det, transpose, dot, cross and resultant are functions in an expression

BREAKING-CHANGES.md

@@ -263,20 +263,18 @@ 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`, `arg` and `det` are refused by name
+### `conj` and `arg` are refused by name
 
 **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, and `det` is the determinant, which a `Matrix` has as the property `Determinant` but an
-expression cannot call. `re` and `im` are still read as products, as before: two letters is short enough to be a
+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)).
 
 | Input | Was (2.6.0) | Now |
 |---|---|---|
 | `"arg(z)".ToEntity()` | `arg * z` | throws `UnrecognizedFunctionParseException` |
 | `"conj(z)".ToEntity()` | `conj * z` | throws `UnrecognizedFunctionParseException` |
-| `"det([[1, 2], [3, 4]])".ToEntity()` | `det * [[1, 2], [3, 4]]` | throws `UnrecognizedFunctionParseException` |
 
 ### Over the reals, a modulus of a polynomial is split at the polynomial's real roots
 
@@ -357,6 +355,26 @@ is rated no shorter ([#2135](https://github.com/asc-community/AngouriMath/issues
 | `"cos(a + b)".Expand()` | `cos(a + b)` | `cos(a) * cos(b) + -sin(a) * sin(b)` |
 | `"cos(a - b)".Expand()` | `cos(a - b)` | `cos(a) * cos(b) + sin(a) * sin(b)` |
 
+### `det`, `transpose`, `dot`, `cross` and `resultant` are functions in an expression
+
+**Not silent: these names followed by a bracket are now computed, or refused, where they were read as products or
+did not parse.** `det(M)` is the determinant, `transpose(M)` the transpose, `dot(a, b)` the sum of the products of the
+components, `cross(a, b)` the vector product in three dimensions and `cross(a)` a vector of the plane turned through a
+right angle anticlockwise, as Mathematica's `Cross` of one vector is; `resultant(p, q, x)` eliminates `x`. There is
+no node for any of them, so each is computed when it is parsed, and left as unsimplified as what it stands for would
+be written out: `dot([1, 2], [3, 4])` is `1 * 3 + 2 * 4`. An argument that is not a matrix or a vector of
+the right shape, written out or once its operations are carried out, throws `InvalidArgumentParseException`
+([#2147](https://github.com/asc-community/AngouriMath/issues/2147)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"det([[1, 2], [3, 4]])".ToEntity()` | `det * [[1, 2], [3, 4]]` | `-2` |
+| `"transpose([1, 2])".ToEntity()` | `transpose * [1, 2]` | `[[1, 2]]`, the row |
+| `"transpose(x)".ToEntity()` | `transpose * x` | throws `InvalidArgumentParseException` |
+| `"cross([a, b])".ToEntity()` | `cross * [a, b]` | `[-b, a]` |
+| `"dot([1, 2], [3, 4])".ToEntity()` | throws `UnhandledParseException` | `1 * 3 + 2 * 4` |
+| `"resultant(x^2 - 1, x - a, x)".ToEntity()` | throws `UnhandledParseException` | `a ^ 2 - 1` |
+
 ### A subscript may have a subscript
 
 **Not silent: what was a parse error is a name.** A name took at most one `_`, so `x_1_2` and `X_a_beta` were lexer
@@ -370,6 +388,19 @@ in LaTeX as `X_{a_{\beta}}`. `_` still neither begins nor ends a name, and two d
 | `MathS.Var("X_a_beta").Latexize()` | an `UnhandledParseException` | `X_{a_{\beta}}` |
 | `"x__1".ToEntity()` | an `UnhandledParseException` | an `UnhandledParseException` |
 
