An integer range is listed, and a family of sets has a union and an intersection

BREAKING-CHANGES.md

@@ -621,6 +621,25 @@ too ([#1409](https://github.com/asc-community/AngouriMath/issues/1409)). `subset
 | `{1, 3} in powerset(ZZ)` | `UnrecognizedFunctionParseException` | `True` |
 | `card({1, {}})` | `#{ 1, {  } }` — left as written | `2` |
 
+### An integer range is listed, and a family of sets has a union and an intersection
+
+`ZZ /\ [1; 10]` lists its members now — an integer set cut by a numeric interval with at most
+4096 members in it is the finite set of them, the `[n] = {1, …, n}` of combinatorics being
+`ZZ+ /\ [1; n]`; the reals and the complex numbers cut by an interval are the interval, and the
+rationals stay as written. `union(A_k, k in I)` and `intersection(A_k, k in I)` are
+`Entity.Set.IndexedUnionf` and `Entity.Set.IndexedIntersectionf`, binders like `sum`: folded over
+a listed index set, and over any other an object whose membership is decided by the quantifiers
+(`0 in intersection([0; 1/n), n in ZZ+)` is `True`). `complement(A, U)` is `U \ A`
+([#1409](https://github.com/asc-community/AngouriMath/issues/1409)). `union`, `intersection` and
+`complement` are keywords now, and were names.
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `ZZ /\ [1; 10]` | `ZZ /\ [1; 10]` — left as written | `{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }` |
+| `RR /\ [0; 1]` | `RR /\ [0; 1]` — left as written | `[0; 1]` |
+| `union({k, 2 k}, k in {1, 2, 3})` | `UnhandledParseException` — `union` was a name, and `union(` a juxtaposition that does not parse | `{ 1, 2, 4, 3, 6 }` |
+| `0.1 in intersection([0; 1/n), n in ZZ+)` | `UnhandledParseException` | `False` |
+| `complement({1, 2}, {1, 2, 3})` | `UnhandledParseException` | `{ 3 }` |
 ### An exponential of a multiple of a logarithm is integrated as the power it is
 
 `e^(k ln(q))` is `q^k` — the definition of the principal power, for every complex `q` other than

Sources/.editorconfig

@@ -291,6 +291,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [AngouriMath/Functions/NumberTheory/ResidueClasses.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 
+[Tests/UnitTests/Core/Sets/IndexedSetOperationTest.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/Calculus/ExponentialOfALogarithmIntegralTest.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

@@ -6262,6 +6262,36 @@ public static class Sets
             /// </example>
             public static Entity Subset(Entity sub, Entity super) => new Subsetf(sub, super);
 
+            /// <summary>
+            /// The union of a family of sets indexed by <paramref name="var"/> ranging over
+            /// <paramref name="over"/>: <c>union(A_i, i in I)</c>, the set of what is in some
+            /// <c>A_i</c>. Folded over a listed index set; a membership object otherwise.
+            /// </summary>
+            /// <example>
+            /// <code>
+            /// Console.WriteLine("union({k, 2 k}, k in {1, 2, 3})".ToEntity().Evaled);
+            /// </code>
+            /// Prints
+            /// <code>
+            /// { 1, 2, 4, 3, 6 }
+            /// </code>
+            /// </example>
+            public static Set IndexedUnion(Entity body, Entity var, Entity over) => new IndexedUnionf(var, over, body);
+
+            /// <summary>
+            /// The intersection of a family of sets indexed by <paramref name="var"/> ranging
+            /// over <paramref name="over"/>: <c>intersection(A_i, i in I)</c>, the set of what
+            /// is in every <c>A_i</c>.
+            /// </summary>
+            public static Set IndexedIntersection(Entity body, Entity var, Entity over) => new IndexedIntersectionf(var, over, body);
+
+            /// <summary>
+            /// The complement of <paramref name="set"/> relative to the universe
+            /// <paramref name="universe"/>, which is <c>universe \ set</c>: a complement is
+            /// always relative to a universe, there being no set of everything.
+            /// </summary>
+            public static Set Complement(Entity set, Entity universe) => universe.SetSubtract(set);
+
             /// <returns>A set of all Complexes/>s</returns>
             public static Set C => SpecialSet.Create(Domain.Complex);
 

