The Laplacian, the Jacobian and the Hessian

BREAKING-CHANGES.md

@@ -451,7 +451,7 @@ the right shape, written out or once its operations are carried out, throws `Inv
 products.** An unknown name followed by a bracket is a product, so `zeta(2)` was `zeta * 2` and simplified to
 `2 * zeta`. The long names of the functions the library is to have are refused until each is implemented, as `trunc`
 is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber`, `catalannumber`, `multinomial`, `fallingfactorial`, `factorialpower`,
-`risingfactorial`, `forwarddifference`, `laplacian`, `jacobian` and `hessian`. Names that will not be functions,
+`risingfactorial` and `forwarddifference`. Names that will not be functions,
 because what they mean differs between sources or is already written exactly, are refused with the spelling to use:
 `heaviside`, `unitstep`, `isprime`, `pochhammer`, `doublefactorial`, `factorial2`, `fractionalpart` and `quotient`.
 Each name without a bracket is still a variable, and short names such as `beta` and `norm` are still read as products
@@ -481,6 +481,24 @@ elsewhere. `primepi(x)` counts the primes at most the real number `x`
 | `"primeomega(12)".ToEntity().Simplify()` | `12 * primeomega` | `3` |
 | `"primepi(10)".ToEntity().Evaled` | `primepi * 10` | `4` |
 | `"mobius(0)".ToEntity().Simplify()` | `0` | `NaN` |
+
+### The Laplacian, the Jacobian and the Hessian
+
+**Not silent: `laplacian(f, x)`, `jacobian(F, x)` and `hessian(f, x)` are now computed into derivatives, where they were
+read as products or, with two arguments, were a parse error.** They are taken in the variables listed as a vector,
+`[x, y, z]`, or in one variable. `laplacian` is the sum of the second derivatives of a scalar function. `jacobian` is the
+matrix with a row for each component of `F` and a column for each variable. `hessian` is the matrix of the second
+derivatives, the entry in row `i` and column `j` being the derivative in `x_i` of the derivative in `x_j`. Like `det`
+they are computed when parsed and have no node: the result is made of `derivative` nodes, evaluated as any derivative
+is ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"laplacian(x^2 y + y^3, [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `8 * y` |
+| `"jacobian([x y, x + y], [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `[[y, x], [1, 1]]` |
+| `"hessian(x^3 y^2, [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `[[6 * x * y ^ 2, 6 * x ^ 2 * y], [6 * x ^ 2 * y, 2 * x ^ 3]]` |
+| `"jacobian(x y, {x, y})".ToEntity()` | throws `UnhandledParseException` | throws `InvalidArgumentParseException`: a set has no order for the columns |
+
 ### 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

Sources/.editorconfig

@@ -808,3 +808,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 
 [Tests/UnitTests/Convenience/NumberTheoryFunctionsTest.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/VectorCalculusTest.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

@@ -653,6 +653,9 @@ atom returns[Entity value]
     | '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); }
+    | 'laplacian(' args = function_arguments ')' { Assert("laplacian", 2, $args.list.Count); $value = ParsingHelpers.Laplacian($args.list[0], $args.list[1]); }
+    | 'jacobian(' args = function_arguments ')' { Assert("jacobian", 2, $args.list.Count); $value = ParsingHelpers.Jacobian($args.list[0], $args.list[1]); }
+    | 'hessian(' args = function_arguments ')' { Assert("hessian", 2, $args.list.Count); $value = ParsingHelpers.Hessian($args.list[0], $args.list[1]); }
     | '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 */
@@ -694,9 +697,6 @@ atom returns[Entity value]
     | 'factorialpower(' args = function_arguments ')' { $value = NotImplementedFunction("factorialpower", "falling factorial yet"); }
     | 'risingfactorial(' args = function_arguments ')' { $value = NotImplementedFunction("risingfactorial", "rising factorial yet"); }
     | 'forwarddifference(' args = function_arguments ')' { $value = NotImplementedFunction("forwarddifference", "forward difference yet"); }
-    | 'laplacian(' args = function_arguments ')' { $value = NotImplementedFunction("laplacian", "Laplacian yet"); }
-    | 'jacobian(' args = function_arguments ')' { $value = NotImplementedFunction("jacobian", "Jacobian yet"); }
-    | 'hessian(' args = function_arguments ')' { $value = NotImplementedFunction("hessian", "Hessian yet"); }
     /* Names that will not be functions, refused with the spelling to use: what they mean is
        ambiguous between sources, or is already written exactly another way. */
     | 'heaviside(' args = function_arguments ')' { $value = NotAFunctionHere("heaviside", "its value at 0 is 0, 1/2 or 1 by source; write iverson(x > 0), iverson(x >= 0) or (1 + sgn(x))/2"); }

Sources/AngouriMath/Core/Antlr/AngouriMath.interp

@@ -191,6 +191,9 @@ null
 'transpose('
 'dot('
 'cross('
+'laplacian('
+'jacobian('
+'hessian('
 'resultant('
 'conjugate('
 'conj('
@@ -214,9 +217,6 @@ null
 'factorialpower('
 'risingfactorial('
 'forwarddifference('
-'laplacian('
-'jacobian('
-'hessian('
 'heaviside('
 'unitstep('
 'isprime('

Sources/AngouriMath/Core/Antlr/AngouriMath.tokens

@@ -426,32 +426,32 @@ WS=237
 'transpose('=189
 'dot('=190
 'cross('=191
-'resultant('=192
-'conjugate('=193
-'conj('=194
-'arg('=195
-'Re('=196
-'Im('=197
-'re('=198
-'real('=199
-'im('=200
-'imag('=201
-'trunc('=202
-'zeta('=203
-'riemannzeta('=204
-'hurwitzzeta('=205
-'lambertw('=206
-'productlog('=207
-'harmonicnumber('=208
-'catalannumber('=209
-'multinomial('=210
-'fallingfactorial('=211
-'factorialpower('=212
-'risingfactorial('=213
-'forwarddifference('=214
-'laplacian('=215
-'jacobian('=216
-'hessian('=217
+'laplacian('=192
+'jacobian('=193
+'hessian('=194
+'resultant('=195
+'conjugate('=196
+'conj('=197
+'arg('=198
+'Re('=199
+'Im('=200
+'re('=201
+'real('=202
+'im('=203
+'imag('=204
+'trunc('=205
+'zeta('=206
+'riemannzeta('=207
+'hurwitzzeta('=208
+'lambertw('=209
+'productlog('=210
+'harmonicnumber('=211
+'catalannumber('=212
+'multinomial('=213
+'fallingfactorial('=214
+'factorialpower('=215
+'risingfactorial('=216
+'forwarddifference('=217
 'heaviside('=218
 'unitstep('=219
 'isprime('=220