+### A determinant of entries that are not polynomials is expanded by the library itself
+
+**Silent: the same value, printed differently.** Where the fraction-free elimination cannot read the entries as
+polynomials, `Matrix.Determinant` expanded along the first row with GenericTensor's Laplace expansion. That expansion
+compiles an expression tree, which a native build cannot publish, and `det(M)` in an expression made it reachable from
+every one. It is now written over the entries, with the same expansion along the first row and the cofactors'
+alternating signs as subtractions ([#2147](https://github.com/asc-community/AngouriMath/issues/2147)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"[[sin(x), cos(x)], [-cos(x), sin(x)]]".ToEntity()` as a `Matrix`, `.Determinant` | `sin(x) ^ 2 + -cos(x) * -cos(x)` | `sin(x) ^ 2 - cos(x) * -cos(x)` |
+| `.Determinant.Simplify()` of `[[sqrt(a), b, 1], [c, sin(d), 2], [3, e_1, ln(f)]]` | `e_1 * ((-2) * sqrt(a) + c) + sin(d) * (sqrt(a) * ln(f) - 3) + 6 * b - b * c * ln(f)` | `sqrt(a) * (sin(d) * ln(f) - 2 * e_1) - b * (c * ln(f) - 6) + c * e_1 - 3 * sin(d)` |
+
 ### A numerical definite integral is Gauss–Legendre, with the digits it knows
 
 **Silent: wrong answers, and values where there was NaN.** `Entity.DefiniteIntegral(x, a, b, steps)` was the mean of

Sources/.editorconfig

@@ -240,6 +240,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [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/Convenience/MatrixFunctionsInAnExpressionTest.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
 

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -626,6 +626,15 @@ atom returns[Entity value]
     | 'Ci(' args = function_arguments ')' { Assert("Ci", 1, $args.list.Count); $value = MathS.Ci($args.list[0]); }
     | 'Shi(' args = function_arguments ')' { Assert("Shi", 1, $args.list.Count); $value = MathS.Shi($args.list[0]); }
     | 'Chi(' args = function_arguments ')' { Assert("Chi", 1, $args.list.Count); $value = MathS.Chi($args.list[0]); }
+    /* The determinant, the transpose, the scalar and the vector product, and the resultant, each
+       computed from what it is applied to: there is no node for any of them, so a matrix or a
+       vector has to be written out, or be one once its operations are carried out.
+       https://github.com/asc-community/AngouriMath/issues/2147 */
+    | 'det(' args = function_arguments ')' { Assert("det", 1, $args.list.Count); $value = ParsingHelpers.Determinant($args.list[0]); }
+    | 'transpose(' args = function_arguments ')' { Assert("transpose", 1, $args.list.Count); $value = ParsingHelpers.Transposed($args.list[0]); }
+    | '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]); }
 
     /* 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 --
@@ -634,13 +643,11 @@ atom returns[Entity value]
 
     | '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, and det the
-       determinant, which exists on a matrix but not in an expression. 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 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"); }
-    | 'det(' args = function_arguments ')' { $value = NotImplementedFunction("det", "determinant in an expression; a Matrix has the property Determinant"); }
     | 'domain(' args = function_arguments ')' 
         { 
             Assert("domain", 2, $args.list.Count); 

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -186,14 +186,18 @@ T__184=185
 T__185=186
 T__186=187
 T__187=188
-NEWLINE=189
-NUMBER=190
-SPECIALSET=191
-BOOLEAN=192
-NAN=193
-VARIABLE=194
-COMMENT=195
-WS=196
+T__188=189
+T__189=190
+T__190=191
+T__191=192
+NEWLINE=193
+NUMBER=194
+SPECIALSET=195
+BOOLEAN=196
+NAN=197
+VARIABLE=198
+COMMENT=199
+WS=200
 '!'=1
 '^'=2
 '-'=3
@@ -373,13 +377,17 @@ WS=196
 'Ci('=177
 'Shi('=178
 'Chi('=179
-'trunc('=180
-'conjugate('=181
-'conj('=182
-'arg('=183
-'det('=184
-'domain('=185
-'piecewise('=186
-'apply('=187
-'lambda('=188
-'NaN'=193
+'det('=180
+'transpose('=181
+'dot('=182
+'cross('=183
+'resultant('=184
+'trunc('=185
+'conjugate('=186
+'conj('=187
+'arg('=188
+'domain('=189
+'piecewise('=190
+'apply('=191
+'lambda('=192
+'NaN'=197