fix #3094: function derivative mutates the input expression when it…

… fails

HISTORY.md

@@ -6,6 +6,7 @@
 - Fix #3087: extend function `mod` with support for negative divisors in when
   using `BigNumber` or `Fraction`.
 - Fix #3092: a typo in an error message when converting a string into a number.
+- Fix #3094: function `derivative` mutates the input expression when it fails.
 
 
 # 2023-10-26, 12.0.0

src/function/algebra/derivative.js

@@ -226,10 +226,6 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
     },
 
     'FunctionNode, Object': function (node, constNodes) {
-      if (node.args.length !== 1) {
-        funcArgsCheck(node)
-      }
-
       if (constNodes[node] !== undefined) {
         return createConstantNode(0)
       }
@@ -303,9 +299,12 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
           }
           break
         case 'pow':
-          constNodes[arg1] = constNodes[node.args[1]]
-          // Pass to pow operator node parser
-          return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes)
+          if (node.args.length === 2) {
+            constNodes[arg1] = constNodes[node.args[1]]
+            // Pass to pow operator node parser
+            return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes)
+          }
+          break
         case 'exp':
           // d/dx(e^x) = e^x
           funcDerivative = new FunctionNode('exp', [arg0.clone()])
@@ -563,7 +562,9 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
           ])
           break
         case 'gamma': // Needs digamma function, d/dx(gamma(x)) = gamma(x)digamma(x)
-        default: throw new Error('Function "' + node.name + '" is not supported by derivative, or a wrong number of arguments is passed')
+        default:
+          throw new Error('Cannot process function "' + node.name + '" in derivative: ' +
+          'the function is not supported, undefined, or the number of arguments passed to it are not supported')
       }
 
       let op, func
@@ -740,35 +741,11 @@ export const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({
         ])
       }
 
-      throw new Error('Operator "' + node.op + '" is not supported by derivative, or a wrong number of arguments is passed')
+      throw new Error('Cannot process operator "' + node.op + '" in derivative: ' +
+        'the operator is not supported, undefined, or the number of arguments passed to it are not supported')
     }
   })
 
-  /**
-   * Ensures the number of arguments for a function are correct,
-   * and will throw an error otherwise.
-   *
-   * @param {FunctionNode} node
-   */
-  function funcArgsCheck (node) {
-    // TODO add min, max etc
-    if ((node.name === 'log' || node.name === 'nthRoot' || node.name === 'pow') && node.args.length === 2) {
-      return
-    }
-
-    // There should be an incorrect number of arguments if we reach here
-
-    // Change all args to constants to avoid unidentified
-    // symbol error when compiling function
-    for (let i = 0; i < node.args.length; ++i) {
-      node.args[i] = createConstantNode(0)
-    }
-
-    node.compile().evaluate()
-
-    throw new Error('Function "' + node.name + '" is not supported by derivative, or a wrong number of arguments is passed')
-  }
-
   /**
    * Helper function to create a constant node with a specific type
    * (number, BigNumber, Fraction)

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

@@ -229,30 +229,32 @@ describe('derivative', function () {
     assert.throws(function () {
       const node = new OperatorNode('/', 'myDivide', [c12, c4, x])
       derivative(node, 'x')
-    }, /Error: Operator "\/" is not supported by derivative, or a wrong number of arguments is passed/)
+    }, /Error: Cannot process operator "\/" in derivative: the operator is not supported, undefined, or the number of arguments passed to it are not supported/)
 
     assert.throws(function () {
       const node = new OperatorNode('^', 'myPow', [c12, c4, x])
       derivative(node, 'x')
-    }, /Error: Operator "\^" is not supported by derivative, or a wrong number of arguments is passed/)
+    }, /Error: Cannot process operator "\^" in derivative: the operator is not supported, undefined, or the number of arguments passed to it are not supported/)
   })
 
-  it('should throw error if expressions contain unsupported operators or functions', function () {
-    assert.throws(function () { derivative('x << 2', 'x') }, /Error: Operator "<<" is not supported by derivative, or a wrong number of arguments is passed/)
-    assert.throws(function () { derivative('subset(x)', 'x') }, /Error: Function "subset" is not supported by derivative, or a wrong number of arguments is passed/)
-    assert.throws(function () { derivative('max(x)', 'x') }, /Error: Function "max" is not supported by derivative, or a wrong number of arguments is passed/)
-    assert.throws(function () { derivative('max(x, y)', 'x') }, /Error: Function "max" is not supported by derivative, or a wrong number of arguments is passed/)
-    assert.throws(function () { derivative('max(x, 1)', 'x') }, /Error: Function "max" is not supported by derivative, or a wrong number of arguments is passed/)
-    assert.throws(function () { derivative('add(2,3,x)', 'x') }, /Error: Function "add" is not supported by derivative, or a wrong number of arguments is passed/)
+  it('should not mutate the input expression', function () {
+    const expr = math.parse('min(x, y)')
+    assert.strictEqual(expr.toString(), 'min(x, y)')
+
+    assert.throws(() => { math.derivative(expr, 'x') },
+      /Error: Cannot process function "min" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/
+    )
+
+    assert.strictEqual(expr.toString(), 'min(x, y)')
   })
 
-  it('should have controlled behavior on arguments errors', function () {
-    assert.throws(function () {
-      derivative('sqrt()', 'x')
-    }, /TypeError: Too few arguments in function sqrt \(expected: number or Complex or BigNumber or Unit or Fraction or string or boolean, index: 0\)/)
-    assert.throws(function () {
-      derivative('sqrt(12, 2x)', 'x')
-    }, /TypeError: Too many arguments in function sqrt \(expected: 1, actual: 2\)/)
+  it('should throw error if expressions contain unsupported operators or functions', function () {
+    assert.throws(function () { derivative('x << 2', 'x') }, /Error: Cannot process operator "<<" in derivative: the operator is not supported, undefined, or the number of arguments passed to it are not supported/)
+    assert.throws(function () { derivative('subset(x)', 'x') }, /Error: Cannot process function "subset" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
+    assert.throws(function () { derivative('max(x)', 'x') }, /Error: Cannot process function "max" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
+    assert.throws(function () { derivative('max(x, y)', 'x') }, /Error: Cannot process function "max" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
+    assert.throws(function () { derivative('max(x, 1)', 'x') }, /Error: Cannot process function "max" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
+    assert.throws(function () { derivative('add(2,3,x)', 'x') }, /Error: Cannot process function "add" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
   })
 
   it('should throw error for incorrect argument types', function () {
@@ -279,6 +281,12 @@ describe('derivative', function () {
     }, /TypeError: Too many arguments in function derivative \(expected: 3, actual: 5\)/)
   })
 
+  it('should throw error in case of an unknown function', function () {
+    assert.throws(function () {
+      derivative('foo(x)', 'x')
+    }, /Error: Cannot process function "foo" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported/)
+  })
+
   it('should LaTeX expressions involving derivative', function () {
     compareString(math.parse('derivative(x*y,x)').toTex(), '{d\\over dx}\\left[ x\\cdot y\\right]')
     compareString(math.parse('derivative("x*y",x)').toTex(), '{d\\over dx}\\left[x * y\\right]')