mathjs/lib/esm/function/arithmetic/nthRoots.js

import { factory } from '../../utils/factory.js';
var name = 'nthRoots';
var dependencies = ['config', 'typed', 'divideScalar', 'Complex'];
export var createNthRoots = /* #__PURE__ */factory(name, dependencies, (_ref) => {
  var {
    typed,
    config,
    divideScalar,
    Complex
  } = _ref;

  /**
   * Each function here returns a real multiple of i as a Complex value.
   * @param  {number} val
   * @return {Complex} val, i*val, -val or -i*val for index 0, 1, 2, 3
   */
  // This is used to fix float artifacts for zero-valued components.
  var _calculateExactResult = [function realPos(val) {
    return new Complex(val, 0);
  }, function imagPos(val) {
    return new Complex(0, val);
  }, function realNeg(val) {
    return new Complex(-val, 0);
  }, function imagNeg(val) {
    return new Complex(0, -val);
  }];
  /**
   * Calculate the nth root of a Complex Number a using De Movire's Theorem.
   * @param  {Complex} a
   * @param  {number} root
   * @return {Array} array of n Complex Roots
   */

  function _nthComplexRoots(a, root) {
    if (root < 0) throw new Error('Root must be greater than zero');
    if (root === 0) throw new Error('Root must be non-zero');
    if (root % 1 !== 0) throw new Error('Root must be an integer');
    if (a === 0 || a.abs() === 0) return [new Complex(0, 0)];
    var aIsNumeric = typeof a === 'number';
    var offset; // determine the offset (argument of a)/(pi/2)

    if (aIsNumeric || a.re === 0 || a.im === 0) {
      if (aIsNumeric) {
        offset = 2 * +(a < 0); // numeric value on the real axis
      } else if (a.im === 0) {
        offset = 2 * +(a.re < 0); // complex value on the real axis
      } else {
        offset = 2 * +(a.im < 0) + 1; // complex value on the imaginary axis
      }
    }

    var arg = a.arg();
    var abs = a.abs();
    var roots = [];
    var r = Math.pow(abs, 1 / root);

    for (var k = 0; k < root; k++) {
      var halfPiFactor = (offset + 4 * k) / root;
      /**
       * If (offset + 4*k)/root is an integral multiple of pi/2
       * then we can produce a more exact result.
       */

      if (halfPiFactor === Math.round(halfPiFactor)) {
        roots.push(_calculateExactResult[halfPiFactor % 4](r));
        continue;
      }

      roots.push(new Complex({
        r: r,
        phi: (arg + 2 * Math.PI * k) / root
      }));
    }

    return roots;
  }
  /**
   * Calculate the nth roots of a value.
   * An nth root of a positive real number A,
   * is a positive real solution of the equation "x^root = A".
   * This function returns an array of complex values.
   *
   * Syntax:
   *
   *    math.nthRoots(x)
   *    math.nthRoots(x, root)
   *
   * Examples:
   *
   *    math.nthRoots(1)
   *    // returns [
   *    //   {re: 1, im: 0},
   *    //   {re: -1, im: 0}
   *    // ]
   *    nthRoots(1, 3)
   *    // returns [
   *    //   { re: 1, im: 0 },
   *    //   { re: -0.4999999999999998, im: 0.8660254037844387 },
   *    //   { re: -0.5000000000000004, im: -0.8660254037844385 }
   *    ]
   *
   * See also:
   *
   *    nthRoot, pow, sqrt
   *
   * @param {number | BigNumber | Fraction | Complex} x Number to be rounded
   * @return {number | BigNumber | Fraction | Complex}            Rounded value
   */


  return typed(name, {
    Complex: function Complex(x) {
      return _nthComplexRoots(x, 2);
    },
    'Complex, number': _nthComplexRoots
  });
});