fix: #3253 cannot use identifiers containing special characters in fu…

…nction `derivative`

src/core/function/typed.js

@@ -124,6 +124,7 @@ export const createTyped = /* #__PURE__ */ factory('typed', dependencies, functi
     // string starting with an alphabetic character. It is used (at least)
     // in the definition of the derivative() function, as the argument telling
     // what to differentiate over must (currently) be a variable.
+    // TODO: deprecate the identifier type (it's not used anymore, see https://github.com/josdejong/mathjs/issues/3253)
     {
       name: 'identifier',
       test: s => isString && /^\p{L}[\p{L}\d]*$/u.test(s)

src/function/algebra/derivative.js

@@ -77,12 +77,20 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
     return options.simplify ? simplify(res) : res
   }
 
-  typed.addConversion(
-    { from: 'identifier', to: 'SymbolNode', convert: parse })
+  function parseIdentifier (string) {
+    const symbol = parse(string)
+    if (!symbol.isSymbolNode) {
+      throw new TypeError('Invalid variable. ' +
+        `Cannot parse ${JSON.stringify(string)} into a variable in function derivative`)
+    }
+    return symbol
+  }
 
   const derivative = typed(name, {
     'Node, SymbolNode': plainDerivative,
-    'Node, SymbolNode, Object': plainDerivative
+    'Node, SymbolNode, Object': plainDerivative,
+    'Node, string': (node, symbol) => plainDerivative(node, parseIdentifier(symbol)),
+    'Node, string, Object': (node, symbol, options) => plainDerivative(node, parseIdentifier(symbol), options)
 
     /* TODO: implement and test syntax with order of derivatives -> implement as an option {order: number}
     'Node, SymbolNode, ConstantNode': function (expr, variable, {order}) {
@@ -97,9 +105,6 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
     */
   })
 
-  typed.removeConversion(
-    { from: 'identifier', to: 'SymbolNode', convert: parse })
-
   derivative._simplify = true
 
   derivative.toTex = function (deriv) {

test/unit-tests/function/algebra/derivative.test.js

@@ -202,6 +202,12 @@ describe('derivative', function () {
     compareString(derivative(math.parse('x^2'), math.parse('x')), '2 * x')
   })
 
+  it('should accept string input containing special characters', function () {
+    // NOTE: we use `parse` here on purpose to see whether derivative accepts it
+    compareString(derivative('1 + x', 'x'), '1')
+    compareString(derivative('1 + $x', '$x'), '1')
+  })
+
   describe('expression parser', function () {
     it('should evaluate a derivative containing string value', function () {
       const res = math.evaluate('derivative("x^2", "x")')
@@ -260,7 +266,7 @@ describe('derivative', function () {
   it('should throw error for incorrect argument types', function () {
     assert.throws(function () {
       derivative('42', '42')
-    }, /TypeError: Unexpected type of argument in function derivative \(expected: SymbolNode or identifier, actual: string, index: 1\)/)
+    }, /TypeError: Invalid variable. Cannot parse "42" into a variable in function derivative/)
 
     assert.throws(function () {
       derivative('[1, 2; 3, 4]', 'x')
@@ -274,7 +280,7 @@ describe('derivative', function () {
   it('should throw error if incorrect number of arguments', function () {
     assert.throws(function () {
       derivative('x + 2')
-    }, /TypeError: Too few arguments in function derivative \(expected: SymbolNode or identifier, index: 1\)/)
+    }, /TypeError: Too few arguments in function derivative \(expected: string or SymbolNode or boolean, index: 1\)/)
 
     assert.throws(function () {
       derivative('x + 2', 'x', {}, true, 42)