import { factory } from '../../utils/factory.js'; import { isBigNumber, isComplex, isFraction } from '../../utils/is.js'; import { deepMap } from '../../utils/collection.js'; import { cbrtNumber } from '../../plain/number/index.js'; var name = 'cbrt'; var dependencies = ['config', 'typed', 'isNegative', 'unaryMinus', 'matrix', 'Complex', 'BigNumber', 'Fraction']; export var createCbrt = /* #__PURE__ */factory(name, dependencies, _ref => { var { config, typed, isNegative, unaryMinus, matrix, Complex, BigNumber, Fraction } = _ref; /** * Calculate the cubic root of a value. * * For matrices, the function is evaluated element wise. * * Syntax: * * math.cbrt(x) * math.cbrt(x, allRoots) * * Examples: * * math.cbrt(27) // returns 3 * math.cube(3) // returns 27 * math.cbrt(-64) // returns -4 * math.cbrt(math.unit('27 m^3')) // returns Unit 3 m * math.cbrt([27, 64, 125]) // returns [3, 4, 5] * * const x = math.complex('8i') * math.cbrt(x) // returns Complex 1.7320508075689 + i * math.cbrt(x, true) // returns Matrix [ * // 1.7320508075689 + i * // -1.7320508075689 + i * // -2i * // ] * * See also: * * square, sqrt, cube * * @param {number | BigNumber | Complex | Unit | Array | Matrix} x * Value for which to calculate the cubic root. * @param {boolean} [allRoots] Optional, false by default. Only applicable * when `x` is a number or complex number. If true, all complex * roots are returned, if false (default) the principal root is * returned. * @return {number | BigNumber | Complex | Unit | Array | Matrix} * Returns the cubic root of `x` */ return typed(name, { number: cbrtNumber, // note: signature 'number, boolean' is also supported, // created by typed as it knows how to convert number to Complex Complex: _cbrtComplex, 'Complex, boolean': _cbrtComplex, BigNumber: function BigNumber(x) { return x.cbrt(); }, Unit: _cbrtUnit, 'Array | Matrix': function ArrayMatrix(x) { // deep map collection, skip zeros since cbrt(0) = 0 return deepMap(x, this, true); } }); /** * Calculate the cubic root for a complex number * @param {Complex} x * @param {boolean} [allRoots] If true, the function will return an array * with all three roots. If false or undefined, * the principal root is returned. * @returns {Complex | Array. | Matrix.} Returns the cubic root(s) of x * @private */ function _cbrtComplex(x, allRoots) { // https://www.wikiwand.com/en/Cube_root#/Complex_numbers var arg3 = x.arg() / 3; var abs = x.abs(); // principal root: var principal = new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3).exp()); if (allRoots) { var all = [principal, new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 + Math.PI * 2 / 3).exp()), new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 - Math.PI * 2 / 3).exp())]; return config.matrix === 'Array' ? all : matrix(all); } else { return principal; } } /** * Calculate the cubic root for a Unit * @param {Unit} x * @return {Unit} Returns the cubic root of x * @private */ function _cbrtUnit(x) { if (x.value && isComplex(x.value)) { var result = x.clone(); result.value = 1.0; result = result.pow(1.0 / 3); // Compute the units result.value = _cbrtComplex(x.value); // Compute the value return result; } else { var negate = isNegative(x.value); if (negate) { x.value = unaryMinus(x.value); } // TODO: create a helper function for this var third; if (isBigNumber(x.value)) { third = new BigNumber(1).div(3); } else if (isFraction(x.value)) { third = new Fraction(1, 3); } else { third = 1 / 3; } var _result = x.pow(third); if (negate) { _result.value = unaryMinus(_result.value); } return _result; } } });