Rational numbers

2023-07-22 23:25:53 +02:00
parent 262dca3a4d
commit 7ee6d469b4
13 changed files with 16515 additions and 0 deletions
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+import { Rational } from "./rational-numbers";
+
+describe("Addition", () => {
+  it("Add two positive rational numbers", () => {
+    const expected = new Rational(7, 6);
+    expect(new Rational(1, 2).add(new Rational(2, 3))).toEqual(expected);
+  });
+
+  it("Add a positive rational number and a negative rational number", () => {
+    const expected = new Rational(-1, 6);
+    expect(new Rational(1, 2).add(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  it("Add two negative rational numbers", () => {
+    const expected = new Rational(-7, 6);
+    expect(new Rational(-1, 2).add(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  it("Add a rational number to its additive inverse", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(1, 2).add(new Rational(-1, 2))).toEqual(expected);
+  });
+});
+
+describe("Subtraction", () => {
+  xit("Subtract two positive rational numbers", () => {
+    const expected = new Rational(-1, 6);
+    expect(new Rational(1, 2).sub(new Rational(2, 3))).toEqual(expected);
+  });
+
+  xit("Subtract a positive rational number and a negative rational number", () => {
+    const expected = new Rational(7, 6);
+    expect(new Rational(1, 2).sub(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  xit("Subtract two negative rational numbers", () => {
+    const expected = new Rational(1, 6);
+    expect(new Rational(-1, 2).sub(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  xit("Subtract a rational number from itself", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(1, 2).sub(new Rational(1, 2))).toEqual(expected);
+  });
+});
+
+describe("Multiplication", () => {
+  xit("Multiply two positive rational numbers", () => {
+    const expected = new Rational(1, 3);
+    expect(new Rational(1, 2).mul(new Rational(2, 3))).toEqual(expected);
+  });
+
+  xit("Multiply a negative rational number by a positive rational number", () => {
+    const expected = new Rational(-1, 3);
+    expect(new Rational(-1, 2).mul(new Rational(2, 3))).toEqual(expected);
+  });
+
+  xit("Multiply two negative rational numbers", () => {
+    const expected = new Rational(1, 3);
+    expect(new Rational(-1, 2).mul(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  xit("Multiply a rational number by its reciprocal", () => {
+    const expected = new Rational(1, 1);
+    expect(new Rational(1, 2).mul(new Rational(2, 1))).toEqual(expected);
+  });
+
+  xit("Multiply a rational number by 1", () => {
+    const expected = new Rational(1, 2);
+    expect(new Rational(1, 2).mul(new Rational(1, 1))).toEqual(expected);
+  });
+
+  xit("Multiply a rational number by 0", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(1, 2).mul(new Rational(0, 1))).toEqual(expected);
+  });
+});
+
+describe("Division", () => {
+  xit("Divide two positive rational numbers", () => {
+    const expected = new Rational(3, 4);
+    expect(new Rational(1, 2).div(new Rational(2, 3))).toEqual(expected);
+  });
+
+  xit("Divide a positive rational number by a negative rational number", () => {
+    const expected = new Rational(-3, 4);
+    expect(new Rational(1, 2).div(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  xit("Divide two negative rational numbers", () => {
+    const expected = new Rational(3, 4);
+    expect(new Rational(-1, 2).div(new Rational(-2, 3))).toEqual(expected);
+  });
+
+  xit("Divide a rational number by 1", () => {
+    const expected = new Rational(1, 2);
+    expect(new Rational(1, 2).div(new Rational(1, 1))).toEqual(expected);
+  });
+});
+
+describe("Absolute value", () => {
+  xit("Absolute value of a positive rational number", () => {
+    const expected = new Rational(1, 2);
+    expect(new Rational(1, 2).abs()).toEqual(expected);
+  });
+
+  xit("Absolute value of a negative rational number", () => {
+    const expected = new Rational(1, 2);
+    expect(new Rational(-1, 2).abs()).toEqual(expected);
+  });
+
+  xit("Absolute value of zero", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(0, 1).abs()).toEqual(expected);
+  });
+});
+
+describe("Exponentiation of a rational number", () => {
+  xit("Raise a positive rational number to a positive integer power", () => {
+    const expected = new Rational(1, 8);
+    expect(new Rational(1, 2).exprational(3)).toEqual(expected);
+  });
+
+  xit("Raise a negative rational number to a positive integer power", () => {
+    const expected = new Rational(-1, 8);
+    expect(new Rational(-1, 2).exprational(3)).toEqual(expected);
+  });
+
+  xit("Raise zero to an integer power", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(0, 1).exprational(5)).toEqual(expected);
+  });
+
+  xit("Raise one to an integer power", () => {
+    const expected = new Rational(1, 1);
+    expect(new Rational(1, 1).exprational(4)).toEqual(expected);
+  });
+
+  xit("Raise a positive rational number to the power of zero", () => {
+    const expected = new Rational(1, 1);
+    expect(new Rational(1, 2).exprational(0)).toEqual(expected);
+  });
+
+  xit("Raise a negative rational number to the power of zero", () => {
+    const expected = new Rational(1, 1);
+    expect(new Rational(-1, 2).exprational(0)).toEqual(expected);
+  });
+});
+
+describe("Exponentiation of a real number to a rational number", () => {
+  xit("Raise a real number to a positive rational number", () => {
+    const expected = 16.0;
+    expect(new Rational(4, 3).expreal(8)).toEqual(expected);
+  });
+
+  xit("Raise a real number to a negative rational number", () => {
+    const expected = 1.0 / 3.0;
+    expect(new Rational(-1, 2).expreal(9)).toBeCloseTo(expected, 15);
+  });
+
+  xit("Raise a real number to a zero rational number", () => {
+    const expected = 1.0;
+    expect(new Rational(0, 1).expreal(2)).toEqual(expected);
+  });
+});
+
+describe("Reduction to lowest terms", () => {
+  xit("Reduce a positive rational number to lowest terms", () => {
+    const expected = new Rational(1, 2);
+    expect(new Rational(2, 4).reduce()).toEqual(expected);
+  });
+
+  xit("Reduce a negative rational number to lowest terms", () => {
+    const expected = new Rational(-2, 3);
+    expect(new Rational(-4, 6).reduce()).toEqual(expected);
+  });
+
+  xit("Reduce a rational number with a negative denominator to lowest terms", () => {
+    const expected = new Rational(-1, 3);
+    expect(new Rational(3, -9).reduce()).toEqual(expected);
+  });
+
+  xit("Reduce zero to lowest terms", () => {
+    const expected = new Rational(0, 1);
+    expect(new Rational(0, 6).reduce()).toEqual(expected);
+  });
+
+  xit("Reduce an integer to lowest terms", () => {
+    const expected = new Rational(-2, 1);
+    expect(new Rational(-14, 7).reduce()).toEqual(expected);
+  });
+
+  xit("Reduce one to lowest terms", () => {
+    const expected = new Rational(1, 1);
+    expect(new Rational(13, 13).reduce()).toEqual(expected);
+  });
+});