diff --git a/BREAKING-CHANGES.md b/BREAKING-CHANGES.md index c78613901..d4758ffda 100644 --- a/BREAKING-CHANGES.md +++ b/BREAKING-CHANGES.md @@ -1597,6 +1597,25 @@ undeclared variable. | `"erfc(1)".Simplify()` | `erfc` | `erfc(1)`, and `0.157299207050285…` evaluated | | `"erf(x)".Differentiate("x")` | `UnrecognizedFunctionParseException` | `2 / sqrt(pi) * e ^ (-x ^ 2)` | +### `Ei` and `li` are functions + +**Addition, and two silent misreadings fixed.** The exponential integral +`Ei(z) = gamma + (ln z - ln(1/z))/2 + sum z^k/(k k!)` and the logarithmic integral `li(z) = Ei(ln z)` +are nodes (`MathS.Ei`, `MathS.Li`), the next of #1501's special functions. On the real line `Ei(x)` +is the principal value of `int_-oo^x e^t/t dt` and `li(x)` that of `int_0^x dt/ln t`, both real, as +SymPy's, mpmath's and Mathematica's are. Each is differentiated, printed in LaTeX as +`\operatorname{Ei}` and `\operatorname{li}`, and evaluated to the working precision anywhere in the +complex plane (`Entity.Number.Ei`, `Li`). Neither name was refused, so each was read as a product +with an undeclared variable +([#1501](https://github.com/asc-community/AngouriMath/issues/1501)). + +| Input | Was (2.5.0) | Now | +|---|---|---| +| `"Ei(x)"` | `Ei * x` | `Ei(x)` | +| `"li(2)".Simplify()` | `2 * li` | `li(2)`, and `1.045163780117492…` evaluated | +| `"Ei(1)".Simplify()` | `Ei` | `Ei(1)`, and `1.895117816355936…` evaluated | +| `"Ei(x)".Differentiate("x")` | `Ei` | `e ^ x / x` | + ### A definite integral is the limit at a bound where its antiderivative is undefined `integral(x * e^(-x), x, 0, +oo)` was `NaN`, this library's way of saying a value does not diff --git a/Sources/.editorconfig b/Sources/.editorconfig index af38df176..416159525 100644 --- a/Sources/.editorconfig +++ b/Sources/.editorconfig @@ -645,3 +645,12 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed [Tests/UnitTests/Calculus/ExponentialOfAQuadraticInALogarithmTest.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/Number/ExponentialIntegrals.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.ExponentialIntegrals.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/Convenience/ExponentialIntegralTest.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 24dad47d2..4b93d299c 100644 --- a/Sources/AngouriMath/Convenience/MathS.cs +++ b/Sources/AngouriMath/Convenience/MathS.cs @@ -1392,6 +1392,30 @@ public static Entity VectorLength(Matrix v) [MethodImpl(MethodImplOptions.AggressiveInlining)] public static Entity Erfi(Entity a) => new Erfif(a); + /// The exponential integral, Ei(z) = gamma + (ln z - ln(1/z))/2 + sum z^k/(k k!) + /// The argument, any complex number but 0 + /// The node + /// + /// On the real line Ei(x) is the principal value of int_-oo^x e^t/t dt, real on + /// either side of 0, so it is what int e^x/x dx is in closed form. Off it, the cut is + /// the negative real axis, as for ln, but Ei keeps its real value on the cut + /// itself: Ei(-1) is about -0.2194, and just above the axis it is i pi more. + /// https://github.com/asc-community/AngouriMath/issues/1501 + /// + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static Entity Ei(Entity a) => new Eif(a); + + /// The logarithmic integral, li(z) = Ei(ln z) + /// The argument, any complex number but 1 + /// The node + /// + /// On x > 0, li(x) is the principal value of int_0^x dt/ln t, so it is what + /// int 1/ln(x) dx is in closed form: real, 0 at 0 and -oo at 1. + /// https://github.com/asc-community/AngouriMath/issues/1501 + /// + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static Entity Li(Entity a) => new Lif(a); + /// Boolean negation /// Wikipedia /// Argument node of which Negation function will be taken diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.g b/Sources/AngouriMath/Core/Antlr/AngouriMath.g index 1a8fdd7db..9253939f3 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.g +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.g @@ -600,6 +600,9 @@ atom returns[Entity value] | '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]); } | 'erfi(' args = function_arguments ')' { Assert("erfi", 1, $args.list.Count); $value = MathS.Erfi($args.list[0]); } + /* The exponential and logarithmic integrals. https://github.com/asc-community/AngouriMath/issues/1501 */ + | 'Ei(' args = function_arguments ')' { Assert("Ei", 1, $args.list.Count); $value = MathS.Ei($args.list[0]); } + | 'li(' args = function_arguments ')' { Assert("li", 1, $args.list.Count); $value = MathS.Li($args.list[0]); } /* Names the library does not have. Each is a function every other CAS spells this way, so a caller reaches for it, and without these rules each is silently read as a product -- diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp index 7555b07ab..bef65e098 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.interp @@ -169,6 +169,8 @@ null 'erf(' 'erfc(' 'erfi(' +'Ei(' +'li(' 'trunc(' 'conjugate(' 'domain(' @@ -361,6 +363,8 @@ null null null null +null +null NEWLINE NUMBER SPECIALSET @@ -400,4 +404,4 @@ statement atn: -[4, 1, 183, 1085, 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, 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0, 1035, 1036, 5, 31, 0, 0, 1036, 1037, 6, 24, -1, 0, 1037, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 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, 1089, 1, 0, 0, 0, 1088, 430, 1, 0, 0, 0, 1088, 432, 1, 0, 0, 0, 1088, 434, 1, 0, 0, 0, 1088, 436, 1, 0, 0, 0, 1088, 438, 1, 0, 0, 0, 1088, 440, 1, 0, 0, 0, 1088, 442, 1, 0, 0, 0, 1088, 444, 1, 0, 0, 0, 1088, 449, 1, 0, 0, 0, 1088, 453, 1, 0, 0, 0, 1088, 458, 1, 0, 0, 0, 1088, 463, 1, 0, 0, 0, 1088, 468, 1, 0, 0, 0, 1088, 473, 1, 0, 0, 0, 1088, 478, 1, 0, 0, 0, 1088, 483, 1, 0, 0, 0, 1088, 488, 1, 0, 0, 0, 1088, 493, 1, 0, 0, 0, 1088, 498, 1, 0, 0, 0, 1088, 503, 1, 0, 0, 0, 1088, 508, 1, 0, 0, 0, 1088, 513, 1, 0, 0, 0, 1088, 518, 1, 0, 0, 0, 1088, 523, 1, 0, 0, 0, 1088, 528, 1, 0, 0, 0, 1088, 533, 1, 0, 0, 0, 1088, 538, 1, 0, 0, 0, 1088, 543, 1, 0, 0, 0, 1088, 548, 1, 0, 0, 0, 1088, 553, 1, 0, 0, 0, 1088, 558, 1, 0, 0, 0, 1088, 563, 1, 0, 0, 0, 1088, 568, 1, 0, 0, 0, 1088, 573, 1, 0, 0, 0, 1088, 578, 1, 0, 0, 0, 1088, 583, 1, 0, 0, 0, 1088, 588, 1, 0, 0, 0, 1088, 593, 1, 0, 0, 0, 1088, 598, 1, 0, 0, 0, 1088, 603, 1, 0, 0, 0, 1088, 608, 1, 0, 0, 0, 1088, 613, 1, 0, 0, 0, 1088, 618, 1, 0, 0, 0, 1088, 623, 1, 0, 0, 0, 1088, 628, 1, 0, 0, 0, 1088, 633, 1, 0, 0, 0, 1088, 638, 1, 0, 0, 0, 1088, 643, 1, 0, 0, 0, 1088, 648, 1, 0, 0, 0, 1088, 653, 1, 0, 0, 0, 1088, 658, 1, 0, 0, 0, 1088, 663, 1, 0, 0, 0, 1088, 668, 1, 0, 0, 0, 1088, 673, 1, 0, 0, 0, 1088, 678, 1, 0, 0, 0, 1088, 683, 1, 0, 0, 0, 1088, 688, 1, 0, 0, 0, 1088, 693, 1, 0, 0, 0, 1088, 698, 1, 0, 0, 0, 1088, 703, 1, 0, 0, 0, 1088, 708, 1, 0, 0, 0, 1088, 713, 1, 0, 0, 0, 1088, 718, 1, 0, 0, 0, 1088, 723, 1, 0, 0, 0, 1088, 728, 1, 0, 0, 0, 1088, 733, 1, 0, 0, 0, 1088, 738, 1, 0, 0, 0, 1088, 743, 1, 0, 0, 0, 1088, 748, 1, 0, 0, 0, 1088, 753, 1, 0, 0, 0, 1088, 758, 1, 0, 0, 0, 1088, 763, 1, 0, 0, 0, 1088, 768, 1, 0, 0, 0, 1088, 773, 1, 0, 0, 0, 1088, 778, 1, 0, 0, 0, 1088, 783, 1, 0, 0, 0, 1088, 788, 1, 0, 0, 0, 1088, 793, 1, 0, 0, 0, 1088, 798, 1, 0, 0, 0, 1088, 803, 1, 0, 0, 0, 1088, 808, 1, 0, 0, 0, 1088, 813, 1, 0, 0, 0, 1088, 818, 1, 0, 0, 0, 1088, 823, 1, 0, 0, 0, 1088, 828, 1, 0, 0, 0, 1088, 833, 1, 0, 0, 0, 1088, 838, 1, 0, 0, 0, 1088, 843, 1, 0, 0, 0, 1088, 848, 1, 0, 0, 0, 1088, 853, 1, 0, 0, 0, 1088, 858, 1, 0, 0, 0, 1088, 863, 1, 0, 0, 0, 1088, 868, 1, 0, 0, 0, 1088, 873, 1, 0, 0, 0, 1088, 878, 1, 0, 0, 0, 1088, 883, 1, 0, 0, 0, 1088, 888, 1, 0, 0, 0, 1088, 893, 1, 0, 0, 0, 1088, 898, 1, 0, 0, 0, 1088, 903, 1, 0, 0, 0, 1088, 908, 1, 0, 0, 0, 1088, 913, 1, 0, 0, 0, 1088, 918, 1, 0, 0, 0, 1088, 923, 1, 0, 0, 0, 1088, 928, 1, 0, 0, 0, 1088, 933, 1, 0, 0, 0, 1088, 938, 1, 0, 0, 0, 1088, 943, 1, 0, 0, 0, 1088, 948, 1, 0, 0, 0, 1088, 953, 1, 0, 0, 0, 1088, 958, 1, 0, 0, 0, 1088, 963, 1, 0, 0, 0, 1088, 968, 1, 0, 0, 0, 1088, 973, 1, 0, 0, 0, 1088, 978, 1, 0, 0, 0, 1088, 983, 1, 0, 0, 0, 1088, 988, 1, 0, 0, 0, 1088, 993, 1, 0, 0, 0, 1088, 998, 1, 0, 0, 0, 1088, 1003, 1, 0, 0, 0, 1088, 1008, 1, 0, 0, 0, 1088, 1013, 1, 0, 0, 0, 1088, 1018, 1, 0, 0, 0, 1088, 1023, 1, 0, 0, 0, 1088, 1028, 1, 0, 0, 0, 1088, 1033, 1, 0, 0, 0, 1088, 1038, 1, 0, 0, 0, 1088, 1043, 1, 0, 0, 0, 1088, 1048, 1, 0, 0, 0, 1088, 1053, 1, 0, 0, 0, 1088, 1058, 1, 0, 0, 0, 1088, 1063, 1, 0, 0, 0, 1088, 1068, 1, 0, 0, 0, 1088, 1073, 1, 0, 0, 0, 1088, 1078, 1, 0, 0, 0, 1088, 1083, 1, 0, 0, 0, 1089, 49, 1, 0, 0, 0, 1090, 1091, 3, 32, 16, 0, 1091, 1092, 5, 0, 0, 1, 1092, 1093, 6, 25, -1, 0, 1093, 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, 1088] \ No newline at end of file diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens index 0604e95bb..069f48578 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMath.tokens @@ -173,14 +173,16 @@ T__171=172 T__172=173 T__173=174 T__174=175 -NEWLINE=176 -NUMBER=177 -SPECIALSET=178 -BOOLEAN=179 -NAN=180 -VARIABLE=181 -COMMENT=182 -WS=183 +T__175=176 +T__176=177 +NEWLINE=178 +NUMBER=179 +SPECIALSET=180 +BOOLEAN=181 +NAN=182 +VARIABLE=183 +COMMENT=184 +WS=185 '!'=1 '^'=2 '-'=3 @@ -350,10 +352,12 @@ WS=183 'erf('=167 'erfc('=168 'erfi('=169 -'trunc('=170 -'conjugate('=171 -'domain('=172 -'piecewise('=173 -'apply('=174 -'lambda('=175 -'NaN'=180 +'Ei('=170 +'li('=171 +'trunc('=172 +'conjugate('=173 +'domain('=174 +'piecewise('=175 +'apply('=176 +'lambda('=177 +'NaN'=182 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs index d1ace7a3a..04acd2452 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs @@ -60,8 +60,8 @@ public const int T__155=156, T__156=157, T__157=158, T__158=159, T__159=160, T__160=161, T__161=162, T__162=163, T__163=164, T__164=165, T__165=166, T__166=167, T__167=168, T__168=169, T__169=170, T__170=171, T__171=172, T__172=173, - T__173=174, T__174=175, NEWLINE=176, NUMBER=177, SPECIALSET=178, BOOLEAN=179, - NAN=180, VARIABLE=181, COMMENT=182, WS=183; + T__173=174, T__174=175, T__175=176, T__176=177, NEWLINE=178, NUMBER=179, + SPECIALSET=180, BOOLEAN=181, NAN=182, VARIABLE=183, COMMENT=184, WS=185; public static string[] channelNames = { "DEFAULT_TOKEN_CHANNEL", "HIDDEN" }; @@ -94,8 +94,8 @@ public const int "T__154", "T__155", "T__156", "T__157", "T__158", "T__159", "T__160", "T__161", "T__162", "T__163", "T__164", "T__165", "T__166", "T__167", "T__168", "T__169", "T__170", "T__171", "T__172", "T__173", "T__174", - "NEWLINE", "EXPONENT", "NUMBER", "SPECIALSET", "BOOLEAN", "NAN", "VARIABLE", - "COMMENT", "WS" + "T__175", "T__176", "NEWLINE", "EXPONENT", "NUMBER", "SPECIALSET", "BOOLEAN", + "NAN", "VARIABLE", "COMMENT", "WS" }; @@ -141,8 +141,9 @@ 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('", - "'erf('", "'erfc('", "'erfi('", "'trunc('", "'conjugate('", "'domain('", - "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" + "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'trunc('", "'conjugate('", + "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, + null, "'NaN'" }; private