feat:node-modules

node_modules/mathjs/lib/cjs/function/algebra/polynomialRoot.js

@@ -0,0 +1,128 @@
+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.createPolynomialRoot = void 0;
+var _factory = require("../../utils/factory.js");
+const name = 'polynomialRoot';
+const dependencies = ['typed', 'isZero', 'equalScalar', 'add', 'subtract', 'multiply', 'divide', 'sqrt', 'unaryMinus', 'cbrt', 'typeOf', 'im', 're'];
+const createPolynomialRoot = exports.createPolynomialRoot = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
+  let {
+    typed,
+    isZero,
+    equalScalar,
+    add,
+    subtract,
+    multiply,
+    divide,
+    sqrt,
+    unaryMinus,
+    cbrt,
+    typeOf,
+    im,
+    re
+  } = _ref;
+  /**
+   * Finds the numerical values of the distinct roots of a polynomial with real or complex coefficients.
+   * Currently operates only on linear, quadratic, and cubic polynomials using the standard
+   * formulas for the roots.
+   *
+   * Syntax:
+   *
+   *     math.polynomialRoot(constant, linearCoeff, quadraticCoeff, cubicCoeff)
+   *
+   * Examples:
+   *     // linear
+   *     math.polynomialRoot(6, 3)                                        // [-2]
+   *     math.polynomialRoot(math.complex(6,3), 3)                        // [-2 - i]
+   *     math.polynomialRoot(math.complex(6,3), math.complex(2,1))        // [-3 + 0i]
+   *     // quadratic
+   *     math.polynomialRoot(2, -3, 1)                                    // [2, 1]
+   *     math.polynomialRoot(8, 8, 2)                                     // [-2]
+   *     math.polynomialRoot(-2, 0, 1)                                    // [1.4142135623730951, -1.4142135623730951]
+   *     math.polynomialRoot(2, -2, 1)                                    // [1 + i, 1 - i]
+   *     math.polynomialRoot(math.complex(1,3), math.complex(-3, -2), 1)  // [2 + i, 1 + i]
+   *     // cubic
+   *     math.polynomialRoot(-6, 11, -6, 1)                               // [1, 3, 2]
+   *     math.polynomialRoot(-8, 0, 0, 1)                                 // [-1 - 1.7320508075688774i, 2, -1 + 1.7320508075688774i]
+   *     math.polynomialRoot(0, 8, 8, 2)                                  // [0, -2]
+   *     math.polynomialRoot(1, 1, 1, 1)                                  // [-1 + 0i, 0 - i, 0 + i]
+   *
+   * See also:
+   *     cbrt, sqrt
+   *
+   * @param {... number | Complex} coeffs
+   *     The coefficients of the polynomial, starting with with the constant coefficent, followed
+   *     by the linear coefficient and subsequent coefficients of increasing powers.
+   * @return {Array} The distinct roots of the polynomial
+   */
+
+  return typed(name, {
+    'number|Complex, ...number|Complex': (constant, restCoeffs) => {
+      const coeffs = [constant, ...restCoeffs];
+      while (coeffs.length > 0 && isZero(coeffs[coeffs.length - 1])) {
+        coeffs.pop();
+      }
+      if (coeffs.length < 2) {
+        throw new RangeError(`Polynomial [${constant}, ${restCoeffs}] must have a non-zero non-constant coefficient`);
+      }
+      switch (coeffs.length) {
+        case 2:
+          // linear
+          return [unaryMinus(divide(coeffs[0], coeffs[1]))];
+        case 3:
+          {
+            // quadratic
+            const [c, b, a] = coeffs;
+            const denom = multiply(2, a);
+            const d1 = multiply(b, b);
+            const d2 = multiply(4, a, c);
+            if (equalScalar(d1, d2)) return [divide(unaryMinus(b), denom)];
+            const discriminant = sqrt(subtract(d1, d2));
+            return [divide(subtract(discriminant, b), denom), divide(subtract(unaryMinus(discriminant), b), denom)];
+          }
+        case 4:
+          {
+            // cubic, cf. https://en.wikipedia.org/wiki/Cubic_equation
+            const [d, c, b, a] = coeffs;
+            const denom = unaryMinus(multiply(3, a));
+            const D0_1 = multiply(b, b);
+            const D0_2 = multiply(3, a, c);
+            const D1_1 = add(multiply(2, b, b, b), multiply(27, a, a, d));
+            const D1_2 = multiply(9, a, b, c);
+            if (equalScalar(D0_1, D0_2) && equalScalar(D1_1, D1_2)) {
+              return [divide(b, denom)];
+            }
+            const Delta0 = subtract(D0_1, D0_2);
+            const Delta1 = subtract(D1_1, D1_2);
+            const discriminant1 = add(multiply(18, a, b, c, d), multiply(b, b, c, c));
+            const discriminant2 = add(multiply(4, b, b, b, d), multiply(4, a, c, c, c), multiply(27, a, a, d, d));
+            if (equalScalar(discriminant1, discriminant2)) {
+              return [divide(subtract(multiply(4, a, b, c), add(multiply(9, a, a, d), multiply(b, b, b))), multiply(a, Delta0)),
+              // simple root
+              divide(subtract(multiply(9, a, d), multiply(b, c)), multiply(2, Delta0)) // double root
+              ];
+            }
+            // OK, we have three distinct roots
+            let Ccubed;
+            if (equalScalar(D0_1, D0_2)) {
+              Ccubed = Delta1;
+            } else {
+              Ccubed = divide(add(Delta1, sqrt(subtract(multiply(Delta1, Delta1), multiply(4, Delta0, Delta0, Delta0)))), 2);
+            }
+            const allRoots = true;
+            const rawRoots = cbrt(Ccubed, allRoots).toArray().map(C => divide(add(b, C, divide(Delta0, C)), denom));
+            return rawRoots.map(r => {
+              if (typeOf(r) === 'Complex' && equalScalar(re(r), re(r) + im(r))) {
+                return re(r);
+              }
+              return r;
+            });
+          }
+        default:
+          throw new RangeError(`only implemented for cubic or lower-order polynomials, not ${coeffs}`);
+      }
+    }
+  });
+});