AngouriMath.Entity+Alephf.Replace(System.Func) : AngouriMath.Entity
+AngouriMath.Entity+Alephf.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity
+AngouriMath.Entity+Alephf.ToString() : System.String
+AngouriMath.Entity+Alephf.ctor(AngouriMath.Entity)
+AngouriMath.Entity+Alephf.op_Equality(AngouriMath.Entity+Alephf, AngouriMath.Entity+Alephf) : System.Boolean
+AngouriMath.Entity+Alephf.op_Inequality(AngouriMath.Entity+Alephf, AngouriMath.Entity+Alephf) : System.Boolean
AngouriMath.Entity+Andf.$() : AngouriMath.Entity+Andf
AngouriMath.Entity+Andf.Codomain { } : AngouriMath.Core.Domain
AngouriMath.Entity+Andf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void
@@ -3112,6 +3131,7 @@ AngouriMath.MathS+Utils.TryGetPolyLinear(AngouriMath.Entity, AngouriMath.Entity+
AngouriMath.MathS+Utils.TryGetPolyQuadratic(AngouriMath.Entity, AngouriMath.Entity+Variable, AngouriMath.Entity&, AngouriMath.Entity&, AngouriMath.Entity&) : System.Boolean
AngouriMath.MathS+Utils.TryGetPolynomial(AngouriMath.Entity, AngouriMath.Entity+Variable, System.Collections.Generic.Dictionary&) : System.Boolean
AngouriMath.MathS.Abs(AngouriMath.Entity) : AngouriMath.Entity
+AngouriMath.MathS.Aleph(AngouriMath.Entity) : AngouriMath.Entity
AngouriMath.MathS.Apply(AngouriMath.Entity, AngouriMath.Entity[]) : AngouriMath.Entity
AngouriMath.MathS.Arccos(AngouriMath.Entity) : AngouriMath.Entity
AngouriMath.MathS.Arccosec(AngouriMath.Entity) : AngouriMath.Entity
@@ -3300,6 +3320,7 @@ class AngouriMath.Core.Transformations.RewriteRules
class AngouriMath.Core.Transformations.Transformation
class AngouriMath.Entity
class AngouriMath.Entity+Absf
+class AngouriMath.Entity+Alephf
class AngouriMath.Entity+Andf
class AngouriMath.Entity+Application
class AngouriMath.Entity+Arccosecantf
diff --git a/Sources/Tests/UnitTests/Core/CardinalityTest.cs b/Sources/Tests/UnitTests/Core/CardinalityTest.cs
index 3e91a4ab2..4da7f89e3 100644
--- a/Sources/Tests/UnitTests/Core/CardinalityTest.cs
+++ b/Sources/Tests/UnitTests/Core/CardinalityTest.cs
@@ -46,18 +46,159 @@ public void ASetWithASymbolInItIsNotCountedUntilItsElementsAreKnown()
Assert.Equal("1".ToEntity(), card.Substitute("x", 1).Evaled);
}
- // Infinite sets have a cardinality the library has no number for, and a set builder is
- // not enumerated: both stay as written rather than being answered with anything.
+ ///
+ /// An infinite set's size is an aleph, or a power of 2 of one: the reals are
+ /// 2^aleph(0), and not aleph(1), which would be the continuum hypothesis.
+ ///
+ [Theory]
+ [InlineData("card(ZZ)", "aleph(0)")]
+ [InlineData("card(QQ)", "aleph(0)")]
+ [InlineData("card(PP)", "aleph(0)")]
+ [InlineData("card(ZZ+)", "aleph(0)")]
+ [InlineData("card(RR)", "2^aleph(0)")]
+ [InlineData("card(CC)", "2^aleph(0)")]
+ [InlineData("card([0; 1])", "2^aleph(0)")]
+ [InlineData("card(powerset(ZZ+))", "2^aleph(0)")]
+ [InlineData("card(powerset(RR))", "2^2^aleph(0)")]
+ [InlineData("card(ZZ \\/ [0; 1])", "2^aleph(0)")]
+ [InlineData("card(BB)", "2")]
+ public void AnInfiniteSetsSizeIsAnAleph(string card, string expected)
+ => Assert.Equal(expected.ToEntity(), card.ToEntity().Simplify());
+
+ // A set builder is not enumerated, and a set with symbolic ends or no set at all has no
+ // size read: each stays as written rather than being answered with anything.
