The complex conjugate and the principal argument are functions

BREAKING-CHANGES.md

@@ -263,19 +263,23 @@ the expression's own domain as its condition ([#2142](https://github.com/asc-com
 | `"(1 - cos(a))/(1 + cos(a))/tan(a/2)^2".Simplify()` | `(1 - cos(a)) / ((cos(a) + 1) * tan(a / 2) ^ 2)` | `1 provided not cos(a) + 1 = 0 and not tan(a / 2) = 0 and not cos(a / 2) = 0` |
 | `"(cos(2*x) - 1)^2 + sin(2*x)^2 - 4*sin(x)^2".Simplify()` ([#2133](https://github.com/asc-community/AngouriMath/issues/2133)) | `2 + (-2) * cos(2 * x) + (-4) * sin(x) ^ 2` | `0` |
 
-### `conj` and `arg` are refused by name
+### `conjugate`, `conj` and `arg` are functions
 
-**Not silent: these now throw `UnrecognizedFunctionParseException` where they parsed.** A name the parser does not
-know, followed by a bracket, is read as a product, so `arg(z)` was the variable `arg` times `z`, and `arg(z) = 1`
-solved to `{ 1 / arg }`. `conjugate` was already refused by name; `conj` and `arg` are the conjugate and the argument
-as other systems spell them. `re` and `im` are still read as products, as before: two letters is short enough to be a
-variable's name ([#2136](https://github.com/asc-community/AngouriMath/issues/2136)).
+**Not silent: these names followed by a bracket are now the complex conjugate and the principal argument, where they
+were read as products or refused.** A name the parser does not know, followed by a bracket, is read as a product, so
+`arg(z)` was the variable `arg` times `z`, and `arg(z) = 1` solved to `{ 1 / arg }`. `conjugate(z)` and `conj(z)` are
+`Entity.Conjugatef`, carried through sums, differences, products, quotients and whole powers and not through a root or
+a logarithm; `arg(z)` is `Entity.Argf`, in `(-pi, pi]`, with no value at `0`
+([#2136](https://github.com/asc-community/AngouriMath/issues/2136),
+[#2145](https://github.com/asc-community/AngouriMath/issues/2145)). `re` and `im` are still read as products.
 
 | Input | Was (2.6.0) | Now |
 |---|---|---|
-| `"arg(z)".ToEntity()` | `arg * z` | throws `UnrecognizedFunctionParseException` |
-| `"conj(z)".ToEntity()` | `conj * z` | throws `UnrecognizedFunctionParseException` |
-
+| `"conjugate(z)".ToEntity()` | throws `UnrecognizedFunctionParseException` | `conjugate(z)` |
+| `"conj(z)".ToEntity()` | `conj * z` | `conjugate(z)` |
+| `"conj(3 + 4i)".ToEntity().Simplify()` | `(3 + 4i) * conj` | `3 - 4i` |
+| `"arg(z)".ToEntity()` | `arg * z` | `arg(z)` |
+| `"arg(-1)".ToEntity().Simplify()` | `-arg` | `pi` |
 ### Over the reals, a modulus of a polynomial is split at the polynomial's real roots
 
 **Silent: an answer with entries that solve nothing is exact.** With the real codomain an equation in moduli was

Sources/.editorconfig

@@ -237,6 +237,9 @@ 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/ConjugateAndArgumentTest.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
 
@@ -398,6 +401,8 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 
 [AngouriMath/Core/Entity/Continuous/Entity.Continuous.Iverson.Classes.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+[AngouriMath/Core/Entity/Continuous/Entity.Continuous.ComplexParts.Classes.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 [AngouriMath/Core/Entity/Continuous/Entity.Continuous.Aleph.Classes.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 

Sources/AngouriMath/Convenience/MathS.cs

@@ -1394,6 +1394,54 @@ public static Entity VectorLength(Matrix v)
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public static Entity Iverson(Entity statement) => new Iversonf(statement);
 