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -550,6 +550,9 @@ atom returns[Entity value]
     | 'phi(' args = function_arguments ')' { Assert("phi", 1, $args.list.Count); $value = MathS.NumberTheory.Phi($args.list[0]); }
     | 'card(' args = function_arguments ')' { Assert("card", 1, $args.list.Count); $value = MathS.Sets.Card($args.list[0]); }
     | 'powerset(' args = function_arguments ')' { Assert("powerset", 1, $args.list.Count); $value = MathS.Sets.PowerSet($args.list[0]); }
+    | 'union(' args = function_arguments ')' { Assert("union", 2, $args.list.Count); $value = $args.list[1] is Entity.Set.Inf { Element: Variable } unionRange ? MathS.Sets.IndexedUnion($args.list[0], unionRange.Element, unionRange.SupSet) : throw new InvalidArgumentParseException("union expects its second argument to say which name ranges over which set, as in union(A_i, i in I)"); }
+    | 'intersection(' args = function_arguments ')' { Assert("intersection", 2, $args.list.Count); $value = $args.list[1] is Entity.Set.Inf { Element: Variable } intersectionRange ? MathS.Sets.IndexedIntersection($args.list[0], intersectionRange.Element, intersectionRange.SupSet) : throw new InvalidArgumentParseException("intersection expects its second argument to say which name ranges over which set, as in intersection(A_i, i in I)"); }
+    | 'complement(' args = function_arguments ')' { Assert("complement", 2, $args.list.Count); $value = MathS.Sets.Complement($args.list[0], $args.list[1]); }
     | 'floor(' args = function_arguments ')' { Assert("floor", 1, $args.list.Count); $value = MathS.Floor($args.list[0]); }
     | 'ceil(' args = function_arguments ')' { Assert("ceil", 1, $args.list.Count); $value = MathS.Ceil($args.list[0]); }
     /* SymPy's spelling, accepted so that an expression copied from there parses. Stringize

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -162,14 +162,17 @@ T__160=161
 T__161=162
 T__162=163
 T__163=164
-NEWLINE=165
-NUMBER=166
-SPECIALSET=167
-BOOLEAN=168
-NAN=169
-VARIABLE=170
-COMMENT=171
-WS=172
+T__164=165
+T__165=166
+T__166=167
+NEWLINE=168
+NUMBER=169
+SPECIALSET=170
+BOOLEAN=171
+NAN=172
+VARIABLE=173
+COMMENT=174
+WS=175
 '!'=1
 '^'=2
 '-'=3
@@ -316,22 +319,25 @@ WS=172
 'phi('=144
 'card('=145
 'powerset('=146
-'floor('=147
-'ceil('=148
-'ceiling('=149
-'round('=150
-'min('=151
-'max('=152
-'argmax('=153
-'argmin('=154
-'gcd('=155
-'lcm('=156
-'binomial('=157
-'trunc('=158
-'erf('=159
-'conjugate('=160
-'domain('=161
-'piecewise('=162
-'apply('=163
-'lambda('=164
-'NaN'=169
+'union('=147
+'intersection('=148
+'complement('=149
+'floor('=150
+'ceil('=151
+'ceiling('=152
+'round('=153
+'min('=154
+'max('=155
+'argmax('=156
+'argmin('=157
+'gcd('=158
+'lcm('=159
+'binomial('=160
+'trunc('=161
+'erf('=162
+'conjugate('=163
+'domain('=164
+'piecewise('=165
+'apply('=166
+'lambda('=167
+'NaN'=172