数学 - 線型代数 - JavaScript - 複素数、複素ベクトル空間(複素数, 共役複素数、四則演算)

線型代数入門

学習環境/開発環境

• Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
• Windows 10 Pro (OS)
• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax
• OS X El Capitan - Apple (OS)
• Emacs (Text Editor)
• JavaScript (プログラミング言語)
• kjs-math-number (JavaScript Library)
• Safari(Web browser)

線型代数入門 (松坂 和夫(著)、岩波書店)の第4章(複素数、複素ベクトル空間)、1(複素数)、問2.を取り組んでみる。

問2.

$\begin{array}{l}\alpha =a+bi,\beta =c+di\\ \\ \alpha \pm \beta =\left(a\pm c\right)+\left(b\pm d\right)i\\ \overline{\alpha }\pm \overline{\beta }=\left(a+c\right)-\left(b\pm d\right)i\\ \\ \alpha \beta =\left(ac-bd\right)+\left(ad-bc\right)i\\ \overline{\alpha }\overline{\beta }=\left(a-bi\right)\left(c-di\right)\\ =\left(ac-bd\right)-\left(ad+bc\right)i\\ \\ \frac{\alpha }{\beta }=\frac{a+bi}{c+di}\\ =\frac{\left(a+bi\right)\left(c-di\right)}{c^2+d^2}\\ =\frac{\left(ac+bd\right)-\left(ad-bc\right)i}{c^2+d^2}\\ \frac{\overline{\alpha }}{\overline{\beta }}=\frac{a-bi}{c-di}\\ =\frac{\left(a-bi\right)\left(c+di\right)}{c^2+d^2}\\ =\frac{\left(ac+bd\right)+\left(ad-bc\right)i}{c^2+d^2}\end{array}$

number.js で確認。

JavaScript

コード(Emacs)

(function () {
    'use strict';
    var nl = '<br><br>',
        div_output = document.querySelector('#output0'),
        button_calc = document.querySelector('#calc0'),
        calc;

    calc = function () {
        var sign1 = Math.random() < 0.5 ? 1 : -1,
            sign2 = Math.random() < 0.5 ? 1 : -1,
            sign3 = Math.random() < 0.5 ? 1 : -1,
            sign4 = Math.random() < 0.5 ? 1 : -1,
            a = new Complex(sign1 * Math.random() * 100,
                            sign2 * Math.random() * 100),
            b = new Complex(sign3 * Math.random() * 100,
                            sign4 * Math.random() * 100),
            z1,
            z2,
            z = [],
            output = '';    
        
        z1 = a.add(b).conjugate();
        z2 = a.conjugate().add(b.conjugate());
        z[0] = ['+', z1, z2];

        z1 = a.sub(b).conjugate();
        z2 = a.conjugate().sub(b.conjugate());
        z[1] = ['-', z1, z2];

        z1 = a.mul(b).conjugate();
        z2 = a.conjugate().mul(b.conjugate());
        z[2] = ['*', z1, z2];

        z1 = a.div(b).conjugate();
        z2 = a.conjugate().div(b.conjugate());
        z[3] = ['/', z1, z2];

        output +=
            'a = <math>' + a + '</math>' + nl +
            'b = <math>' + b + '</math>' + nl;

        z.forEach(function (x) {
            output += x[0] + ': ' + x[1].isEqual(x[2]) + nl;
        });

        div_output.innerHTML = output;
    };

    button_calc.onclick = calc;
}());