static readonly string[] _SymbolicNames = { null, null, null, null, null, null, null, null, null, null, null, null, @@ -159,8 +160,8 @@ public AngouriMathLexer(ICharStream input, TextWriter output, TextWriter errorOu null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, - null, null, null, null, null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", - "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS" + null, null, null, null, null, null, null, null, null, null, "NEWLINE", + "NUMBER", "SPECIALSET", "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS" }; public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames); @@ -190,7 +191,7 @@ static AngouriMathLexer() { } } private static int[] _serializedATN = { - 4,0,183,1577,6,-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, + 4,0,185,1589,6,-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, @@ -218,104 +219,105 @@ static AngouriMathLexer() { 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, - 7,182,2,183,7,183,1,0,1,0,1,1,1,1,1,2,1,2,1,3,1,3,1,4,1,4,1,5,1,5,1,5, - 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, - 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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, + 1,165,1,166,1,166,1,166,1,166,1,166,1,167,1,167,1,167,1,167,1,167,1,167, + 1,168,1,168,1,168,1,168,1,168,1,168,1,169,1,169,1,169,1,169,1,170,1,170, + 1,170,1,170,1,171,1,171,1,171,1,171,1,171,1,171,1,171,1,172,1,172,1,172, + 1,172,1,172,1,172,1,172,1,172,1,172,1,172,1,172,1,173,1,173,1,173,1,173, + 1,173,1,173,1,173,1,173,1,174,1,174,1,174,1,174,1,174,1,174,1,174,1,174, + 1,174,1,174,1,174,1,175,1,175,1,175,1,175,1,175,1,175,1,175,1,176,1,176, + 1,176,1,176,1,176,1,176,1,176,1,176,1,177,3,177,1443,8,177,1,177,4,177, + 1446,8,177,11,177,12,177,1447,1,177,1,177,1,178,1,178,3,178,1454,8,178, + 1,178,4,178,1457,8,178,11,178,12,178,1458,1,179,4,179,1462,8,179,11,179, + 12,179,1463,1,179,1,179,5,179,1468,8,179,10,179,12,179,1471,9,179,1,179, + 3,179,1474,8,179,1,179,3,179,1477,8,179,1,179,3,179,1480,8,179,1,179,4, + 179,1483,8,179,11,179,12,179,1484,1,179,3,179,1488,8,179,1,179,3,179,1491, + 8,179,1,179,3,179,1494,8,179,1,180,1,180,1,180,1,180,1,180,1,180,1,180, + 1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,180,1,180,3,180, + 1514,8,180,1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181, + 1,181,1,181,1,181,1,181,1,181,1,181,1,181,1,181,3,181,1534,8,181,1,182, + 1,182,1,182,1,182,1,183,4,183,1541,8,183,11,183,12,183,1542,1,183,1,183, + 4,183,1547,8,183,11,183,12,183,1548,3,183,1551,8,183,1,184,1,184,1,184, + 1,184,5,184,1557,8,184,10,184,12,184,1560,9,184,1,184,3,184,1563,8,184, + 1,184,3,184,1566,8,184,1,184,1,184,1,184,1,184,5,184,1572,8,184,10,184, + 12,184,1575,9,184,1,184,1,184,3,184,1579,8,184,1,184,1,184,1,185,4,185, + 1584,8,185,11,185,12,185,1585,1,185,1,185,1,1573,0,186,1,1,3,2,5,3,7,4, 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, @@ -333,404 +335,408 @@ static AngouriMathLexer() { 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, - 175,351,176,353,0,355,177,357,178,359,179,361,180,363,181,365,182,367, - 183,1,0,6,2,0,69,69,101,101,2,0,43,43,45,45,4,0,65,90,97,122,880,1279, - 7936,8191,5,0,48,57,65,90,97,122,880,1279,7936,8191,2,0,10,10,13,13,2, - 0,9,9,32,32,1608,0,1,1,0,0,0,0,3,1,0,0,0,0,5,1,0,0,0,0,7,1,0,0,0,0,9,1, - 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, - 0,0,0,0,259,1,0,0,0,0,261,1,0,0,0,0,263,1,0,0,0,0,265,1,0,0,0,0,267,1, - 0,0,0,0,269,1,0,0,0,0,271,1,0,0,0,0,273,1,0,0,0,0,275,1,0,0,0,0,277,1, - 0,0,0,0,279,1,0,0,0,0,281,1,0,0,0,0,283,1,0,0,0,0,285,1,0,0,0,0,287,1, - 0,0,0,0,289,1,0,0,0,0,291,1,0,0,0,0,293,1,0,0,0,0,295,1,0,0,0,0,297,1, - 0,0,0,0,299,1,0,0,0,0,301,1,0,0,0,0,303,1,0,0,0,0,305,1,0,0,0,0,307,1, - 0,0,0,0,309,1,0,0,0,0,311,1,0,0,0,0,313,1,0,0,0,0,315,1,0,0,0,0,317,1, - 0,0,0,0,319,1,0,0,0,0,321,1,0,0,0,0,323,1,0,0,0,0,325,1,0,0,0,0,327,1, - 0,0,0,0,329,1,0,0,0,0,331,1,0,0,0,0,333,1,0,0,0,0,335,1,0,0,0,0,337,1, - 0,0,0,0,339,1,0,0,0,0,341,1,0,0,0,0,343,1,0,0,0,0,345,1,0,0,0,0,347,1, - 0,0,0,0,349,1,0,0,0,0,351,1,0,0,0,0,355,1,0,0,0,0,357,1,0,0,0,0,359,1, - 0,0,0,0,361,1,0,0,0,0,363,1,0,0,0,0,365,1,0,0,0,0,367,1,0,0,0,1,369,1, - 0,0,0,3,371,1,0,0,0,5,373,1,0,0,0,7,375,1,0,0,0,9,377,1,0,0,0,11,379,1, - 0,0,0,13,383,1,0,0,0,15,385,1,0,0,0,17,387,1,0,0,0,19,391,1,0,0,0,21,401, - 1,0,0,0,23,404,1,0,0,0,25,410,1,0,0,0,27,413,1,0,0,0,29,425,1,0,0,0,31, - 427,1,0,0,0,33,430,1,0,0,0,35,437,1,0,0,0,37,439,1,0,0,0,39,448,1,0,0, - 0,41,450,1,0,0,0,43,458,1,0,0,0,45,460,1,0,0,0,47,463,1,0,0,0,49,466,1, - 0,0,0,51,468,1,0,0,0,53,470,1,0,0,0,55,472,1,0,0,0,57,475,1,0,0,0,59,477, - 1,0,0,0,61,479,1,0,0,0,63,481,1,0,0,0,65,485,1,0,0,0,67,489,1,0,0,0,69, - 491,1,0,0,0,71,495,1,0,0,0,73,498,1,0,0,0,75,506,1,0,0,0,77,509,1,0,0, - 0,79,518,1,0,0,0,81,521,1,0,0,0,83,523,1,0,0,0,85,530,1,0,0,0,87,532,1, - 0,0,0,89,540,1,0,0,0,91,543,1,0,0,0,93,550,1,0,0,0,95,552,1,0,0,0,97,554, - 1,0,0,0,99,556,1,0,0,0,101,560,1,0,0,0,103,564,1,0,0,0,105,567,1,0,0,0, - 107,570,1,0,0,0,109,572,1,0,0,0,111,574,1,0,0,0,113,577,1,0,0,0,115,579, - 1,0,0,0,117,581,1,0,0,0,119,583,1,0,0,0,121,588,1,0,0,0,123,595,1,0,0, - 0,125,601,1,0,0,0,127,606,1,0,0,0,129,612,1,0,0,0,131,618,1,0,0,0,133, - 623,1,0,0,0,135,627,1,0,0,0,137,632,1,0,0,0,139,637,1,0,0,0,141,642,1, - 0,0,0,143,647,1,0,0,0,145,654,1,0,0,0,147,659,1,0,0,0,149,664,1,0,0,0, - 151,671,1,0,0,0,153,676,1,0,0,0,155,684,1,0,0,0,157,692,1,0,0,0,159,700, - 1,0,0,0,161,710,1,0,0,0,163,718,1,0,0,0,165,728,1,0,0,0,167,736,1,0,0, - 0,169,742,1,0,0,0,171,748,1,0,0,0,173,754,1,0,0,0,175,760,1,0,0,0,177, - 768,1,0,0,0,179,774,1,0,0,0,181,782,1,0,0,0,183,788,1,0,0,0,185,796,1, - 0,0,0,187,802,1,0,0,0,189,806,1,0,0,0,191,812,1,0,0,0,193,816,1,0,0,0, - 195,822,1,0,0,0,197,826,1,0,0,0,199,834,1,0,0,0,201,840,1,0,0,0,203,845, - 1,0,0,0,205,851,1,0,0,0,207,856,1,0,0,0,209,864,1,0,0,0,211,870,1,0,0, - 0,213,877,1,0,0,0,215,885,1,0,0,0,217,891,1,0,0,0,219,900,1,0,0,0,221, - 907,1,0,0,0,223,915,1,0,0,0,225,921,1,0,0,0,227,930,1,0,0,0,229,937,1, - 0,0,0,231,945,1,0,0,0,233,951,1,0,0,0,235,960,1,0,0,0,237,967,1,0,0,0, - 239,975,1,0,0,0,241,984,1,0,0,0,243,994,1,0,0,0,245,1001,1,0,0,0,247,1012, - 1,0,0,0,249,1019,1,0,0,0,251,1027,1,0,0,0,253,1034,1,0,0,0,255,1043,1, - 0,0,0,257,1052,1,0,0,0,259,1062,1,0,0,0,261,1070,1,0,0,0,263,1081,1,0, - 0,0,265,1088,1,0,0,0,267,1099,1,0,0,0,269,1106,1,0,0,0,271,1118,1,0,0, - 0,273,1128,1,0,0,0,275,1135,1,0,0,0,277,1146,1,0,0,0,279,1158,1,0,0,0, - 281,1163,1,0,0,0,283,1172,1,0,0,0,285,1180,1,0,0,0,287,1185,1,0,0,0,289, - 1191,1,0,0,0,291,1196,1,0,0,0,293,1201,1,0,0,0,295,1208,1,0,0,0,297,1219, - 1,0,0,0,299,1225,1,0,0,0,301,1235,1,0,0,0,303,1242,1,0,0,0,305,1256,1, - 0,0,0,307,1268,1,0,0,0,309,1275,1,0,0,0,311,1285,1,0,0,0,313,1292,1,0, - 0,0,315,1298,1,0,0,0,317,1307,1,0,0,0,319,1314,1,0,0,0,321,1319,1,0,0, - 0,323,1324,1,0,0,0,325,1332,1,0,0,0,327,1340,1,0,0,0,329,1345,1,0,0,0, - 331,1350,1,0,0,0,333,1360,1,0,0,0,335,1365,1,0,0,0,337,1371,1,0,0,0,339, - 1377,1,0,0,0,341,1384,1,0,0,0,343,1395,1,0,0,0,345,1403,1,0,0,0,347,1414, - 1,0,0,0,349,1421,1,0,0,0,351,1433,1,0,0,0,353,1439,1,0,0,0,355,1481,1, - 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5,99,0,0,848,849,5,104,0,0,849,850,5,40,0,0,850,204,1,0,0,0,851,852,5, - 115,0,0,852,853,5,99,0,0,853,854,5,104,0,0,854,855,5,40,0,0,855,206,1, - 0,0,0,856,857,5,99,0,0,857,858,5,111,0,0,858,859,5,115,0,0,859,860,5,101, - 0,0,860,861,5,99,0,0,861,862,5,104,0,0,862,863,5,40,0,0,863,208,1,0,0, - 0,864,865,5,99,0,0,865,866,5,115,0,0,866,867,5,99,0,0,867,868,5,104,0, - 0,868,869,5,40,0,0,869,210,1,0,0,0,870,871,5,97,0,0,871,872,5,115,0,0, - 872,873,5,105,0,0,873,874,5,110,0,0,874,875,5,104,0,0,875,876,5,40,0,0, - 876,212,1,0,0,0,877,878,5,97,0,0,878,879,5,114,0,0,879,880,5,115,0,0,880, - 881,5,105,0,0,881,882,5,110,0,0,882,883,5,104,0,0,883,884,5,40,0,0,884, - 214,1,0,0,0,885,886,5,97,0,0,886,887,5,114,0,0,887,888,5,115,0,0,888,889, - 5,104,0,0,889,890,5,40,0,0,890,216,1,0,0,0,891,892,5,97,0,0,892,893,5, - 114,0,0,893,894,5,99,0,0,894,895,5,115,0,0,895,896,5,105,0,0,896,897,5, - 110,0,0,897,898,5,104,0,0,898,899,5,40,0,0,899,218,1,0,0,0,900,901,5,97, - 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954,955,5,116,0,0,955,956,5,97,0,0,956,957,5,110,0,0,957,958,5,104,0,0, - 958,959,5,40,0,0,959,234,1,0,0,0,960,961,5,97,0,0,961,962,5,99,0,0,962, - 963,5,111,0,0,963,964,5,116,0,0,964,965,5,104,0,0,965,966,5,40,0,0,966, - 236,1,0,0,0,967,968,5,97,0,0,968,969,5,114,0,0,969,970,5,99,0,0,970,971, - 5,111,0,0,971,972,5,116,0,0,972,973,5,104,0,0,973,974,5,40,0,0,974,238, - 1,0,0,0,975,976,5,97,0,0,976,977,5,99,0,0,977,978,5,111,0,0,978,979,5, - 116,0,0,979,980,5,97,0,0,980,981,5,110,0,0,981,982,5,104,0,0,982,983,5, - 40,0,0,983,240,1,0,0,0,984,985,5,97,0,0,985,986,5,114,0,0,986,987,5,99, - 0,0,987,988,5,111,0,0,988,989,5,116,0,0,989,990,5,97,0,0,990,991,5,110, - 0,0,991,992,5,104,0,0,992,993,5,40,0,0,993,242,1,0,0,0,994,995,5,97,0, - 0,995,996,5,114,0,0,996,997,5,99,0,0,997,998,5,116,0,0,998,999,5,104,0, - 0,999,1000,5,40,0,0,1000,244,1,0,0,0,1001,1002,5,97,0,0,1002,1003,5,114, - 0,0,1003,1004,5,99,0,0,1004,1005,5,99,0,0,1005,1006,5,111,0,0,1006,1007, - 5,116,0,0,1007,1008,5,97,0,0,1008,1009,5,110,0,0,1009,1010,5,104,0,0,1010, - 1011,5,40,0,0,1011,246,1,0,0,0,1012,1013,5,97,0,0,1013,1014,5,115,0,0, - 1014,1015,5,101,0,0,1015,1016,5,99,0,0,1016,1017,5,104,0,0,1017,1018,5, - 40,0,0,1018,248,1,0,0,0,1019,1020,5,97,0,0,1020,1021,5,114,0,0,1021,1022, - 5,115,0,0,1022,1023,5,101,0,0,1023,1024,5,99,0,0,1024,1025,5,104,0,0,1025, - 1026,5,40,0,0,1026,250,1,0,0,0,1027,1028,5,97,0,0,1028,1029,5,114,0,0, - 1029,1030,5,115,0,0,1030,1031,5,99,0,0,1031,1032,5,104,0,0,1032,1033,5, - 40,0,0,1033,252,1,0,0,0,1034,1035,5,97,0,0,1035,1036,5,114,0,0,1036,1037, - 5,99,0,0,1037,1038,5,115,0,0,1038,1039,5,101,0,0,1039,1040,5,99,0,0,1040, - 1041,5,104,0,0,1041,1042,5,40,0,0,1042,254,1,0,0,0,1043,1044,5,97,0,0, - 1044,1045,5,99,0,0,1045,1046,5,111,0,0,1046,1047,5,115,0,0,1047,1048,5, - 101,0,0,1048,1049,5,99,0,0,1049,1050,5,104,0,0,1050,1051,5,40,0,0,1051, - 256,1,0,0,0,1052,1053,5,97,0,0,1053,1054,5,114,0,0,1054,1055,5,99,0,0, - 1055,1056,5,111,0,0,1056,1057,5,115,0,0,1057,1058,5,101,0,0,1058,1059, - 5,99,0,0,1059,1060,5,104,0,0,1060,1061,5,40,0,0,1061,258,1,0,0,0,1062, - 1063,5,97,0,0,1063,1064,5,114,0,0,1064,1065,5,99,0,0,1065,1066,5,115,0, - 0,1066,1067,5,99,0,0,1067,1068,5,104,0,0,1068,1069,5,40,0,0,1069,260,1, - 0,0,0,1070,1071,5,97,0,0,1071,1072,5,114,0,0,1072,1073,5,99,0,0,1073,1074, - 5,99,0,0,1074,1075,5,111,0,0,1075,1076,5,115,0,0,1076,1077,5,101,0,0,1077, - 1078,5,99,0,0,1078,1079,5,104,0,0,1079,1080,5,40,0,0,1080,262,1,0,0,0, - 1081,1082,5,97,0,0,1082,1083,5,99,0,0,1083,1084,5,115,0,0,1084,1085,5, - 