Initial Commit

lib/math/fractions.ts

@@ -0,0 +1,107 @@
+export function gcd(a: number, b: number): number {
+  a = Math.abs(a);
+  b = Math.abs(b);
+  while (b) {
+    [a, b] = [b, a % b];
+  }
+  return a;
+}
+
+export function lcm(a: number, b: number): number {
+  return Math.abs(a * b) / gcd(a, b);
+}
+
+export function simplify(num: number, den: number): [number, number] {
+  if (den === 0) return [num, den];
+  const g = gcd(Math.abs(num), Math.abs(den));
+  const sign = den < 0 ? -1 : 1;
+  return [(num / g) * sign, (den / g) * sign];
+}
+
+export function add(
+  n1: number, d1: number,
+  n2: number, d2: number,
+): [number, number] {
+  const num = n1 * d2 + n2 * d1;
+  const den = d1 * d2;
+  return simplify(num, den);
+}
+
+export function subtract(
+  n1: number, d1: number,
+  n2: number, d2: number,
+): [number, number] {
+  const num = n1 * d2 - n2 * d1;
+  const den = d1 * d2;
+  return simplify(num, den);
+}
+
+export function multiply(
+  n1: number, d1: number,
+  n2: number, d2: number,
+): [number, number] {
+  return simplify(n1 * n2, d1 * d2);
+}
+
+export function divide(
+  n1: number, d1: number,
+  n2: number, d2: number,
+): [number, number] {
+  return simplify(n1 * d2, d1 * n2);
+}
+
+export function toDecimal(num: number, den: number): number {
+  return num / den;
+}
+
+export function fromDecimal(decimal: number, precision: number = 6): [number, number] {
+  const str = decimal.toFixed(precision);
+  const parts = str.split(".");
+  if (!parts[1]) return [parseInt(parts[0]), 1];
+  const den = Math.pow(10, parts[1].length);
+  const num = Math.round(decimal * den);
+  return simplify(num, den);
+}
+
+export function compare(
+  n1: number, d1: number,
+  n2: number, d2: number,
+): -1 | 0 | 1 {
+  const diff = n1 * d2 - n2 * d1;
+  if (diff > 0) return 1;
+  if (diff < 0) return -1;
+  return 0;
+}
+
+export function fractionOfQuantity(num: number, den: number, quantity: number): number {
+  return (num / den) * quantity;
+}
+
+export function wholeFromFraction(num: number, den: number, part: number): number {
+  return (part * den) / num;
+}
+
+export function isProper(num: number, den: number): boolean {
+  return Math.abs(num) < Math.abs(den);
+}
+
+export function toMixed(num: number, den: number): [number, number, number] {
+  const whole = Math.floor(Math.abs(num) / Math.abs(den));
+  const remainder = Math.abs(num) % Math.abs(den);
+  const sign = (num < 0) !== (den < 0) ? -1 : 1;
+  return [whole * sign, remainder, Math.abs(den)];
+}
+
+export function fromMixed(whole: number, num: number, den: number): [number, number] {
+  const sign = whole < 0 ? -1 : 1;
+  return [sign * (Math.abs(whole) * den + num), den];
+}
+
+export function isSimplified(num: number, den: number): boolean {
+  return gcd(Math.abs(num), Math.abs(den)) === 1;
+}
+
+export function toKatex(num: number, den: number): string {
+  if (den === 1) return `${num}`;
+  return `\\frac{${num}}{${den}}`;
+}