[Theory]
- [InlineData("card(RR)")]
- [InlineData("card(ZZ)")]
- [InlineData("card([0; 1])")]
[InlineData("card((a; b))")]
[InlineData("card({ x : x > 0 })")]
[InlineData("card(S)")]
- public void WhatIsNotAFiniteSetOfNumbersIsLeftAsWritten(string card)
+ public void WhatIsNotReadIsLeftAsWritten(string card)
=> Assert.IsType(card.ToEntity().Simplify());
+ ///
+ /// A sum or a product of sizes, one of them infinite, is the larger: the Hilbert hotel,
+ /// Sullivan and Mackey's §7.6.3.
+ ///
+ [Theory]
+ [InlineData("aleph(0) + 1", "aleph(0)")]
+ [InlineData("aleph(0) + aleph(0)", "aleph(0)")]
+ [InlineData("3 * aleph(0)", "aleph(0)")]
+ [InlineData("aleph(0) * aleph(1)", "aleph(1)")]
+ [InlineData("2^aleph(0) + aleph(0)", "2^aleph(0)")]
+ [InlineData("0 * aleph(0)", "0")]
+ [InlineData("card(ZZ) + 1 = card(ZZ)", "True")]
+ public void ASumOrAProductOfSizesIsTheLarger(string input, string expected)
+ => Assert.Equal(expected.ToEntity(), input.ToEntity().Simplify());
+
+ ///
+ /// A difference or a quotient of sizes has no value, and neither has a size with a
+ /// negative or a fractional number added or multiplied: taking the even numbers from the
+ /// whole numbers leaves aleph(0) of them, and taking all of them leaves none. No
+ /// value is NaN, as for log(0).
+ ///
+ [Theory]
+ [InlineData("aleph(0) - aleph(0)")]
+ [InlineData("aleph(1) - aleph(0)")]
+ [InlineData("aleph(0) - 1")]
+ [InlineData("aleph(0) / 2")]
+ [InlineData("aleph(0) / aleph(0)")]
+ [InlineData("aleph(0) + 1/2")]
+ [InlineData("-aleph(0)")]
+ public void ArithmeticWithoutAValueIsNaN(string input)
+ {
+ var result = input.ToEntity().Simplify();
+ Assert.True(result.IsNaN, $"{input} simplified to {result}");
+ }
+
+ [Theory]
+ [InlineData("aleph(-1)")]
+ [InlineData("aleph(1/2)")]
+ public void AnAlephIsIndexedByAWholeNumberFromZero(string input)
+ => Assert.True(input.ToEntity().Simplify().IsNaN);
+
+ [Fact]
+ public void AnAlephPrintsAsItIsWrittenAndInLatexAsAnAleph()
+ {
+ Assert.Equal("aleph(0)", "aleph(0)".ToEntity().Stringize());
+ Assert.Equal(@"\aleph_{0}", "aleph(0)".ToEntity().Latexize());
+ Assert.Equal("aleph(k)".ToEntity(), "aleph(k)".ToEntity().Stringize().ToEntity());
+ Assert.Equal("aleph(0)".ToEntity(), MathS.Aleph(0));
+ }
+
+ ///
+ /// Sizes that are not numbers compare as sizes, Sullivan and Mackey's §7.6: the whole
+ /// numbers, the positive ones and the rationals are one size, the reals and every interval
+ /// a larger one, and the power set of ZZ+ is the size of the reals. Equality is
+ /// never read off the difference of the two expressions, which is not zero.