99,0,0,1085,1086,5,104,0,0,1086,1087,5,40,0,0,1087,264,1,0,0,0,1088,1089, - 5,102,0,0,1089,1090,5,97,0,0,1090,1091,5,99,0,0,1091,1092,5,116,0,0,1092, - 1093,5,111,0,0,1093,1094,5,114,0,0,1094,1095,5,105,0,0,1095,1096,5,97, - 0,0,1096,1097,5,108,0,0,1097,1098,5,40,0,0,1098,266,1,0,0,0,1099,1100, - 5,103,0,0,1100,1101,5,97,0,0,1101,1102,5,109,0,0,1102,1103,5,109,0,0,1103, - 1104,5,97,0,0,1104,1105,5,40,0,0,1105,268,1,0,0,0,1106,1107,5,100,0,0, - 1107,1108,5,101,0,0,1108,1109,5,114,0,0,1109,1110,5,105,0,0,1110,1111, - 5,118,0,0,1111,1112,5,97,0,0,1112,1113,5,116,0,0,1113,1114,5,105,0,0,1114, - 1115,5,118,0,0,1115,1116,5,101,0,0,1116,1117,5,40,0,0,1117,270,1,0,0,0, - 1118,1119,5,105,0,0,1119,1120,5,110,0,0,1120,1121,5,116,0,0,1121,1122, - 5,101,0,0,1122,1123,5,103,0,0,1123,1124,5,114,0,0,1124,1125,5,97,0,0,1125, - 1126,5,108,0,0,1126,1127,5,40,0,0,1127,272,1,0,0,0,1128,1129,5,108,0,0, - 1129,1130,5,105,0,0,1130,1131,5,109,0,0,1131,1132,5,105,0,0,1132,1133, - 5,116,0,0,1133,1134,5,40,0,0,1134,274,1,0,0,0,1135,1136,5,108,0,0,1136, - 1137,5,105,0,0,1137,1138,5,109,0,0,1138,1139,5,105,0,0,1139,1140,5,116, - 0,0,1140,1141,5,108,0,0,1141,1142,5,101,0,0,1142,1143,5,102,0,0,1143,1144, - 5,116,0,0,1144,1145,5,40,0,0,1145,276,1,0,0,0,1146,1147,5,108,0,0,1147, - 1148,5,105,0,0,1148,1149,5,109,0,0,1149,1150,5,105,0,0,1150,1151,5,116, - 0,0,1151,1152,5,114,0,0,1152,1153,5,105,0,0,1153,1154,5,103,0,0,1154,1155, - 5,104,0,0,1155,1156,5,116,0,0,1156,1157,5,40,0,0,1157,278,1,0,0,0,1158, - 1159,5,115,0,0,1159,1160,5,117,0,0,1160,1161,5,109,0,0,1161,1162,5,40, - 0,0,1162,280,1,0,0,0,1163,1164,5,112,0,0,1164,1165,5,114,0,0,1165,1166, - 5,111,0,0,1166,1167,5,100,0,0,1167,1168,5,117,0,0,1168,1169,5,99,0,0,1169, - 1170,5,116,0,0,1170,1171,5,40,0,0,1171,282,1,0,0,0,1172,1173,5,115,0,0, - 1173,1174,5,105,0,0,1174,1175,5,103,0,0,1175,1176,5,110,0,0,1176,1177, - 5,117,0,0,1177,1178,5,109,0,0,1178,1179,5,40,0,0,1179,284,1,0,0,0,1180, - 1181,5,115,0,0,1181,1182,5,103,0,0,1182,1183,5,110,0,0,1183,1184,5,40, - 0,0,1184,286,1,0,0,0,1185,1186,5,115,0,0,1186,1187,5,105,0,0,1187,1188, - 5,103,0,0,1188,1189,5,110,0,0,1189,1190,5,40,0,0,1190,288,1,0,0,0,1191, - 1192,5,97,0,0,1192,1193,5,98,0,0,1193,1194,5,115,0,0,1194,1195,5,40,0, - 0,1195,290,1,0,0,0,1196,1197,5,112,0,0,1197,1198,5,104,0,0,1198,1199,5, - 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1523,1,0,0,0,1533,1528,1,0,0,0,1534,364,1,0,0,0,1535,1536,5,78,0,0,1536, + 1537,5,97,0,0,1537,1538,5,78,0,0,1538,366,1,0,0,0,1539,1541,7,2,0,0,1540, + 1539,1,0,0,0,1541,1542,1,0,0,0,1542,1540,1,0,0,0,1542,1543,1,0,0,0,1543, + 1550,1,0,0,0,1544,1546,5,95,0,0,1545,1547,7,3,0,0,1546,1545,1,0,0,0,1547, + 1548,1,0,0,0,1548,1546,1,0,0,0,1548,1549,1,0,0,0,1549,1551,1,0,0,0,1550, + 1544,1,0,0,0,1550,1551,1,0,0,0,1551,368,1,0,0,0,1552,1553,5,47,0,0,1553, + 1554,5,47,0,0,1554,1558,1,0,0,0,1555,1557,8,4,0,0,1556,1555,1,0,0,0,1557, + 1560,1,0,0,0,1558,1556,1,0,0,0,1558,1559,1,0,0,0,1559,1565,1,0,0,0,1560, + 1558,1,0,0,0,1561,1563,5,13,0,0,1562,1561,1,0,0,0,1562,1563,1,0,0,0,1563, + 1564,1,0,0,0,1564,1566,5,10,0,0,1565,1562,1,0,0,0,1565,1566,1,0,0,0,1566, + 1579,1,0,0,0,1567,1568,5,47,0,0,1568,1569,5,42,0,0,1569,1573,1,0,0,0,1570, + 1572,9,0,0,0,1571,1570,1,0,0,0,1572,1575,1,0,0,0,1573,1574,1,0,0,0,1573, + 1571,1,0,0,0,1574,1576,1,0,0,0,1575,1573,1,0,0,0,1576,1577,5,42,0,0,1577, + 1579,5,47,0,0,1578,1552,1,0,0,0,1578,1567,1,0,0,0,1579,1580,1,0,0,0,1580, + 1581,6,184,0,0,1581,370,1,0,0,0,1582,1584,7,5,0,0,1583,1582,1,0,0,0,1584, + 1585,1,0,0,0,1585,1583,1,0,0,0,1585,1586,1,0,0,0,1586,1587,1,0,0,0,1587, + 1588,6,185,0,0,1588,372,1,0,0,0,25,0,1442,1447,1453,1458,1463,1469,1473, + 1476,1479,1484,1487,1490,1493,1513,1533,1542,1548,1550,1558,1562,1565, + 1573,1578,1585,1,6,0,0 }; public static readonly ATN _ATN = diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp index 6f40e44ac..8d4a5bbe1 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.interp @@ -169,6 +169,8 @@ null 'erf(' 'erfc(' 'erfi(' +'Ei(' +'li(' 'trunc(' 'conjugate(' 'domain(' @@ -361,6 +363,8 @@ null null null null +null +null NEWLINE NUMBER SPECIALSET @@ -546,6 +550,8 @@ T__171 T__172 T__173 T__174 +T__175 +T__176 NEWLINE EXPONENT NUMBER @@ -564,4 +570,4 @@ mode names: DEFAULT_MODE atn: -[4, 0, 183, 1577, 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, 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, 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1381, 1382, 5, 69, 0, 0, 1382, 1383, 5, 105, 0, 0, 1383, 1384, 5, 40, 0, 0, 1384, 340, 1, 0, 0, 0, 1385, 1386, 5, 108, 0, 0, 1386, 1387, 5, 105, 0, 0, 1387, 1388, 5, 40, 0, 0, 1388, 342, 1, 0, 0, 0, 1389, 1390, 5, 116, 0, 0, 1390, 1391, 5, 114, 0, 0, 1391, 1392, 5, 117, 0, 0, 1392, 1393, 5, 110, 0, 0, 1393, 1394, 5, 99, 0, 0, 1394, 1395, 5, 40, 0, 0, 1395, 344, 1, 0, 0, 0, 1396, 1397, 5, 99, 0, 0, 1397, 1398, 5, 111, 0, 0, 1398, 1399, 5, 110, 0, 0, 1399, 1400, 5, 106, 0, 0, 1400, 1401, 5, 117, 0, 0, 1401, 1402, 5, 103, 0, 0, 1402, 1403, 5, 97, 0, 0, 1403, 1404, 5, 116, 0, 0, 1404, 1405, 5, 101, 0, 0, 1405, 1406, 5, 40, 0, 0, 1406, 346, 1, 0, 0, 0, 1407, 1408, 5, 100, 0, 0, 1408, 1409, 5, 111, 0, 0, 1409, 1410, 5, 109, 0, 0, 1410, 1411, 5, 97, 0, 0, 1411, 1412, 5, 105, 0, 0, 1412, 1413, 5, 110, 0, 0, 1413, 1414, 5, 40, 0, 0, 1414, 348, 1, 0, 0, 0, 1415, 1416, 5, 112, 0, 0, 1416, 1417, 5, 105, 0, 0, 1417, 1418, 5, 101, 0, 0, 1418, 1419, 5, 99, 0, 0, 1419, 1420, 5, 101, 0, 0, 1420, 1421, 5, 119, 0, 0, 1421, 1422, 5, 105, 0, 0, 1422, 1423, 5, 115, 0, 0, 1423, 1424, 5, 101, 0, 0, 1424, 1425, 5, 40, 0, 0, 1425, 350, 1, 0, 0, 0, 1426, 1427, 5, 97, 0, 0, 1427, 1428, 5, 112, 0, 0, 1428, 1429, 5, 112, 0, 0, 1429, 1430, 5, 108, 0, 0, 1430, 1431, 5, 121, 0, 0, 1431, 1432, 5, 40, 0, 0, 1432, 352, 1, 0, 0, 0, 1433, 1434, 5, 108, 0, 0, 1434, 1435, 5, 97, 0, 0, 1435, 1436, 5, 109, 0, 0, 1436, 1437, 5, 98, 0, 0, 1437, 1438, 5, 100, 0, 0, 1438, 1439, 5, 97, 0, 0, 1439, 1440, 5, 40, 0, 0, 1440, 354, 1, 0, 0, 0, 1441, 1443, 5, 13, 0, 0, 1442, 1441, 1, 0, 0, 0, 1442, 1443, 1, 0, 0, 0, 1443, 1444, 1, 0, 0, 0, 1444, 1446, 5, 10, 0, 0, 1445, 1442, 1, 0, 0, 0, 1446, 1447, 1, 0, 0, 0, 1447, 1445, 1, 0, 0, 0, 1447, 1448, 1, 0, 0, 0, 1448, 1449, 1, 0, 0, 0, 1449, 1450, 6, 177, 0, 0, 1450, 356, 1, 0, 0, 0, 1451, 1453, 7, 0, 0, 0, 1452, 1454, 7, 1, 0, 0, 1453, 1452, 1, 0, 0, 0, 1453, 1454, 1, 0, 0, 0, 1454, 1456, 1, 0, 0, 0, 1455, 1457, 2, 48, 57, 0, 1456, 1455, 1, 0, 0, 0, 1457, 1458, 1, 0, 0, 0, 1458, 1456, 1, 0, 0, 0, 1458, 1459, 1, 0, 0, 0, 1459, 358, 1, 0, 0, 0, 1460, 1462, 2, 48, 57, 0, 1461, 1460, 1, 0, 0, 0, 1462, 1463, 1, 0, 0, 0, 1463, 1461, 1, 0, 0, 0, 1463, 1464, 1, 0, 0, 0, 1464, 1465, 1, 0, 0, 0, 1465, 1469, 5, 46, 0, 0, 1466, 1468, 2, 48, 57, 0, 1467, 1466, 1, 0, 0, 0, 1468, 1471, 1, 0, 0, 0, 1469, 1467, 1, 0, 0, 0, 1469, 1470, 1, 0, 0, 0, 1470, 1473, 1, 0, 0, 0, 1471, 1469, 1, 0, 0, 0, 1472, 1474, 3, 357, 178, 0, 1473, 1472, 1, 0, 0, 0, 1473, 1474, 1, 0, 0, 0, 1474, 1476, 1, 0, 0, 0, 1475, 1477, 5, 105, 0, 0, 1476, 1475, 1, 0, 0, 0, 1476, 1477, 1, 0, 0, 0, 1477, 1494, 1, 0, 0, 0, 1478, 1480, 5, 46, 0, 0, 1479, 1478, 1, 0, 0, 0, 1479, 1480, 1, 0, 0, 0, 1480, 1482, 1, 0, 0, 0, 1481, 1483, 2, 48, 57, 0, 1482, 1481, 1, 0, 0, 0, 1483, 1484, 1, 0, 0, 0, 1484, 1482, 1, 0, 0, 0, 1484, 1485, 1, 0, 0, 0, 1485, 1487, 1, 0, 0, 0, 1486, 1488, 3, 357, 178, 0, 1487, 1486, 1, 0, 0, 0, 1487, 1488, 1, 0, 0, 0, 1488, 1490, 1, 0, 0, 0, 1489, 1491, 5, 105, 0, 0, 1490, 1489, 1, 0, 0, 0, 1490, 1491, 1, 0, 0, 0, 1491, 1494, 1, 0, 0, 0, 1492, 1494, 5, 105, 0, 0, 1493, 1461, 1, 0, 0, 0, 1493, 1479, 1, 0, 0, 0, 1493, 1492, 1, 0, 0, 0, 1494, 360, 1, 0, 0, 0, 1495, 1496, 5, 67, 0, 0, 1496, 1514, 5, 67, 0, 0, 1497, 1498, 5, 82, 0, 0, 1498, 1514, 5, 82, 0, 0, 1499, 1500, 5, 81, 0, 0, 1500, 1514, 5, 81, 0, 0, 1501, 1502, 5, 90, 0, 0, 1502, 1514, 5, 90, 0, 0, 1503, 1504, 5, 66, 0, 0, 1504, 1514, 5, 66, 0, 0, 1505, 1506, 5, 90, 0, 0, 1506, 1507, 5, 90, 0, 0, 1507, 1514, 5, 42, 0, 0, 1508, 1509, 5, 90, 0, 0, 1509, 1510, 5, 90, 0, 0, 1510, 1514, 5, 43, 0, 0, 1511, 1512, 5, 80, 0, 0, 1512, 1514, 5, 80, 0, 0, 1513, 1495, 1, 0, 0, 0, 1513, 1497, 1, 0, 0, 0, 1513, 1499, 1, 0, 0, 0, 1513, 1501, 1, 0, 0, 0, 1513, 1503, 1, 0, 0, 0, 1513, 1505, 1, 0, 0, 0, 1513, 1508, 1, 0, 0, 0, 1513, 1511, 1, 0, 0, 0, 1514, 362, 1, 0, 0, 0, 1515, 1516, 5, 116, 0, 0, 1516, 1517, 5, 114, 0, 0, 1517, 1518, 5, 117, 0, 0, 1518, 1534, 5, 101, 0, 0, 1519, 1520, 5, 84, 0, 0, 1520, 1521, 5, 114, 0, 0, 1521, 1522, 5, 117, 0, 0, 1522, 1534, 5, 101, 0, 0, 1523, 1524, 5, 102, 0, 0, 1524, 1525, 5, 97, 0, 0, 1525, 1526, 5, 108, 0, 0, 1526, 1527, 5, 115, 0, 0, 1527, 1534, 5, 101, 0, 0, 1528, 1529, 5, 70, 0, 0, 1529, 1530, 5, 97, 0, 0, 1530, 1531, 5, 108, 0, 0, 1531, 1532, 5, 115, 0, 0, 1532, 1534, 5, 101, 0, 0, 1533, 1515, 1, 0, 0, 0, 1533, 1519, 1, 0, 0, 0, 1533, 1523, 1, 0, 0, 0, 1533, 1528, 1, 0, 0, 0, 1534, 364, 1, 0, 0, 0, 1535, 1536, 5, 78, 0, 0, 1536, 1537, 5, 97, 0, 0, 1537, 1538, 5, 78, 0, 0, 1538, 366, 1, 0, 0, 0, 1539, 1541, 7, 2, 0, 0, 1540, 1539, 1, 0, 0, 0, 1541, 1542, 1, 0, 0, 0, 1542, 1540, 1, 0, 0, 0, 1542, 1543, 1, 0, 0, 0, 1543, 1550, 1, 0, 0, 0, 1544, 1546, 5, 95, 0, 0, 1545, 1547, 7, 3, 0, 0, 1546, 1545, 1, 0, 0, 0, 1547, 1548, 1, 0, 0, 0, 1548, 1546, 1, 0, 0, 0, 1548, 1549, 1, 0, 0, 0, 1549, 1551, 1, 0, 0, 0, 1550, 1544, 1, 0, 0, 0, 1550, 1551, 1, 0, 0, 0, 1551, 368, 1, 0, 0, 0, 1552, 1553, 5, 47, 0, 0, 1553, 1554, 5, 47, 0, 0, 1554, 1558, 1, 0, 0, 0, 1555, 1557, 8, 4, 0, 0, 1556, 1555, 1, 0, 0, 0, 1557, 1560, 1, 0, 0, 0, 1558, 1556, 1, 0, 0, 0, 1558, 1559, 1, 0, 0, 0, 1559, 1565, 1, 0, 0, 0, 1560, 1558, 1, 0, 0, 0, 1561, 1563, 5, 13, 0, 0, 1562, 1561, 1, 0, 0, 0, 1562, 1563, 1, 0, 0, 0, 1563, 1564, 1, 0, 0, 0, 1564, 1566, 5, 10, 0, 0, 1565, 1562, 1, 0, 0, 0, 1565, 1566, 1, 0, 0, 0, 1566, 1579, 1, 0, 0, 0, 1567, 1568, 5, 47, 0, 0, 1568, 1569, 5, 42, 0, 0, 1569, 1573, 1, 0, 0, 0, 1570, 1572, 9, 0, 0, 0, 1571, 1570, 1, 0, 0, 0, 1572, 1575, 1, 0, 0, 0, 1573, 1574, 1, 0, 0, 0, 1573, 1571, 1, 0, 0, 0, 1574, 1576, 1, 0, 0, 0, 1575, 1573, 1, 0, 0, 0, 1576, 1577, 5, 42, 0, 0, 1577, 1579, 5, 47, 0, 0, 1578, 1552, 1, 0, 0, 0, 1578, 1567, 1, 0, 0, 0, 1579, 1580, 1, 0, 0, 0, 1580, 1581, 6, 184, 0, 0, 1581, 370, 1, 0, 0, 0, 1582, 1584, 7, 5, 0, 0, 1583, 1582, 1, 0, 0, 0, 1584, 1585, 1, 0, 0, 0, 1585, 1583, 1, 0, 0, 0, 1585, 1586, 1, 0, 0, 0, 1586, 1587, 1, 0, 0, 0, 1587, 1588, 6, 185, 0, 0, 1588, 372, 1, 0, 0, 0, 25, 0, 1442, 1447, 1453, 1458, 1463, 1469, 1473, 1476, 1479, 1484, 1487, 1490, 1493, 1513, 1533, 1542, 1548, 1550, 1558, 1562, 1565, 1573, 1578, 1585, 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 0604e95bb..069f48578 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathLexer.tokens @@ -173,14 +173,16 @@ T__171=172 T__172=173 T__173=174 T__174=175 -NEWLINE=176 -NUMBER=177 -SPECIALSET=178 -BOOLEAN=179 -NAN=180 -VARIABLE=181 -COMMENT=182 -WS=183 +T__175=176 +T__176=177 +NEWLINE=178 +NUMBER=179 +SPECIALSET=180 +BOOLEAN=181 +NAN=182 +VARIABLE=183 +COMMENT=184 +WS=185 '!'