学習環境
- Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
- Windows 10 Pro (OS)
- Nebo(Windows アプリ)
- iPad Pro + Apple Pencil
- MyScript Nebo(iPad アプリ)
- 参考書籍
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)、2(複素平面)、問題3.を取り組んでみる。
幾何学的解釈。
平行四辺形の2つの対角線の2乗の和は、2つの辺の2乗の和の2倍と等しい。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, I a, b = symbols('a, b', imag=True) l = abs(a + b) ** 2 + abs(a - b) ** 2 r = 2 * (abs(a) ** 2 + abs(b) ** 2) for t in [l, r, l.factor() == r.factor()]: pprint(t) print() a, b, c, d = symbols('a, b, c, d', real=True) za = a + b * I zb = c + d * I l = abs(za + zb) ** 2 + abs(za - zb) ** 2 r = 2 * (abs(za) ** 2 + abs(zb) ** 2) for t in [l, r, l == r]: pprint(t) print()
入出力結果(Terminal, Jupyter(IPython))
$ ./sample3.py 2 2 │a - b│ + │a + b│ 2 2 2⋅│a│ + 2⋅│b│ False 2 2 2 2 2⋅a + 2⋅b + 2⋅c + 2⋅d 2 2 2 2 2⋅a + 2⋅b + 2⋅c + 2⋅d True $
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="0.5"> <label for="dx">dx = </label> <input id="dx" type="number" min="0" step="0.0001" value="0.001"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-10"> <label for="x2">x2 = </label> <input id="x2" type="number" value="10"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-10"> <label for="y2">y2 = </label> <input id="y2" type="number" value="10"> <br> <label for="a0">a0 = </label> <input id="a0" type="number" step="1" value="1"> <label for="b0">b0 = </label> <input id="b0" type="number" step="1" value="4"> <br> <label for="c0">c0 = </label> <input id="c0" type="number" step="1" value="2"> <label for="d0">d0 = </label> <input id="d0" type="number" step="1" value="3"> <button id="draw0">draw</button> <button id="clear0">clear</button> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script> <script src="sample3.js"></script>
JavaScript
let div0 = document.querySelector('#graph0'), pre0 = document.querySelector('#output0'), width = 600, height = 600, padding = 50, btn0 = document.querySelector('#draw0'), btn1 = document.querySelector('#clear0'), input_r = document.querySelector('#r0'), input_dx = document.querySelector('#dx'), input_x1 = document.querySelector('#x1'), input_x2 = document.querySelector('#x2'), input_y1 = document.querySelector('#y1'), input_y2 = document.querySelector('#y2'), input_a0 = document.querySelector('#a0'), input_b0 = document.querySelector('#b0'), input_c0 = document.querySelector('#c0'), input_d0 = document.querySelector('#d0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_a0, input_b0, input_c0, input_d0], p = (x) => pre0.textContent += x + '\n', range = (start, end, step=1) => { let res = []; for (let i = start; i < end; i += step) { res.push(i); } return res; }; let fx = (a, x, y) => x * Math.cos(a) - y * Math.sin(a), fy = (a, x, y) => x * Math.sin(a) + y * Math.cos(a); let draw = () => { pre0.textContent = ''; let r = parseFloat(input_r.value), dx = parseFloat(input_dx.value), x1 = parseFloat(input_x1.value), x2 = parseFloat(input_x2.value), y1 = parseFloat(input_y1.value), y2 = parseFloat(input_y2.value), a0 = parseFloat(input_a0.value), b0 = parseFloat(input_b0.value), c0 = parseFloat(input_c0.value), d0 = parseFloat(input_d0.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [[0, 0, a0, b0, 'red'], [0, 0, c0, d0, 'green'], [0, 0, a0 + c0, b0 + d0, 'blue']], fns = [], fns1 = [], fns2 = []; fns .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx) { let y = f(x); points.push([x, y, color]); } }); fns2 .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx0) { let g = f(x); lines.push([x1, g(x1), x2, g(x2), color]); } }); let xscale = d3.scaleLinear() .domain([x1, x2]) .range([padding, width - padding]); let yscale = d3.scaleLinear() .domain([y1, y2]) .range([height - padding, padding]); let xaxis = d3.axisBottom().scale(xscale); let yaxis = d3.axisLeft().scale(yscale); div0.innerHTML = ''; let svg = d3.select('#graph0') .append('svg') .attr('width', width) .attr('height', height); svg.selectAll('line') .data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines)) .enter() .append('line') .attr('x1', (d) => xscale(d[0])) .attr('y1', (d) => yscale(d[1])) .attr('x2', (d) => xscale(d[2])) .attr('y2', (d) => yscale(d[3])) .attr('stroke', (d) => d[4] || 'black'); svg.selectAll('circle') .data(points) .enter() .append('circle') .attr('cx', (d) => xscale(d[0])) .attr('cy', (d) => yscale(d[1])) .attr('r', r) .attr('fill', (d) => d[2] || 'green'); svg.append('g') .attr('transform', `translate(0, ${height - padding})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${padding}, 0)`) .call(yaxis); [fns, fns1, fns2].forEach((fs) => p(fs.join('\n'))); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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