+        /// <summary>The complex conjugate <c>conjugate(z)</c>: <c>a - b i</c> for <c>z = a + b i</c></summary>
+        /// <param name="z">The argument, any complex number</param>
+        /// <returns>The <see cref="Entity.Conjugatef"/> node</returns>
+        /// <remarks>
+        /// It is carried through sums, products, quotients and whole powers, and fixes what is known to
+        /// be real: a number, and a node whose codomain is real, such as a modulus or <c>domain(x, RR)</c>.
+        /// https://github.com/asc-community/AngouriMath/issues/2145
+        /// </remarks>
+        /// <example>
+        /// <code>
+        /// using System;
+        /// using static AngouriMath.MathS;
+        ///
+        /// Console.WriteLine(Conjugate("3 + 4i").Simplify());
+        /// Console.WriteLine(Conjugate("a * b + i").Simplify());
+        /// </code>
+        /// Prints
+        /// <code>
+        /// 3 - 4i
+        /// -i + conjugate(a) * conjugate(b)
+        /// </code>
+        /// </example>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Entity Conjugate(Entity z) => new Conjugatef(z);
+
+        /// <summary>The principal argument <c>arg(z)</c>, in <c>(-pi, pi]</c>, so that <c>z = |z| e^(i arg(z))</c></summary>
+        /// <param name="z">The argument, any complex number but 0, where it has no value</param>
+        /// <returns>The <see cref="Entity.Argf"/> node</returns>
+        /// <remarks>https://github.com/asc-community/AngouriMath/issues/2145</remarks>
+        /// <example>
+        /// <code>
+        /// using System;
+        /// using static AngouriMath.MathS;
+        ///
+        /// Console.WriteLine(Arg("-1").Simplify());
+        /// Console.WriteLine(Arg("1 + i").Simplify());
+        /// Console.WriteLine(Arg("-1 - i").Simplify());
+        /// </code>
+        /// Prints
+        /// <code>
+        /// pi
+        /// pi / 4
+        /// -3/4 * pi
+        /// </code>
+        /// </example>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Entity Arg(Entity z) => new Argf(z);
+
         /// <summary>The aleph number <c>aleph(k)</c>, the size of an infinite set</summary>
         /// <param name="index">The index, a whole number from zero</param>
         /// <returns>The <see cref="Entity.Alephf"/> node</returns>

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -635,19 +635,19 @@ atom returns[Entity value]
     | 'dot(' args = function_arguments ')' { Assert("dot", 2, $args.list.Count); $value = ParsingHelpers.Dot($args.list[0], $args.list[1]); }
     | 'cross(' args = function_arguments ')' { Assert("cross", (1, 2), $args.list.Count); $value = ParsingHelpers.Cross($args.list); }
     | 'resultant(' args = function_arguments ')' { Assert("resultant", 3, $args.list.Count); $value = ParsingHelpers.Resultant($args.list[0], $args.list[1], $args.list[2]); }
+    /* The complex conjugate, by its name and by the shorter one other systems use.
+       https://github.com/asc-community/AngouriMath/issues/2145 */
+    | 'conjugate(' args = function_arguments ')' { Assert("conjugate", 1, $args.list.Count); $value = MathS.Conjugate($args.list[0]); }
+    | 'conj(' args = function_arguments ')' { Assert("conj", 1, $args.list.Count); $value = MathS.Conjugate($args.list[0]); }
+    /* The principal argument, in (-pi, pi]. https://github.com/asc-community/AngouriMath/issues/2145 */
+    | 'arg(' args = function_arguments ')' { Assert("arg", 1, $args.list.Count); $value = MathS.Arg($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 --
        see NotImplementedFunction above. Refusing is not the feature; it is the difference
        between a missing function and a wrong answer. */
 
     | 'trunc(' args = function_arguments ')' { $value = NotImplementedFunction("trunc", "rounding functions"); }
-    | 'conjugate(' args = function_arguments ')' { $value = NotImplementedFunction("conjugate", "complex conjugate as a symbolic function"); }
-    /* conj and arg are the conjugate and the argument as other systems spell them. Each was read
-       as a product: arg(z) was arg * z. re and im are left as products, as
-       MissingFunctionNamesRefusedTest records. https://github.com/asc-community/AngouriMath/issues/2136 */
-    | 'conj(' args = function_arguments ')' { $value = NotImplementedFunction("conj", "complex conjugate as a symbolic function"); }
-    | 'arg(' args = function_arguments ')' { $value = NotImplementedFunction("arg", "complex argument as a symbolic function"); }
     | 'domain(' args = function_arguments ')' 
         { 
             Assert("domain", 2, $args.list.Count); 

Sources/AngouriMath/Core/Antlr/AngouriMath.interp

@@ -184,10 +184,10 @@ null
 'dot('
 'cross('
 'resultant('
-'trunc('
 'conjugate('
 'conj('
 'arg('
+'trunc('
 'domain('
 'piecewise('
 'apply('

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -382,10 +382,10 @@ WS=200
 'dot('=182
 'cross('=183
 'resultant('=184
-'trunc('=185
-'conjugate('=186
-'conj('=187
-'arg('=188
+'conjugate('=185
+'conj('=186
+'arg('=187
+'trunc('=188
 'domain('=189
 'piecewise('=190
 'apply('=191