=1 '^'=2 '-'=3 @@ -350,10 +352,12 @@ WS=183 'erf('=167 'erfc('=168 'erfi('=169 -'trunc('=170 -'conjugate('=171 -'domain('=172 -'piecewise('=173 -'apply('=174 -'lambda('=175 -'NaN'=180 +'Ei('=170 +'li('=171 +'trunc('=172 +'conjugate('=173 +'domain('=174 +'piecewise('=175 +'apply('=176 +'lambda('=177 +'NaN'=182 diff --git a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs index 8dedd987a..c3205965e 100644 --- a/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs +++ b/Sources/AngouriMath/Core/Antlr/AngouriMathParser.cs @@ -72,8 +72,8 @@ public const int T__155=156, T__156=157, T__157=158, T__158=159, T__159=160, T__160=161, T__161=162, T__162=163, T__163=164, T__164=165, T__165=166, T__166=167, T__167=168, T__168=169, T__169=170, T__170=171, T__171=172, T__172=173, - T__173=174, T__174=175, NEWLINE=176, NUMBER=177, SPECIALSET=178, BOOLEAN=179, - NAN=180, VARIABLE=181, COMMENT=182, WS=183; + T__173=174, T__174=175, T__175=176, T__176=177, NEWLINE=178, NUMBER=179, + SPECIALSET=180, BOOLEAN=181, NAN=182, VARIABLE=183, COMMENT=184, WS=185; 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, @@ -120,8 +120,9 @@ public const int "'powerset('", "'union('", "'intersection('", "'complement('", "'image('", "'preimage('", "'floor('", "'ceil('", "'ceiling('", "'round('", "'min('", "'max('", "'argmax('", "'argmin('", "'gcd('", "'lcm('", "'binomial('", - "'erf('", "'erfc('", "'erfi('", "'trunc('", "'conjugate('", "'domain('", - "'piecewise('", "'apply('", "'lambda('", null, null, null, null, "'NaN'" + "'erf('", "'erfc('", "'erfi('", "'Ei('", "'li('", "'trunc('", "'conjugate('", + "'domain('", "'piecewise('", "'apply('", "'lambda('", null, null, null, + null, "'NaN'" }; private static readonly string[] _SymbolicNames = { null, null, null, null, null, null, null, null, null, null, null, null, @@ -138,8 +139,8 @@ public const int null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, - null, null, null, null, null, null, null, null, "NEWLINE", "NUMBER", "SPECIALSET", - "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS" + null, null, null, null, null, null, null, null, null, null, "NEWLINE", + "NUMBER", "SPECIALSET", "BOOLEAN", "NAN", "VARIABLE", "COMMENT", "WS" }; public static readonly IVocabulary DefaultVocabulary = new Vocabulary(_LiteralNames, _SymbolicNames); @@ -740,6 +741,8 @@ public Mult_expressionContext mult_expression() { case T__172: case T__173: case T__174: + case T__175: + case T__176: case NUMBER: case SPECIALSET: case BOOLEAN: @@ -990,6 +993,8 @@ public Sum_expressionContext sum_expression() { case T__172: case T__173: case T__174: + case T__175: + case T__176: case NUMBER: case SPECIALSET: case BOOLEAN: @@ -2162,6 +2167,8 @@ public ExpressionContext expression() { case T__172: case T__173: case T__174: + case T__175: + case T__176: case NUMBER: case SPECIALSET: case BOOLEAN: @@ -2527,7 +2534,7 @@ 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)) & 17732923532771327L) != 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)) & 70931694131085311L) != 0)) { { State = 383; _localctx.e = expression(); @@ -2603,7 +2610,7 @@ 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)) & 17732923532771327L) != 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)) & 70931694131085311L) != 0)) { { State = 401; ErrorHandler.Sync(this); @@ -2740,6 +2747,8 @@ public Set_itemsContext set_items() { case T__172: case T__173: case T__174: + case T__175: + case T__176: case NUMBER: case SPECIALSET: case BOOLEAN: @@ -2912,6 +2921,8 @@ public Set_itemsContext set_items() { case T__172: case T__173: case T__174: + case T__175: + case T__176: case NUMBER: case SPECIALSET: case BOOLEAN: @@ -3131,7 +3142,7 @@ public AtomContext atom() { AtomContext _localctx = new AtomContext(Context, State); EnterRule(_localctx, 48, RULE_atom); try { - State = 1078; + State = 1088; ErrorHandler.Sync(this); switch ( Interpreter.AdaptivePredict(TokenStream,41,Context) ) { case 1: @@ -4678,7 +4689,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1050; Match(T__30); - _localctx.value = NotImplementedFunction("trunc", "rounding functions"); + Assert("Ei", 1, _localctx.args.list.Count); _localctx.value = MathS.Ei(_localctx.args.list[0]); } break; case 130: @@ -4690,7 +4701,7 @@ public AtomContext atom() { _localctx.args = function_arguments(); State = 1055; Match(T__30); - _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function"); + Assert("li", 1, _localctx.args.list.Count); _localctx.value = MathS.Li(_localctx.args.list[0]); } break; case 131: @@ -4701,6 +4712,30 @@ public AtomContext atom() { State = 1059; _localctx.args = function_arguments(); State = 1060; + Match(T__30); + _localctx.value = NotImplementedFunction("trunc", "rounding functions"); + } + break; + case 132: + EnterOuterAlt(_localctx, 132); + { + State = 1063; + Match(T__172); + State = 1064; + _localctx.args = function_arguments(); + State = 1065; + Match(T__30); + _localctx.value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function"); + } + break; + case 133: + EnterOuterAlt(_localctx, 133); + { + State = 1068; + Match(T__173); + State = 1069; + _localctx.args = function_arguments(); + State = 1070; Match(T__30); Assert("domain", 2, _localctx.args.list.Count); @@ -4727,14 +4762,14 @@ public AtomContext atom() { } break; - case 132: - EnterOuterAlt(_localctx, 132); + case 134: + EnterOuterAlt(_localctx, 134); { - State = 1063; - Match(T__172); - State = 1064; + State = 1073; + Match(T__174); + State = 1074; _localctx.args = function_arguments(); - State = 1065; + State = 1075; Match(T__30); var cases = new List(); @@ -4747,14 +4782,14 @@ public AtomContext atom() { } break; - case 133: - EnterOuterAlt(_localctx, 133); + case 135: + EnterOuterAlt(_localctx, 135); { - State = 1068; - Match(T__173); - State = 1069; + State = 1078; + Match(T__175); + State = 1079; _localctx.args = function_arguments(); - State = 1070; + State = 1080; Match(T__30); if (_localctx.args.list.Count < 2) @@ -4763,14 +4798,14 @@ public AtomContext atom() { } break; - case 134: - EnterOuterAlt(_localctx, 134); + case 136: + EnterOuterAlt(_localctx, 136); { - State = 1073; - Match(T__174); - State = 1074; + State = 1083; + Match(T__176); + State = 1084; _localctx.args = function_arguments(); - State = 1075; + State = 1085; Match(T__30); if (_localctx.args.list.Count < 2) @@ -4833,9 +4868,9 @@ public StatementContext statement() { try { EnterOuterAlt(_localctx, 1); { - State = 1080; + State = 1090; _localctx._expression = expression(); - State = 1081; + State = 1091; Match(Eof); Result = _localctx._expression.value; } @@ -4852,7 +4887,7 @@ public StatementContext statement() { } private static int[] _serializedATN = { - 4,1,183,1085,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2, + 4,1,185,1095,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,2,6,7,6,2, 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, @@ -4928,313 +4963,317 @@ public StatementContext statement() { 1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24, 1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24, 1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24, - 1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,1,24,3,24,1079,8,24,1,25, - 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, - 1249,0,59,1,0,0,0,2,77,1,0,0,0,4,79,1,0,0,0,6,109,1,0,0,0,8,111,1,0,0, - 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, - 0,48,1078,1,0,0,0,50,1080,1,0,0,0,52,53,3,48,24,0,53,54,5,1,0,0,54,55, - 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,-1,0,273,282,1,0,0,0,274,275,5,32,0,0,275,276,3, - 34,17,0,276,277,6,10,-1,0,277,282,1,0,0,0,278,279,3,18,9,0,279,280,6,10, - -1,0,280,282,1,0,0,0,281,266,1,0,0,0,281,270,1,0,0,0,281,274,1,0,0,0,281, - 278,1,0,0,0,282,21,1,0,0,0,283,284,3,20,10,0,284,295,6,11,-1,0,285,286, - 5,33,0,0,286,287,3,20,10,0,287,288,6,11,-1,0,288,294,1,0,0,0,289,290,5, - 34,0,0,290,291,3,20,10,0,291,292,6,11,-1,0,292,294,1,0,0,0,293,285,1,0, - 0,0,293,289,1,0,0,0,294,297,1,0,0,0,295,293,1,0,0,0,295,296,1,0,0,0,296, - 23,1,0,0,0,297,295,1,0,0,0,298,299,3,22,11,0,299,306,6,12,-1,0,300,301, - 5,35,0,0,301,302,3,22,11,0,302,303,6,12,-1,0,303,305,1,0,0,0,304,300,1, - 0,0,0,305,308,1,0,0,0,306,304,1,0,0,0,306,307,1,0,0,0,307,25,1,0,0,0,308, - 306,1,0,0,0,309,310,3,24,12,0,310,317,6,13,-1,0,311,312,5,36,0,0,312,313, - 3,24,12,0,313,314,6,13,-1,0,314,316,1,0,0,0,315,311,1,0,0,0,316,319,1, - 0,0,0,317,315,1,0,0,0,317,318,1,0,0,0,318,27,1,0,0,0,319,317,1,0,0,0,320, - 321,3,26,13,0,321,332,6,14,-1,0,322,323,5,37,0,0,323,324,3,26,13,0,324, - 325,6,14,-1,0,325,331,1,0,0,0,326,327,5,38,0,0,327,328,3,26,13,0,328,329, - 6,14,-1,0,329,331,1,0,0,0,330,322,1,0,0,0,330,326,1,0,0,0,331,334,1,0, - 0,0,332,330,1,0,0,0,332,333,1,0,0,0,333,29,1,0,0,0,334,332,1,0,0,0,335, - 336,3,28,14,0,336,341,6,15,-1,0,337,338,5,39,0,0,338,339,3,30,15,0,339, - 340,6,15,-1,0,340,342,1,0,0,0,341,337,1,0,0,0,341,342,1,0,0,0,342,31,1, - 0,0,0,343,344,3,30,15,0,344,349,6,16,-1,0,345,346,5,40,0,0,346,347,3,32, - 16,0,347,348,6,16,-1,0,348,350,1,0,0,0,349,345,1,0,0,0,349,350,1,0,0,0, - 350,355,1,0,0,0,351,352,3,34,17,0,352,353,6,16,-1,0,353,355,1,0,0,0,354, - 343,1,0,0,0,354,351,1,0,0,0,355,33,1,0,0,0,356,357,3,36,18,0,357,358,3, - 38,19,0,358,359,5,41,0,0,359,360,3,32,16,0,360,361,6,17,-1,0,361,35,1, - 0,0,0,362,363,7,1,0,0,363,369,6,18,-1,0,364,365,7,2,0,0,365,369,6,18,-1, - 0,366,367,7,3,0,0,367,369,6,18,-1,0,368,362,1,0,0,0,368,364,1,0,0,0,368, - 366,1,0,0,0,369,37,1,0,0,0,370,371,3,16,8,0,371,378,6,19,-1,0,372,373, - 5,48,0,0,373,374,3,16,8,0,374,375,6,19,-1,0,375,377,1,0,0,0,376,372,1, - 0,0,0,377,380,1,0,0,0,378,376,1,0,0,0,378,379,1,0,0,0,379,381,1,0,0,0, - 380,378,1,0,0,0,381,382,6,19,-1,0,382,39,1,0,0,0,383,384,3,32,16,0,384, - 391,6,20,-1,0,385,386,5,48,0,0,386,387,3,32,16,0,387,388,6,20,-1,0,388, - 390,1,0,0,0,389,385,1,0,0,0,390,393,1,0,0,0,391,389,1,0,0,0,391,392,1, - 0,0,0,392,395,1,0,0,0,393,391,1,0,0,0,394,383,1,0,0,0,394,395,1,0,0,0, - 395,41,1,0,0,0,396,397,3,32,16,0,397,398,6,21,-1,0,398,402,1,0,0,0,399, - 400,7,0,0,0,400,402,6,21,-1,0,401,396,1,0,0,0,401,399,1,0,0,0,402,413, - 1,0,0,0,403,409,5,48,0,0,404,405,3,32,16,0,405,406,6,21,-1,0,406,410,1, - 0,0,0,407,408,7,0,0,0,408,410,6,21,-1,0,409,404,1,0,0,0,409,407,1,0,0, - 0,410,412,1,0,0,0,411,403,1,0,0,0,412,415,1,0,0,0,413,411,1,0,0,0,413, - 414,1,0,0,0,414,417,1,0,0,0,415,413,1,0,0,0,416,401,1,0,0,0,416,417,1, - 0,0,0,417,43,1,0,0,0,418,419,3,32,16,0,419,420,6,22,-1,0,420,421,5,49, - 0,0,421,422,3,32,16,0,422,423,6,22,-1,0,423,45,1,0,0,0,424,425,3,32,16, - 0,425,426,6,23,-1,0,426,427,5,41,0,0,427,428,3,32,16,0,428,429,6,23,-1, - 0,429,47,1,0,0,0,430,431,5,50,0,0,431,1079,6,24,-1,0,432,433,5,51,0,0, - 433,1079,6,24,-1,0,434,435,5,180,0,0,435,1079,6,24,-1,0,436,437,5,177, - 