mathjs/lib/cjs/function/algebra/symbolicEqual.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.createSymbolicEqual = void 0;
var _is = require("../../utils/is.js");
var _factory = require("../../utils/factory.js");
var name = 'symbolicEqual';
var dependencies = ['parse', 'simplify', 'typed', 'OperatorNode'];
var createSymbolicEqual = exports.createSymbolicEqual = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
  var parse = _ref.parse,
    simplify = _ref.simplify,
    typed = _ref.typed,
    OperatorNode = _ref.OperatorNode;
  /**
   * Attempts to determine if two expressions are symbolically equal, i.e.
   * one is the result of valid algebraic manipulations on the other.
   * Currently, this simply checks if the difference of the two expressions
   * simplifies down to 0. So there are two important caveats:
   * 1. whether two expressions are symbolically equal depends on the
   *     manipulations allowed. Therefore, this function takes an optional
   *     third argument, which are the options that control the behavior
   *     as documented for the `simplify()` function.
   * 2. it is in general intractable to find the minimal simplification of
   *     an arbitrarily complicated expression. So while a `true` value
   *     of `symbolicEqual` ensures that the two expressions can be manipulated
   *     to match each other, a `false` value does not absolutely rule this out.
   *
   * Syntax:
   *
   *     math.symbolicEqual(expr1, expr2)
   *     math.symbolicEqual(expr1, expr2, options)
   *
   * Examples:
   *
   *     math.symbolicEqual('x*y', 'y*x') // Returns true
   *     math.symbolicEqual('x*y', 'y*x', {context: {multiply: {commutative: false}}}) // Returns false
   *     math.symbolicEqual('x/y', '(y*x^(-1))^(-1)') // Returns true
   *     math.symbolicEqual('abs(x)','x') // Returns false
   *     math.symbolicEqual('abs(x)','x', simplify.positiveContext) // Returns true
   *
   * See also:
   *
   *     simplify, evaluate
   *
   * @param {Node|string} expr1  The first expression to compare
   * @param {Node|string} expr2  The second expression to compare
   * @param {Object} [options] Optional option object, passed to simplify
   * @returns {boolean}
   *     Returns true if a valid manipulation making the expressions equal
   *     is found.
   */
  function _symbolicEqual(e1, e2) {
    var options = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : {};
    var diff = new OperatorNode('-', 'subtract', [e1, e2]);
    var simplified = simplify(diff, {}, options);
    return (0, _is.isConstantNode)(simplified) && !simplified.value;
  }
  return typed(name, {
    'Node, Node': _symbolicEqual,
    'Node, Node, Object': _symbolicEqual
  });
});