+ ///
+ [Theory]
+ [InlineData("card(ZZ) = card(QQ)", "True")]
+ [InlineData("card(ZZ+) = card(ZZ)", "True")]
+ [InlineData("card(PP) = card(ZZ*)", "True")]
+ [InlineData("card(ZZ) < card(RR)", "True")]
+ [InlineData("card(RR) > card(QQ)", "True")]
+ [InlineData("card(ZZ) <= card(QQ)", "True")]
+ [InlineData("card(RR) <= card(ZZ)", "False")]
+ [InlineData("card(RR) = card(CC)", "True")]
+ [InlineData("card([0; 1]) = card(RR)", "True")]
+ [InlineData("card((0; 1)) = card([0; 2])", "True")]
+ [InlineData("card(RR) = card(powerset(ZZ+))", "True")]
+ [InlineData("card(RR) < card(powerset(RR))", "True")]
+ [InlineData("card(RR \\ QQ) = card(RR)", "True")]
+ [InlineData("card(ZZ \\/ [0; 1]) = card(RR)", "True")]
+ [InlineData("card(ZZ) > 1000", "True")]
+ [InlineData("card(ZZ) = 5", "False")]
+ [InlineData("card({ 1, 2 }) < card(ZZ)", "True")]
+ [InlineData("card({ x, 1 }) < card(ZZ)", "True")]
+ // Appendix A.6.3 says every interval [a, b] is uncountable; with a = b it has one member.
+ [InlineData("card([1; 1]) < card(RR)", "True")]
+ // What ZFC proves of alephs and powers of 2: 2^aleph(0) is past aleph(0), so at least
+ // aleph(1); a power of 2 of a larger aleph is no smaller; a tower is past its base.
+ [InlineData("aleph(1) < aleph(2)", "True")]
+ [InlineData("2^aleph(0) >= aleph(1)", "True")]
+ [InlineData("2^aleph(0) > aleph(0)", "True")]
+ [InlineData("2^aleph(0) <= 2^aleph(1)", "True")]
+ [InlineData("2^2^aleph(0) > 2^aleph(0)", "True")]
+ [InlineData("aleph(0) < 2^aleph(0)", "True")]
+ public void SizesThatAreNotNumbersCompare(string statement, string expected)
+ => Assert.Equal(expected.ToEntity(), statement.ToEntity().Simplify());
+
+ ///
+ /// Cantor's theorem, Thm 7.6.5: a set is smaller than its power set, whatever the set.
+ ///
+ [Theory]
+ [InlineData("card(S) < card(powerset(S))", "True")]
+ [InlineData("card(powerset(S)) <= card(S)", "False")]
+ [InlineData("card(S) = card(powerset(S))", "False")]
+ public void ASetIsSmallerThanItsPowerSet(string statement, string expected)
+ => Assert.Equal(expected.ToEntity(), statement.ToEntity().Simplify());
+
+ ///
+ /// Lemma 7.6.11: a subset is no larger than its superset, which settles one side and
+ /// leaves the other open.
+ ///
+ [Theory]
+ [InlineData("card(A /\\ B) <= card(A)", "True")]
+ [InlineData("card(A) <= card(A \\/ B)", "True")]
+ [InlineData("card(A /\\ B) > card(A)", "False")]
+ public void ASubsetIsNoLargerThanItsSuperset(string statement, string expected)
+ => Assert.Equal(expected.ToEntity(), statement.ToEntity().Simplify());
+
+ ///
+ /// Two sizes nothing is known about stay written, and so does a comparison with an
+ /// infinity, which is not a size -- the book refuses |S| = oo -- and one ZFC does
+ /// not decide.
+ ///
+ [Theory]
+ [InlineData("card(A) < card(B)")]
+ [InlineData("card(A /\\ B) < card(A)")]
+ [InlineData("card(ZZ) = +oo")]
+ // The continuum hypothesis, and its generalisation one aleph up: ZFC decides neither.
+ [InlineData("2^aleph(0) = aleph(1)")]
+ [InlineData("2^aleph(1) = aleph(2)")]
+ [InlineData("2^aleph(0) < 2^aleph(1)")]
+ public void ASizeThatIsNotReadIsLeftAsWritten(string statement)
+ => Assert.IsNotType(statement.ToEntity().Simplify());
+
// Canonical is the prefix `#`; `card( )` is accepted on input and prints as `#`.
[Theory]
[InlineData("card({ 1, 2 })", "#{ 1, 2 }")]
diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs
index 6be125a12..d49f30808 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(60, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types");
+ => Stated(61, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types");
[Fact]
public void ReplacementAPatternOrCode()