0,0,437,1079,6,24,-1,0,438,439,5,179,0,0,439,1079,6,24,-1,0,440,441,5, - 178,0,0,441,1079,6,24,-1,0,442,443,5,181,0,0,443,1079,6,24,-1,0,444,445, - 5,52,0,0,445,446,3,32,16,0,446,447,5,53,0,0,447,448,6,24,-1,0,448,1079, - 1,0,0,0,449,450,5,54,0,0,450,451,3,48,24,0,451,452,6,24,-1,0,452,1079, - 1,0,0,0,453,454,5,55,0,0,454,455,3,40,20,0,455,456,5,56,0,0,456,457,6, - 24,-1,0,457,1079,1,0,0,0,458,459,5,55,0,0,459,460,3,40,20,0,460,461,5, - 57,0,0,461,462,6,24,-1,0,462,1079,1,0,0,0,463,464,5,30,0,0,464,465,3,44, - 22,0,465,466,5,31,0,0,466,467,6,24,-1,0,467,1079,1,0,0,0,468,469,5,55, - 0,0,469,470,3,44,22,0,470,471,5,31,0,0,471,472,6,24,-1,0,472,1079,1,0, - 0,0,473,474,5,55,0,0,474,475,3,44,22,0,475,476,5,57,0,0,476,477,6,24,-1, - 0,477,1079,1,0,0,0,478,479,5,30,0,0,479,480,3,44,22,0,480,481,5,57,0,0, - 481,482,6,24,-1,0,482,1079,1,0,0,0,483,484,5,30,0,0,484,485,3,32,16,0, - 485,486,5,31,0,0,486,487,6,24,-1,0,487,1079,1,0,0,0,488,489,5,58,0,0,489, - 490,3,46,23,0,490,491,5,59,0,0,491,492,6,24,-1,0,492,1079,1,0,0,0,493, - 494,5,58,0,0,494,495,3,42,21,0,495,496,5,59,0,0,496,497,6,24,-1,0,497, - 1079,1,0,0,0,498,499,5,60,0,0,499,500,3,40,20,0,500,501,5,31,0,0,501,502, - 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0,939,940,3,40,20,0,940,941,5,31,0,0,941,942,6,24,-1,0,942,1089,1,0,0, + 0,943,944,5,149,0,0,944,945,3,40,20,0,945,946,5,31,0,0,946,947,6,24,-1, + 0,947,1089,1,0,0,0,948,949,5,150,0,0,949,950,3,40,20,0,950,951,5,31,0, + 0,951,952,6,24,-1,0,952,1089,1,0,0,0,953,954,5,151,0,0,954,955,3,40,20, + 0,955,956,5,31,0,0,956,957,6,24,-1,0,957,1089,1,0,0,0,958,959,5,152,0, + 0,959,960,3,40,20,0,960,961,5,31,0,0,961,962,6,24,-1,0,962,1089,1,0,0, + 0,963,964,5,153,0,0,964,965,3,40,20,0,965,966,5,31,0,0,966,967,6,24,-1, + 0,967,1089,1,0,0,0,968,969,5,154,0,0,969,970,3,40,20,0,970,971,5,31,0, + 0,971,972,6,24,-1,0,972,1089,1,0,0,0,973,974,5,155,0,0,974,975,3,40,20, + 0,975,976,5,31,0,0,976,977,6,24,-1,0,977,1089,1,0,0,0,978,979,5,156,0, + 0,979,980,3,40,20,0,980,981,5,31,0,0,981,982,6,24,-1,0,982,1089,1,0,0, + 0,983,984,5,157,0,0,984,985,3,40,20,0,985,986,5,31,0,0,986,987,6,24,-1, + 0,987,1089,1,0,0,0,988,989,5,158,0,0,989,990,3,40,20,0,990,991,5,31,0, + 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1040,3,40,20,0,1040,1041,5,31,0,0,1041,1042,6,24,-1,0,1042,1089,1,0,0, + 0,1043,1044,5,169,0,0,1044,1045,3,40,20,0,1045,1046,5,31,0,0,1046,1047, + 6,24,-1,0,1047,1089,1,0,0,0,1048,1049,5,170,0,0,1049,1050,3,40,20,0,1050, + 1051,5,31,0,0,1051,1052,6,24,-1,0,1052,1089,1,0,0,0,1053,1054,5,171,0, + 0,1054,1055,3,40,20,0,1055,1056,5,31,0,0,1056,1057,6,24,-1,0,1057,1089, + 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,-1,0,1062,1089,1,0,0,0,1063,1064,5,173,0,0,1064,1065,3,40,20, + 0,1065,1066,5,31,0,0,1066,1067,6,24,-1,0,1067,1089,1,0,0,0,1068,1069,5, + 174,0,0,1069,1070,3,40,20,0,1070,1071,5,31,0,0,1071,1072,6,24,-1,0,1072, + 1089,1,0,0,0,1073,1074,5,175,0,0,1074,1075,3,40,20,0,1075,1076,5,31,0, + 0,1076,1077,6,24,-1,0,1077,1089,1,0,0,0,1078,1079,5,176,0,0,1079,1080, + 3,40,20,0,1080,1081,5,31,0,0,1081,1082,6,24,-1,0,1082,1089,1,0,0,0,1083, + 1084,5,177,0,0,1084,1085,3,40,20,0,1085,1086,5,31,0,0,1086,1087,6,24,-1, + 0,1087,1089,1,0,0,0,1088,430,1,0,0,0,1088,432,1,0,0,0,1088,434,1,0,0,0, + 1088,436,1,0,0,0,1088,438,1,0,0,0,1088,440,1,0,0,0,1088,442,1,0,0,0,1088, + 444,1,0,0,0,1088,449,1,0,0,0,1088,453,1,0,0,0,1088,458,1,0,0,0,1088,463, + 1,0,0,0,1088,468,1,0,0,0,1088,473,1,0,0,0,1088,478,1,0,0,0,1088,483,1, + 0,0,0,1088,488,1,0,0,0,1088,493,1,0,0,0,1088,498,1,0,0,0,1088,503,1,0, + 0,0,1088,508,1,0,0,0,1088,513,1,0,0,0,1088,518,1,0,0,0,1088,523,1,0,0, + 0,1088,528,1,0,0,0,1088,533,1,0,0,0,1088,538,1,0,0,0,1088,543,1,0,0,0, + 1088,548,1,0,0,0,1088,553,1,0,0,0,1088,558,1,0,0,0,1088,563,1,0,0,0,1088, + 568,1,0,0,0,1088,573,1,0,0,0,1088,578,1,0,0,0,1088,583,1,0,0,0,1088,588, + 1,0,0,0,1088,593,1,0,0,0,1088,598,1,0,0,0,1088,603,1,0,0,0,1088,608,1, + 0,0,0,1088,613,1,0,0,0,1088,618,1,0,0,0,1088,623,1,0,0,0,1088,628,1,0, + 0,0,1088,633,1,0,0,0,1088,638,1,0,0,0,1088,643,1,0,0,0,1088,648,1,0,0, + 0,1088,653,1,0,0,0,1088,658,1,0,0,0,1088,663,1,0,0,0,1088,668,1,0,0,0, + 1088,673,1,0,0,0,1088,678,1,0,0,0,1088,683,1,0,0,0,1088,688,1,0,0,0,1088, + 693,1,0,0,0,1088,698,1,0,0,0,1088,703,1,0,0,0,1088,708,1,0,0,0,1088,713, + 1,0,0,0,1088,718,1,0,0,0,1088,723,1,0,0,0,1088,728,1,0,0,0,1088,733,1, + 0,0,0,1088,738,1,0,0,0,1088,743,1,0,0,0,1088,748,1,0,0,0,1088,753,1,0, + 0,0,1088,758,1,0,0,0,1088,763,1,0,0,0,1088,768,1,0,0,0,1088,773,1,0,0, + 0,1088,778,1,0,0,0,1088,783,1,0,0,0,1088,788,1,0,0,0,1088,793,1,0,0,0, + 1088,798,1,0,0,0,1088,803,1,0,0,0,1088,808,1,0,0,0,1088,813,1,0,0,0,1088, + 818,1,0,0,0,1088,823,1,0,0,0,1088,828,1,0,0,0,1088,833,1,0,0,0,1088,838, + 1,0,0,0,1088,843,1,0,0,0,1088,848,1,0,0,0,1088,853,1,0,0,0,1088,858,1, + 0,0,0,1088,863,1,0,0,0,1088,868,1,0,0,0,1088,873,1,0,0,0,1088,878,1,0, + 0,0,1088,883,1,0,0,0,1088,888,1,0,0,0,1088,893,1,0,0,0,1088,898,1,0,0, + 0,1088,903,1,0,0,0,1088,908,1,0,0,0,1088,913,1,0,0,0,1088,918,1,0,0,0, + 1088,923,1,0,0,0,1088,928,1,0,0,0,1088,933,1,0,0,0,1088,938,1,0,0,0,1088, + 943,1,0,0,0,1088,948,1,0,0,0,1088,953,1,0,0,0,1088,958,1,0,0,0,1088,963, + 1,0,0,0,1088,968,1,0,0,0,1088,973,1,0,0,0,1088,978,1,0,0,0,1088,983,1, + 0,0,0,1088,988,1,0,0,0,1088,993,1,0,0,0,1088,998,1,0,0,0,1088,1003,1,0, + 0,0,1088,1008,1,0,0,0,1088,1013,1,0,0,0,1088,1018,1,0,0,0,1088,1023,1, + 0,0,0,1088,1028,1,0,0,0,1088,1033,1,0,0,0,1088,1038,1,0,0,0,1088,1043, + 1,0,0,0,1088,1048,1,0,0,0,1088,1053,1,0,0,0,1088,1058,1,0,0,0,1088,1063, + 1,0,0,0,1088,1068,1,0,0,0,1088,1073,1,0,0,0,1088,1078,1,0,0,0,1088,1083, + 1,0,0,0,1089,49,1,0,0,0,1090,1091,3,32,16,0,1091,1092,5,0,0,1,1092,1093, + 6,25,-1,0,1093,51,1,0,0,0,42,59,67,75,77,84,94,104,109,119,129,131,144, + 150,152,167,169,190,192,225,227,246,253,262,281,293,295,306,317,330,332, + 341,349,354,368,378,391,394,401,409,413,416,1088 }; public static readonly ATN _ATN = diff --git a/Sources/AngouriMath/Core/Domains.Classes.cs b/Sources/AngouriMath/Core/Domains.Classes.cs index cd5ff05b8..0a4fe22f4 100644 --- a/Sources/AngouriMath/Core/Domains.Classes.cs +++ b/Sources/AngouriMath/Core/Domains.Classes.cs @@ -334,6 +334,22 @@ partial record Erfif internal override Domain DefaultCodomain => Domain.Complex; } + partial record Eif + { + /// + public override Domain Codomain { get; protected init; } = Domain.Complex; + /// + internal override Domain DefaultCodomain => Domain.Complex; + } + + partial record Lif + { + /// + public override Domain Codomain { get; protected init; } = Domain.Complex; + /// + internal override Domain DefaultCodomain => Domain.Complex; + } + partial record Absf { /// diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.ExponentialIntegrals.Classes.cs b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.ExponentialIntegrals.Classes.cs new file mode 100644 index 000000000..8efcfceee --- /dev/null +++ b/Sources/AngouriMath/Core/Entity/Continuous/Entity.Continuous.ExponentialIntegrals.Classes.cs @@ -0,0 +1,50 @@ +// +// 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 exponential integral, Ei(z) = gamma + (ln z - ln(1/z))/2 + sum_(k >= 1) z^k/(k k!), + /// which on the real line is the principal value of int_-oo^x e^t/t dt. + /// + /// https://github.com/asc-community/AngouriMath/issues/1501 + public sealed partial record Eif(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + private Eif New(Entity arg) => + ReferenceEquals(Argument, arg) ? this : new(arg) { Codomain = Codomain }; + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + + /// + /// The logarithmic integral, li(z) = Ei(ln z), which on x > 0 is the principal + /// value of int_0^x dt/ln t. + /// + /// https://github.com/asc-community/AngouriMath/issues/1501 + public sealed partial record Lif(Entity Argument) : Function, IUnaryNode + { + /// + public Entity NodeChild => Argument; + + private Lif New(Entity arg) => + ReferenceEquals(Argument, arg) ? this : new(arg) { Codomain = Codomain }; + /// + public override Entity Replace(Func func) => func(New(Argument.Replace(func))); + /// + protected override Entity[] InitDirectChildren() => new[] { Argument }; + } + } +} diff --git a/Sources/AngouriMath/Core/Entity/Continuous/Number/ExponentialIntegrals.cs b/Sources/AngouriMath/Core/Entity/Continuous/Number/ExponentialIntegrals.cs new file mode 100644 index 000000000..1e63c3941 --- /dev/null +++ b/Sources/AngouriMath/Core/Entity/Continuous/Number/ExponentialIntegrals.cs @@ -0,0 +1,205 @@ +// +// 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 System.Collections.Concurrent; +using PeterO.Numbers; + +namespace AngouriMath +{ + partial record Entity + { + partial record Number + { + /// + /// The exponential integral, Ei(z) = gamma + (ln z - ln(1/z))/2 + sum_(k >= 1) z^k/(k k!), + /// at the working precision, for every complex z; Ei(0) is -oo. + /// + /// + /// + /// (ln z - ln(1/z))/2 is ln z off the negative real axis and ln |z| + /// on it, so Ei is real on the whole real line but 0, as SymPy's, mpmath's and + /// Mathematica's is: on the positive axis it is the principal value of + /// int_-oo^x e^t/t dt, on the negative axis -E1(-x), and just above or below + /// the negative axis it is i pi more or less. + /// + /// + /// With P digits of working precision, up to |z| = (P + 5) ln 10 it is summed + /// as written. The terms peak near k = |z| at about e^|z|/|z|, while + /// Ei(z) is about e^Re(z)/|z|, so the sum cancels (|z| - Re z)/ln 10 + /// digits, which are carried as guard digits: none on the positive real axis, and twice + /// |x|/ln 10 on the negative one. + /// + /// + /// Beyond that it is e^z/z sum_k k!