The Iverson bracket is a function: iverson(P) is 1 where P holds and 0 where it does not

BREAKING-CHANGES.md

@@ -834,6 +834,21 @@ carried a condition the piecewise read as no value, so the sum was `0` at `n = 0
 | `"sum(binomial(n, k), k, 0, n)".ToEntity().Evaled` | `UnhandledParseException` | `piecewise((2 ^ n) provided (n >= 0), 0 provided True)` |
 | `"sum(n! / (k! (n - k)!) (-1)^k, k, 0, n)".ToEntity().Evaled` | `piecewise(0 provided True)` — wrong at `n = 0` | `piecewise(1 provided (n = 0), 0 provided True)` |
 
+### `iverson(P)` is the Iverson bracket, and was a product
+
+`iverson(P)` is `1` where the statement `P` holds and `0` where it does not, and is kept as written
+where `P` is not decided, so a count is a sum of brackets: `sum(iverson(k divides 12), k, 1, 12)` is
+`6`. A number is not a statement and is left as written; a statement with no truth value, such as
+`i > 0`, gives `NaN`. It prints as `[\![P]\!]` in LaTeX and as a `Piecewise` for SymPy
+([#1478](https://github.com/asc-community/AngouriMath/issues/1478)). In 2.5.0 the name was read as a
+variable multiplying its argument, and a product with a truth value is `NaN`.
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `"iverson(2 > 1)".ToEntity().Simplify()` | `NaN` — `iverson * (2 > 1)` | `1` |
+| `"iverson(x > 0)".ToEntity().Simplify()` | `iverson * (x > 0)` | `iverson(x > 0)` |
+| `"sum(sum(sum(iverson(r + b + g = 4), g, 0, 3), b, 0, 3), r, 0, 3)".ToEntity().Simplify()` | `NaN` | `12` |
+
 ### A statement about a sum up to `n` is decided by induction
 
 `forall n in ZZ+ : sum(f, k, a, n) = g` is proved from the least member of the set: the statement

Sources/.editorconfig

@@ -225,6 +225,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [Tests/UnitTests/Convenience/BinomialTest.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/IversonTest.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/Common/ExponentialOfALogarithmTest.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
 
@@ -330,6 +333,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [AngouriMath/Core/Entity/Continuous/Entity.Continuous.ErrorFunctions.Classes.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 
+[AngouriMath/Core/Entity/Continuous/Entity.Continuous.Iverson.Classes.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+
 [Tests/UnitTests/Core/ProofRecordingTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 

Sources/AngouriMath/Convenience/MathS.cs

@@ -1367,6 +1367,33 @@ public static Entity VectorLength(Matrix v)
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public static Entity Binomial(Entity n, Entity k) => new Binomialf(n, k);
 
+        /// <summary>The Iverson bracket <c>iverson(P)</c>: <c>1</c> where the statement holds, <c>0</c> where it does not</summary>
+        /// <param name="statement">The statement</param>
+        /// <returns>The <see cref="Entity.Iversonf"/> node</returns>
+        /// <remarks>
+        /// A statement that is not decided is kept as the node. A count is a sum of these:
+        /// <c>sum(iverson(k divides 12), k, 1, 12)</c> is the number of divisors of <c>12</c>.
+        /// https://github.com/asc-community/AngouriMath/issues/1478
+        /// </remarks>
+        /// <example>
+        /// <code>
+        /// using System;
+        /// using static AngouriMath.MathS;
+        ///
+        /// Console.WriteLine(Iverson("3 divides 12").Simplify());
+        /// Console.WriteLine(Iverson("2 > 3").Simplify());
+        /// Console.WriteLine(Iverson("x > 0").Simplify());
+        /// </code>
+        /// Prints
+        /// <code>
+        /// 1
+        /// 0
+        /// iverson(x > 0)
+        /// </code>
+        /// </example>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Entity Iverson(Entity statement) => new Iversonf(statement);
+
         /// <summary>The error function, <c>erf(z) = 2/sqrt(pi) int_0^z e^(-t^2) dt</c></summary>
         /// <param name="a">The argument, any complex number</param>
         /// <returns>The <see cref="Entity.Erff"/> node</returns>

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -596,6 +596,9 @@ atom returns[Entity value]
     | 'gcd(' args = function_arguments ')' { AssertAtLeast("gcd", 1, $args.list.Count); $value = $args.list.Aggregate((a, b) => MathS.Gcd(a, b)); }
     | 'lcm(' args = function_arguments ')' { AssertAtLeast("lcm", 1, $args.list.Count); $value = $args.list.Aggregate((a, b) => MathS.Lcm(a, b)); }
     | 'binomial(' args = function_arguments ')' { Assert("binomial", 2, $args.list.Count); $value = MathS.Binomial($args.list[0], $args.list[1]); }
+    /* The Iverson bracket, 1 where a statement holds and 0 where it does not: a count written as
+       a sum. https://github.com/asc-community/AngouriMath/issues/1478 */
+    | 'iverson(' args = function_arguments ')' { Assert("iverson", 1, $args.list.Count); $value = MathS.Iverson($args.list[0]); }
     /* The error functions. https://github.com/asc-community/AngouriMath/issues/1501 */
     | 'erf(' args = function_arguments ')' { Assert("erf", 1, $args.list.Count); $value = MathS.Erf($args.list[0]); }
     | 'erfc(' args = function_arguments ')' { Assert("erfc", 1, $args.list.Count); $value = MathS.Erfc($args.list[0]); }

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -179,14 +179,15 @@ T__177=178
 T__178=179
 T__179=180
 T__180=181
-NEWLINE=182
-NUMBER=183
-SPECIALSET=184
-BOOLEAN=185
-NAN=186
-VARIABLE=187
-COMMENT=188
-WS=189
+T__181=182
+NEWLINE=183
+NUMBER=184
+SPECIALSET=185
+BOOLEAN=186
+NAN=187
+VARIABLE=188
+COMMENT=189
+WS=190
 '!'=1
 '^'=2
 '-'=3
@@ -353,19 +354,20 @@ WS=189
 'gcd('=164
 'lcm('=165
 'binomial('=166
-'erf('=167
-'erfc('=168
-'erfi('=169
-'Ei('=170
-'li('=171
-'Si('=172
-'Ci('=173
-'Shi('=174
-'Chi('=175
-'trunc('=176
-'conjugate('=177
-'domain('=178
-'piecewise('=179
-'apply('=180
-'lambda('=181
-'NaN'=186
+'iverson('=167
+'erf('=168
+'erfc('=169
+'erfi('=170
+'Ei('=171
+'li('=172
+'Si('=173
+'Ci('=174
+'Shi('=175
+'Chi('=176
+'trunc('=177
+'conjugate('=178
+'domain('=179
+'piecewise('=180
+'apply('=181
+'lambda('=182
+'NaN'=187