/z^k (Abramowitz and Stegun 5.1.51), cut at its + /// smallest term, which is about e^(-|z|) of the sum and so below the precision + /// there, and off the real axis the logarithm's branch adds i pi sgn(Im z). + /// + /// + /// The result is rounded to , whose + /// exponent range bounds what can be represented: Ei(-500), about 1e-220, + /// can come out as zero there. + /// + /// https://github.com/asc-community/AngouriMath/issues/1501 + /// + public static Complex Ei(Complex z) + { + var context = MathS.Settings.DecimalPrecisionContext.Value; + var (re, im) = (z.RealPart.EDecimal, z.ImaginaryPart.EDecimal); + if (re.IsNaN() || im.IsNaN()) + return Real.NaN; + if (re.IsInfinity() || im.IsInfinity()) + return im.IsZero && re.IsInfinity() ? (re.IsNegative ? Integer.Zero : Real.PositiveInfinity) : Real.NaN; + if (re.IsZero && im.IsZero) + return Real.NegativeInfinity; + var (eiRe, eiIm) = Ei(re, im, context, extraDigits: 0); + return Complex.Create(eiRe.RoundToPrecision(context), eiIm.RoundToPrecision(context)); + } + + /// + /// The logarithmic integral, li(z) = Ei(ln z), with the principal logarithm, at the + /// working precision, for every complex z: li(0) = 0 and li(1) = -oo. + /// + /// + /// On x > 0 it is the principal value of int_0^x dt/ln t, real, and on + /// 0 < x < 1, where ln x is negative, Ei of a negative number. + /// The logarithm is taken with ten more digits, so that Ei is asked the argument to + /// the precision it answers in. + /// https://github.com/asc-community/AngouriMath/issues/1501 + /// + public static Complex Li(Complex z) + { + var context = MathS.Settings.DecimalPrecisionContext.Value; + var (re, im) = (z.RealPart.EDecimal, z.ImaginaryPart.EDecimal); + if (re.IsNaN() || im.IsNaN()) + return Real.NaN; + if (re.IsInfinity() || im.IsInfinity()) + return im.IsZero && re.IsPositiveInfinity() ? Real.PositiveInfinity : Real.NaN; + if (re.IsZero && im.IsZero) + return Integer.Zero; + if (im.IsZero && re.CompareTo(EDecimal.One) == 0) + return Real.NegativeInfinity; + var work = Working(context, 10); + var modulus = re.Multiply(re, work).Add(im.Multiply(im, work), work).Sqrt(work); + var (lnRe, lnIm) = (modulus.Log(work), im.Arctan2(re, work)); + var (liRe, liIm) = Ei(lnRe, lnIm, context, extraDigits: 10); + return Complex.Create(liRe.RoundToPrecision(context), liIm.RoundToPrecision(context)); + } + + /// + /// Ei(re + i im) in a context of 's precision and + /// more, before any rounding back. + /// + private static (EDecimal Re, EDecimal Im) Ei(EDecimal re, EDecimal im, EContext context, int extraDigits) + { + var precision = context.Precision.ToInt32Checked() + extraDigits; + var modulus = Math.Sqrt(Math.Pow(re.ToDouble(), 2) + Math.Pow(im.ToDouble(), 2)); + if (modulus > (precision + 5) * Math.Log(10)) + return EiByTheAsymptoticSeries(re, im, Working(context, extraDigits + 10)); + // The digits the terms cancel off the positive axis, and ten over. + var cancelled = (int)Math.Ceiling((modulus - re.ToDouble()) / Math.Log(10)); + return EiByTheSeries(re, im, Working(context, extraDigits + cancelled + 10)); + } + + /// + /// gamma + (ln z - ln(1/z))/2 + sum_(k >= 1) z^k/(k k!), summed until a term is below + /// the working precision of the sum once the terms have begun to fall. + /// + private static (EDecimal Re, EDecimal Im) EiByTheSeries(EDecimal re, EDecimal im, EContext work) + { + var epsilon = EDecimal.Create(EInteger.One, EInteger.FromInt32(-work.Precision.ToInt32Checked())); + var peak = EDecimal.FromDouble(Math.Sqrt(Math.Pow(re.ToDouble(), 2) + Math.Pow(im.ToDouble(), 2))); + // z^k/k!, and the sum of those over k. + var power = (Re: EDecimal.One, Im: EDecimal.Zero); + var sum = (Re: EDecimal.Zero, Im: EDecimal.Zero); + for (var k = 1; ; k++) + { + power = Multiply(power, (re, im), work); + var divisor = EDecimal.FromInt32(k); + power = (power.Re.Divide(divisor, work), power.Im.Divide(divisor, work)); + var term = (Re: power.Re.Divide(divisor, work), Im: power.Im.Divide(divisor, work)); + sum = (sum.Re.Add(term.Re, work), sum.Im.Add(term.Im, work)); + if (divisor.CompareTo(peak) > 0 + && Magnitude(term).CompareTo(Magnitude(sum).Add(EDecimal.One, work).Multiply(epsilon, work)) < 0) + break; + } + // (ln z - ln(1/z))/2: ln |z| on the negative axis, where both logarithms add i pi. + var modulus = re.Multiply(re, work).Add(im.Multiply(im, work), work).Sqrt(work); + var logarithm = (Re: modulus.Log(work), Im: im.IsZero && re.IsNegative ? EDecimal.Zero : im.Arctan2(re, work)); + return (sum.Re.Add(logarithm.Re, work).Add(EulerGamma(work), work), sum.Im.Add(logarithm.Im, work)); + } + + /// + /// e^z/z sum_k k!/z^k + i pi sgn(Im z), cut at its smallest term. + /// + private static (EDecimal Re, EDecimal Im) EiByTheAsymptoticSeries(EDecimal re, EDecimal im, EContext work) + { + var epsilon = EDecimal.Create(EInteger.One, EInteger.FromInt32(-work.Precision.ToInt32Checked())); + // 1/z = (re - i im)/|z|^2 + var squaredModulus = re.Multiply(re, work).Add(im.Multiply(im, work), work); + var reciprocal = (Re: re.Divide(squaredModulus, work), Im: im.Negate().Divide(squaredModulus, work)); + var term = (Re: EDecimal.One, Im: EDecimal.Zero); + var sum = term; + var previous = Magnitude(term); + for (var k = 1; ; k++) + { + var next = Multiply(term, reciprocal, work); + next = (next.Re.Multiply(k, work), next.Im.Multiply(k, work)); + var size = Magnitude(next); + // Past the smallest term the series diverges; below the precision it is done. + if (size.CompareTo(previous) >= 0 || size.CompareTo(epsilon) < 0) + break; + sum = (sum.Re.Add(next.Re, work), sum.Im.Add(next.Im, work)); + (term, previous) = (next, size); + } + // e^z/z = e^re (cos im + i sin im) (re - i im)/|z|^2 + var scale = re.Exponential(work); + var exponential = (scale.Multiply(im.Cos(work), work), scale.Multiply(im.Sin(work), work)); + var (valueRe, valueIm) = Multiply(Multiply(exponential, reciprocal, work), sum, work); + if (!im.IsZero) + valueIm = valueIm.Add(im.IsNegative ? EDecimal.PI(work).Negate() : EDecimal.PI(work), work); + return (valueRe, valueIm); + } + + /// + /// Euler's constant, gamma = lim (1 + 1/2 + ... + 1/n - ln n), to the precision of + /// , by Brent and McMillan's algorithm B1: with + /// B_k = (n^k/k!)^2 and A_k = B_k (H_k - ln n), gamma is + /// sum A_k/sum B_k to within pi e^(-4n), so n is a quarter of the + /// digits' ln 10. The terms stay positive past k = n, where they are largest, + /// and ten guard digits cover what the first ones cancel. + /// + private static EDecimal EulerGamma(EContext work) + { + var digits = work.Precision.ToInt32Checked(); + return eulerGamma.GetOrAdd(digits, static digits => + { + var inner = EContext.ForPrecision(digits + 10 + (int)Math.Ceiling(Math.Log10(digits + 10))) + .WithRounding(ERounding.HalfEven).WithUnlimitedExponents(); + var n = (int)Math.Ceiling(digits * Math.Log(10) / 4) + 1; + var nSquared = EDecimal.FromInt32(n).Multiply(EDecimal.FromInt32(n)); + var a = EDecimal.FromInt32(n).Log(inner).Negate(); + var b = EDecimal.One; + var (u, v) = (a, b); + var epsilon = EDecimal.Create(EInteger.One, EInteger.FromInt32(-inner.Precision.ToInt32Checked())); + for (var k = 1; ; k++) + { + var kk = EDecimal.FromInt32(k); + b = b.Multiply(nSquared, inner).Divide(kk.Multiply(kk), inner); + a = a.Multiply(nSquared, inner).Divide(kk, inner).Add(b, inner).Divide(kk, inner); + u = u.Add(a, inner); + v = v.Add(b, inner); + if (k > n && b.CompareTo(v.Multiply(epsilon, inner)) < 0 && a.Abs().CompareTo(u.Abs().Multiply(epsilon, inner)) < 0) + break; + } + return u.Divide(v, inner).RoundToPrecision(EContext.ForPrecision(digits).WithRounding(ERounding.HalfEven).WithUnlimitedExponents()); + }); + } + [ConcurrentField] private static readonly ConcurrentDictionary eulerGamma = new(); + } + } +} diff --git a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs index 613769e06..c06a924bd 100644 --- a/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs +++ b/Sources/AngouriMath/Core/Serialization/Entity.Serialization.cs @@ -122,6 +122,8 @@ [EntityJsonConverter] partial record SpecialSet [EntityJsonConverter] partial record Erff; [EntityJsonConverter] partial record Erfcf; [EntityJsonConverter] partial record Erfif; + [EntityJsonConverter] partial record Eif; + [EntityJsonConverter] partial record Lif; [EntityJsonConverter] partial record Sinf; [EntityJsonConverter] partial record Statement; [EntityJsonConverter] partial record Sumf; diff --git a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs index 4ff8f5a04..5d277d46d 100644 --- a/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs +++ b/Sources/AngouriMath/Core/Transformations/Matching/MatchPattern.cs @@ -474,6 +474,8 @@ internal abstract bool ETryBuild( [typeof(Entity.Erff)] = (1, static c => new Entity.Erff(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])), + [typeof(Entity.Lif)] = (1, static c => new Entity.Lif(c[0])), [typeof(Entity.Floorf)] = (1, static c => new Entity.Floorf(c[0])), [typeof(Entity.Ceilf)] = (1, static c => new Entity.Ceilf(c[0])), [typeof(Entity.Roundf)] = (1, static c => new Entity.Roundf(c[0])), diff --git a/Sources/AngouriMath/Docs/Contributing/WritingARule.md b/Sources/AngouriMath/Docs/Contributing/WritingARule.md index 4617d9dbb..ede313521 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 **53** such types. +pattern used as a **replacement** must be one the library can construct: there are **55** 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 4168df222..087e795d9 100644 --- a/Sources/AngouriMath/Docs/Usage/Syntax.md +++ b/Sources/AngouriMath/Docs/Usage/Syntax.md @@ -283,6 +283,15 @@ definition: the derivative of `erf(x)` is `2 / sqrt(pi) * e ^ (-x ^ 2)`. `erf(0) is `1`, and `erf(+oo)` is `1`. An equation in one of them is left as the set of `x` for which it holds, since the library writes none of their inverses. +**Exponential and logarithmic integrals** — `Ei(z)` `li(z)`. The exponential integral +`Ei(z) = gamma + (ln z - ln(1/z))/2 + sum z^k/(k k!)`, which on the real line is the principal +value of `int_-oo^x e^t/t dt`, and the logarithmic integral `li(z) = Ei(ln z)`, which on `x > 0` is +the principal value of `int_0^x dt/ln t`. Both are real on the real line, `li` for `x >= 0`; the cut +of `Ei` is the negative real axis, on which it keeps its real value, and it is `i pi` more just above +it. Each is evaluated to the working precision anywhere in the complex plane and differentiated +from its definition: the derivative of `Ei(x)` is `e ^ x / x`, and of `li(x)` it is `1 / ln(x)`. +`Ei` is undefined at `0` and `li` at `1`; `li(0)` is `0`. + **Calculus** — `derivative(expr, var, order)`, `integral(expr, var)`, `integral(expr, var, from, to)`, `limit(expr, var, dest)`, `limitleft(...)`, `limitright(...)`; `max(expr, var in set)` and `min` for the extremum of an expression over a set, `argmax` and diff --git a/Sources/AngouriMath/Functions/Continuous/Differentiation.cs b/Sources/AngouriMath/Functions/Continuous/Differentiation.cs index e8119dee5..c971d7888 100644 --- a/Sources/AngouriMath/Functions/Continuous/Differentiation.cs +++ b/Sources/AngouriMath/Functions/Continuous/Differentiation.cs @@ -274,6 +274,23 @@ protected override Entity InnerDifferentiate(Variable variable) => 2 / MathS.Sqrt(MathS.pi) * MathS.Pow(MathS.e, MathS.Sqr(Argument)) * Argument.InnerDifferentiate(variable); } + partial record Eif + { + // Ei(a)' = e^a/a a', the integrand of its definition. + // https://github.com/asc-community/AngouriMath/issues/1501 + /// + protected override Entity InnerDifferentiate(Variable variable) => + MathS.Pow(MathS.e, Argument) / Argument * Argument.InnerDifferentiate(variable); + } + + partial record Lif + { + // li(a)' = a'/ln(a) + /// + protected override Entity InnerDifferentiate(Variable variable) => + Argument.InnerDifferentiate(variable) / MathS.Ln(Argument); + } + partial record Cosf { // cos(a)' = -sin(a) * a' diff --git a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs index 2390afd2c..f4476f2bf 100644 --- a/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs +++ b/Sources/AngouriMath/Functions/Continuous/Solvers/EquationSolver/InvertNode.Classes.cs @@ -242,6 +242,21 @@ partial record Erfif null; } + // Neither integral has an inverse among the library's nodes, and neither preimage is + // empty: Ei(x) = 0 at about 0.3725, and li(x) = 0 at about 1.4513, Soldner's constant. + // https://github.com/asc-community/AngouriMath/issues/1501 + partial record Eif + { + private protected override IEnumerable? InvertNode(Entity value, Entity x) => + null; + } + + partial record Lif + { + private protected override IEnumerable? InvertNode(Entity value, Entity x) => + null; + } + partial record Binomialf { // The preimage of a binomial coefficient is not a function of either argument 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 141a9230f..6f3f6adb0 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 @@ -494,6 +494,47 @@ Set.Interval interval when IntervalArithmetic.Monotone(interval, increasing: tru (@this, a) => ((Erfif)@this).New(a), isExact); } + public partial record Eif + { + // Defined everywhere but at 0, where ln is not: real on either side of it. + // https://github.com/asc-community/AngouriMath/issues/1501 + private protected override Entity IntrinsicCondition => !Argument.EqualTo(0); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => a switch + { + Complex n when !isExact => Number.Ei(n), + Real r when r.EDecimal.IsPositiveInfinity() => Real.PositiveInfinity, + Real r when r.EDecimal.IsNegativeInfinity() => Integer.Zero, + _ => null + }, + (@this, a) => ((Eif)@this).New(a), isExact); + } + + public partial record Lif + { + // Defined everywhere but at 1, where ln is 0; on the real line, where the logarithm + // is real, that is x >= 0, and li(0) = 0. + private protected override Entity IntrinsicCondition => + Codomain < Domain.Complex + ? Argument >= 0 & !Argument.EqualTo(1) + : !Argument.EqualTo(1); + + /// + protected override Entity InnerSimplify(bool isExact) + => ExpandOnOneArgument(Argument, + a => a switch + { + Complex n when !isExact => Number.Li(n), + Integer { IsZero: true } => Integer.Zero, + Real r when r.EDecimal.IsPositiveInfinity() => Real.PositiveInfinity, + _ => null + }, + (@this, a) => ((Lif)@this).New(a), isExact); + } + public partial record Signumf { // Signum is defined everywhere in the complex plane diff --git a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs index 6d50c2ff0..a382f2533 100644 --- a/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/Latex/Latex.Arithmetics.Classes.cs @@ -179,6 +179,20 @@ private protected override string LatexizeNode() => $@"\operatorname{{erfi}}\left({Argument.Latexize()}\right)"; } + partial record Eif + { + /// + private protected override string LatexizeNode() + => $@"\operatorname{{Ei}}\left({Argument.Latexize()}\right)"; + } + + partial record Lif + { + /// + private protected override string LatexizeNode() + => $@"\operatorname{{li}}\left({Argument.Latexize()}\right)"; + } + partial record Absf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs index b277642f8..3ece15747 100644 --- a/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToString/ToString.Arithmetics.Classes.cs @@ -156,6 +156,22 @@ public partial record Erfif public override string ToString() => Stringize(); } + public partial record Eif + { + /// + private protected override string StringizeNode() => $"Ei({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + + public partial record Lif + { + /// + private protected override string StringizeNode() => $"li({Argument.Stringize()})"; + /// + public override string ToString() => Stringize(); + } + public partial record Absf { /// diff --git a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs index cca944ba6..51de15edd 100644 --- a/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs +++ b/Sources/AngouriMath/Functions/Output/ToSympy/ToSympy.Arithmetics.Classes.cs @@ -100,6 +100,18 @@ internal override string ToSymPy() => $@"sympy.erfi({Argument.ToSymPy()})"; } + public partial record Eif + { + internal override string ToSymPy() + => $@"sympy.Ei({Argument.ToSymPy()})"; + } + + public partial record Lif + { + internal override string ToSymPy() + => $@"sympy.li({Argument.ToSymPy()})"; + } + public partial record Absf { internal override string ToSymPy() diff --git a/Sources/AngouriMath/Functions/Substitute.cs b/Sources/AngouriMath/Functions/Substitute.cs index 1165522f9..b4cc6f55e 100644 --- a/Sources/AngouriMath/Functions/Substitute.cs +++ b/Sources/AngouriMath/Functions/Substitute.cs @@ -202,6 +202,20 @@ public override Entity Substitute(Entity x, Entity value) => this == x ? value : New(Argument.Substitute(x, value)); } + partial record Eif + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + + partial record Lif + { + /// + public override Entity Substitute(Entity x, Entity value) + => this == x ? value : New(Argument.Substitute(x, value)); + } + partial record Absf { /// diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs index bff98fbc0..b78164a89 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/RealValued.cs @@ -54,7 +54,7 @@ internal static bool IsRealValued(Entity expr, Variable x) && IsARealNumber(constantBase.Evaled) && ((Complex)constantBase.Evaled).RealPart.IsPositive: return IsRealValued(exponent, x); case Sinf or Cosf or Tanf or Cotanf or Secantf or Cosecantf - or Arctanf or Arccotanf or Signumf or Erff or Erfcf or Erfif: + or Arctanf or Arccotanf or Signumf or Erff or Erfcf or Erfif or Eif: return IsRealValued(expr.DirectChildren[0], x); // A modulus is real whatever it is taken of. case Absf: diff --git a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs index 44a1d2e5c..10197486f 100644 --- a/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs +++ b/Sources/AngouriMath/Functions/TreeAnalyzer/Sort.Classes.cs @@ -250,6 +250,18 @@ private protected override string SortHashName(SortLevel level) => Choice(level, "erf_", "erfi_", "erfi_"); } + public partial record Eif + { + private protected override string SortHashName(SortLevel level) + => Choice(level, "ei_", "ei_", "ei_"); + } + + public partial record Lif + { + private protected override string SortHashName(SortLevel level) + => Choice(level, "ei_", "li_", "li_"); + } + public partial record Absf { private protected override string SortHashName(SortLevel level) diff --git a/Sources/Tests/UnitTests/Common/PublicApi.txt b/Sources/Tests/UnitTests/Common/PublicApi.txt index 925c2785d..adb3fe794 100644 --- a/Sources/Tests/UnitTests/Common/PublicApi.txt +++ b/Sources/Tests/UnitTests/Common/PublicApi.txt @@ -879,6 +879,26 @@ AngouriMath.Entity+Dividesf.ToString() : System.String AngouriMath.Entity+Dividesf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Dividesf.op_Equality(AngouriMath.Entity+Dividesf, AngouriMath.Entity+Dividesf) : System.Boolean AngouriMath.Entity+Dividesf.op_Inequality(AngouriMath.Entity+Dividesf, AngouriMath.Entity+Dividesf) : System.Boolean +AngouriMath.Entity+Eif.$() : AngouriMath.Entity+Eif +AngouriMath.Entity+Eif.Argument { } : AngouriMath.Entity +AngouriMath.Entity+Eif.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+Eif.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+Eif.EqualityContract { } : System.Type +AngouriMath.Entity+Eif.Equals(AngouriMath.Entity+Eif) : System.Boolean +AngouriMath.Entity+Eif.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+Eif.Equals(System.Object) : System.Boolean +AngouriMath.Entity+Eif.GetHashCode() : System.Int32 +AngouriMath.Entity+Eif.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+Eif.InnerDifferentiate(AngouriMath.Entity+Variable) : AngouriMath.Entity +AngouriMath.Entity+Eif.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+Eif.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+Eif.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+Eif.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+Eif.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+Eif.ToString() : System.String +AngouriMath.Entity+Eif.ctor(AngouriMath.Entity) +AngouriMath.Entity+Eif.op_Equality(AngouriMath.Entity+Eif, AngouriMath.Entity+Eif) : System.Boolean +AngouriMath.Entity+Eif.op_Inequality(AngouriMath.Entity+Eif, AngouriMath.Entity+Eif) : System.Boolean AngouriMath.Entity+Equalsf.$() : AngouriMath.Entity+Equalsf AngouriMath.Entity+Equalsf.Codomain { } : AngouriMath.Core.Domain AngouriMath.Entity+Equalsf.Deconstruct(AngouriMath.Entity&, AngouriMath.Entity&) : System.Void @@ -1233,6 +1253,26 @@ AngouriMath.Entity+Lessf.ToString() : System.String AngouriMath.Entity+Lessf.ctor(AngouriMath.Entity, AngouriMath.Entity) AngouriMath.Entity+Lessf.op_Equality(AngouriMath.Entity+Lessf, AngouriMath.Entity+Lessf) : System.Boolean AngouriMath.Entity+Lessf.op_Inequality(AngouriMath.Entity+Lessf, AngouriMath.Entity+Lessf) : System.Boolean +AngouriMath.Entity+Lif.$() : AngouriMath.Entity+Lif +AngouriMath.Entity+Lif.Argument { } : AngouriMath.Entity +AngouriMath.Entity+Lif.Codomain { } : AngouriMath.Core.Domain +AngouriMath.Entity+Lif.Deconstruct(AngouriMath.Entity&) : System.Void +AngouriMath.Entity+Lif.EqualityContract { } : System.Type +AngouriMath.Entity+Lif.Equals(AngouriMath.Entity+Function) : System.Boolean +AngouriMath.Entity+Lif.Equals(AngouriMath.Entity+Lif) : System.Boolean +AngouriMath.Entity+Lif.Equals(System.Object) : System.Boolean +AngouriMath.Entity+Lif.GetHashCode() : System.Int32 +AngouriMath.Entity+Lif.InitDirectChildren() : AngouriMath.Entity[] +AngouriMath.Entity+Lif.InnerDifferentiate(AngouriMath.Entity+Variable) : AngouriMath.Entity +AngouriMath.Entity+Lif.InnerSimplify(System.Boolean) : AngouriMath.Entity +AngouriMath.Entity+Lif.NodeChild { } : AngouriMath.Entity +AngouriMath.Entity+Lif.PrintMembers(System.Text.StringBuilder) : System.Boolean +AngouriMath.Entity+Lif.Replace(System.Func) : AngouriMath.Entity +AngouriMath.Entity+Lif.Substitute(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.Entity+Lif.ToString() : System.String +AngouriMath.Entity+Lif.ctor(AngouriMath.Entity) +AngouriMath.Entity+Lif.op_Equality(AngouriMath.Entity+Lif, AngouriMath.Entity+Lif) : System.Boolean +AngouriMath.Entity+Lif.op_Inequality(AngouriMath.Entity+Lif, AngouriMath.Entity+Lif) : System.Boolean AngouriMath.Entity+Limitf.$() : AngouriMath.Entity+Limitf AngouriMath.Entity+Limitf.ApproachFrom { } : AngouriMath.Core.ApproachFrom AngouriMath.Entity+Limitf.Codomain { } : AngouriMath.Core.Domain @@ -1730,6 +1770,7 @@ AngouriMath.Entity+Number.Arctan(AngouriMath.Entity+Number+Complex) : AngouriMat AngouriMath.Entity+Number.Cos(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.Cosecant(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.Cotan(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex +AngouriMath.Entity+Number.Ei(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.EqualityContract { } : System.Type AngouriMath.Entity+Number.Equals(AngouriMath.Entity+ContinuousNode) : System.Boolean AngouriMath.Entity+Number.Equals(AngouriMath.Entity+Number) : System.Boolean @@ -1750,6 +1791,7 @@ AngouriMath.Entity+Number.IsExact { } : System.Boolean AngouriMath.Entity+Number.IsZero(AngouriMath.Entity+Number+Complex) : System.Boolean AngouriMath.Entity+Number.IsZero(AngouriMath.Entity+Number+Real) : System.Boolean AngouriMath.Entity+Number.IsZero(PeterO.Numbers.EDecimal) : System.Boolean +AngouriMath.Entity+Number.Li(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.Ln(AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.Log(AngouriMath.Entity+Number+Complex, AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex AngouriMath.Entity+Number.Pow(AngouriMath.Entity+Number+Complex, AngouriMath.Entity+Number+Complex) : AngouriMath.Entity+Number+Complex @@ -2988,6 +3030,7 @@ AngouriMath.MathS.Derivative(AngouriMath.Entity, AngouriMath.Entity) : AngouriMa AngouriMath.MathS.Derivative(AngouriMath.Entity, AngouriMath.Entity, System.Int32) : AngouriMath.Entity AngouriMath.MathS.Det(AngouriMath.Entity+Matrix) : AngouriMath.Entity AngouriMath.MathS.Disjunction(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.Ei(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Equality(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Equations(AngouriMath.Entity[]) : AngouriMath.Core.EquationSystem AngouriMath.MathS.Equations(System.Collections.Generic.IEnumerable) : AngouriMath.Core.EquationSystem @@ -3024,6 +3067,7 @@ AngouriMath.MathS.Latex(AngouriMath.Core.ILatexizeable) : System.String AngouriMath.MathS.Lcm(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.LessOrEqualThan(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.LessThan(AngouriMath.Entity, AngouriMath.Entity) : AngouriMath.Entity +AngouriMath.MathS.Li(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Limit(AngouriMath.Entity, AngouriMath.Entity, AngouriMath.Entity, AngouriMath.Core.ApproachFrom) : AngouriMath.Entity AngouriMath.MathS.Ln(AngouriMath.Entity) : AngouriMath.Entity AngouriMath.MathS.Log(AngouriMath.Entity) : AngouriMath.Entity @@ -3173,6 +3217,7 @@ class AngouriMath.Entity+Cotanf class AngouriMath.Entity+Derivativef class AngouriMath.Entity+Divf class AngouriMath.Entity+Dividesf +class AngouriMath.Entity+Eif class AngouriMath.Entity+Equalsf class AngouriMath.Entity+Erfcf class AngouriMath.Entity+Erff @@ -3192,6 +3237,7 @@ class AngouriMath.Entity+Lambda class AngouriMath.Entity+Lcmf class AngouriMath.Entity+LessOrEqualf class AngouriMath.Entity+Lessf +class AngouriMath.Entity+Lif class AngouriMath.Entity+Limitf class AngouriMath.Entity+Logf class AngouriMath.Entity+Matrix diff --git a/Sources/Tests/UnitTests/Convenience/ExponentialIntegralTest.cs b/Sources/Tests/UnitTests/Convenience/ExponentialIntegralTest.cs new file mode 100644 index 000000000..4d22c1a93 --- /dev/null +++ b/Sources/Tests/UnitTests/Convenience/ExponentialIntegralTest.cs @@ -0,0 +1,156 @@ +// +// Copyright (c) 2019-2026 Angouri. +// AngouriMath is licensed under MIT. +// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md. +// Website: https://am.angouri.org. +// + +using AngouriMath; +using AngouriMath.Extensions; +using PeterO.Numbers; +using Xunit; +using static AngouriMath.Entity; +using static AngouriMath.Entity.Number; + +namespace AngouriMath.Tests.Convenience +{ + /// + /// Ei and li: parsed, printed, differentiated, and evaluated to the working + /// precision anywhere in the complex plane, real on the real line. + /// #1501 + /// + [Trait("Area", "Convenience")] + public sealed class ExponentialIntegralTest + { + /// + /// Against mpmath at 200 digits, which agrees with itself at 400, to 40 significant digits + /// of each part. The rows cross the line where the series gives way to the asymptotic + /// series, |z| near 242 at the default hundred digits: on the positive axis, on the + /// negative axis where the series cancels hardest, off both, and to either side of the cut. + /// Evaluated with downcasting off, which would otherwise read a value near an integer as it. + /// + [Theory] + [InlineData("Ei(1)", "1.89511781635593675546652093433163426901706058", "0")] + [InlineData("Ei(-1)", "-0.219383934395520273677163775460121649031047293", "0")] + [InlineData("Ei(1/2)", "0.454219904863173579920523812662802365281405554", "0")] + [InlineData("Ei(10)", "2492.2289762418777591384401439985248489896471", "0")] + [InlineData("Ei(-10)", "-0.00000415696892968532427740285981027818038434629008", "0")] + [InlineData("Ei(-50)", "-3.78326402955045901869896785402128578030289319e-24", "0")] + [InlineData("Ei(1 + i)", "1.76462598556385406842673816135123796600830441", "2.38776985151052241926279208910379606440733385")] + [InlineData("Ei(-2 + 3 * i)", "0.0248262079441993629248773807229211028405695629", "3.1619093285008378611294800795824905828539385")] + [InlineData("Ei(-2 - 3 * i)", "0.0248262079441993629248773807229211028405695629", "-3.1619093285008378611294800795824905828539385")] + [InlineData("Ei(3 * i)", "0.119629786008000327626472281176677850546836525", "3.41944885479436487562905194275172468726309743")] + [InlineData("Ei(250)", "1.50462471265474795301825494931648658537648215e+106", "0")] + [InlineData("Ei(-250)", "-1.06343914395045543733541152348676920552148787e-111", "0")] + [InlineData("Ei(200 + 100 * i)", "1.7622176381354418803681440397433568456677786e+84", "-2.72429575213741943899636543524741744743922712e+84")] + [InlineData("Ei(300 * i)", "-0.00333219991859211177997045482583878506957971328", "3.14167741500864613848363394508061340847609756")] + [InlineData("Ei(-1/1000)", "-6.33153936413614933200278637638633557540146053", "0")] + [InlineData("Ei(1/100000)", "-10.9356998000436955039277854609505294865926943", "0")] + [InlineData("li(2)", "1.04516378011749278484458888919461313652261558", "0")] + [InlineData("li(1/2)", "-0.378671043061087976727207184636560980551234041", "0")] + [InlineData("li(10)", "6.16559950478729793752298175266952274913060281", "0")] + [InlineData("li(1000)", "177.609657990152226687640623948699317978557703", "0")] + [InlineData("li(-1)", "0.0736679120464254859901009652301496718698774623", "3.42273337877736278959237506179774280544439443")] + [InlineData("li(i)", "0.472000651439568650777606107614127836507330543", "2.94155849494938509930099998002132677208944604")] + [InlineData("li(3 + 4 * i)", "3.134375550464577526492014568304543970026172", "2.67692478177787423923844623250717722975494117")] + public void AgreesWithMpmath(string expression, string real, string imaginary) + { + using var _ = MathS.Settings.DowncastingEnabled.Set(false); + var value = MathS.FromString(expression, useCache: false).EvalNumerical(); + Close(EDecimal.FromString(real), value.RealPart.EDecimal); + Close(EDecimal.FromString(imaginary), value.ImaginaryPart.EDecimal); + } + + private static void Close(EDecimal expected, EDecimal actual) + { + var context = EContext.ForPrecision(60); + var scale = expected.Abs().CompareTo(EDecimal.Create(1, -300)) > 0 ? expected.Abs() : EDecimal.Create(1, -300); + var error = actual.Subtract(expected, context).Abs().Divide(scale, context); + Assert.True(error.CompareTo(EDecimal.Create(1, -40)) < 0, $"expected {expected}, got {actual}"); + } + + /// + /// Real on the negative axis, and i pi more just above it: the cut is the negative + /// real axis, as for ln, with the axis itself on neither side. + /// + [Fact] + public void ACutAlongTheNegativeAxisThatIsRealOnIt() + { + using var _ = MathS.Settings.DowncastingEnabled.Set(false); + var onIt = MathS.FromString("Ei(-2)", useCache: false).EvalNumerical(); + var above = MathS.FromString("Ei(-2 + i/10^40)", useCache: false).EvalNumerical(); + Assert.True(onIt.ImaginaryPart.EDecimal.IsZero); + Close(onIt.RealPart.EDecimal, above.RealPart.EDecimal); + Close(EDecimal.PI(EContext.ForPrecision(60)), above.ImaginaryPart.EDecimal); + } + + /// li(z) = Ei(ln z), which is its definition here, off the real line as on it. + [Theory] + [InlineData("2")] + [InlineData("1/3")] + [InlineData("-5")] + [InlineData("2 - 7 * i")] + public void TheLogarithmicIntegralIsTheExponentialIntegralOfTheLogarithm(string z) + { + using var _ = MathS.Settings.DowncastingEnabled.Set(false); + var li = MathS.FromString($"li({z})", useCache: false).EvalNumerical(); + var ei = MathS.FromString($"Ei(ln({z}))", useCache: false).EvalNumerical(); + Close(ei.RealPart.EDecimal, li.RealPart.EDecimal); + Close(ei.ImaginaryPart.EDecimal, li.ImaginaryPart.EDecimal); + } + + [Theory] + [InlineData("Ei(+oo)", "+oo")] + [InlineData("Ei(-oo)", "0")] + [InlineData("li(0)", "0")] + [InlineData("li(+oo)", "+oo")] + public void ExactValues(string expression, string expected) + => Assert.Equal(expected.ToEntity(), expression.ToEntity().InnerSimplified); + + [Theory] + [InlineData("Ei(x)", "e ^ x / x")] + [InlineData("Ei(2 x)", "e ^ (2 x) / x")] + [InlineData("li(x)", "1 / ln(x)")] + [InlineData("li(x ^ 2)", "2 x / ln(x ^ 2)")] + public void TheDerivativeIsTheIntegrandOfTheDefinition(string expression, string derivative) + { + var difference = expression.ToEntity().Differentiate("x") - derivative.ToEntity(); + foreach (var point in new[] { "3/10", "-6/5", "2" }) + Assert.Equal(0, difference.Substitute("x", point.ToEntity()).EvalNumerical().Abs().EDecimal.ToDouble(), 12); + } + + [Theory] + [InlineData("Ei(x)", "Ei(x)", @"\operatorname{Ei}\left(x\right)", "sympy.Ei(x)")] + [InlineData("li(x)", "li(x)", @"\operatorname{li}\left(x\right)", "sympy.li(x)")] + public void PrintsAndReadsBack(string written, string printed, string latex, string sympy) + { + var entity = written.ToEntity(); + Assert.Equal(printed, entity.ToString()); + Assert.Equal(entity, printed.ToEntity()); + Assert.Equal(latex, entity.Latexize()); + Assert.Contains(sympy, MathS.ToSympyCode(entity)); + } + + [Fact] + public void TheEntryPointsAgreeWithTheParser() + { + Assert.Equal("Ei(x)".ToEntity(), MathS.Ei("x")); + Assert.Equal("li(x)".ToEntity(), MathS.Li("x")); + } + + /// + /// Ei is undefined only at 0, and li at 1; over the reals, li also asks + /// for a non-negative argument, whose logarithm is real. + /// + [Theory] + [InlineData("Ei(x)", "0", false)] + [InlineData("Ei(x)", "-3", true)] + [InlineData("li(x)", "1", false)] + [InlineData("li(x)", "1/2", true)] + public void TheDomainLeavesOutOnlyTheSingularity(string expression, string at, bool defined) + { + var condition = expression.ToEntity().DomainConditionIn(MathS.Settings.Codomain).Substitute("x", at.ToEntity()).Simplify(); + Assert.Equal(defined ? Boolean.True : Boolean.False, condition); + } + } +} diff --git a/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs b/Sources/Tests/UnitTests/Core/Transformations/RuleAuthoringGuideTest.cs index c6e4ca411..eb7c4fdeb 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(53, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); + => Stated(55, MatchPattern.BuildableNodeTypes.Count, "the number of buildable node types"); [Fact] public void ReplacementAPatternOrCode()