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
数学読本〈6〉線形写像・1次変換/数論へのプレリュード/集合論へのプレリュード/εとδ/落ち穂拾い など(松坂 和夫(著)、岩波書店)の第22章(図形の変換の方法 - 線形写像・1次変換)、22.3(1次変換による色々な図形の像)、直線を像にもつ図形、問17.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, solve, plot x, y = symbols('x, y') x0, y0 = symbols('x0, y0') d = {x0: x - 2 * y, y0: 2 * x + 3 * y} fs = [y0, y0 - x0, y0 - 2 * x0 + 5, 3 * x0 + y0 - 4] for i, f in enumerate(fs, 1): print(f'({i})') pprint(f.subs(d)) gs = [solve(f.subs(d), y)[0] for f in fs] hs = [solve(f.subs({x0: x, y0: y}), y)[0] for f in fs] for t in zip(hs, gs): pprint(t) p = plot(*hs, *gs, show=False, legend=True) colors = ['red', 'green', 'blue', 'orange', 'brown', 'pink', 'purple', 'yellow'] for i, color in enumerate(colors): p[i].line_color = color p.save('sample17.svg')
入出力結果(Terminal, Jupyter(IPython))
$ ./sample17.py (1) 2⋅x + 3⋅y (2) x + 5⋅y (3) 7⋅y + 5 (4) 5⋅x - 3⋅y - 4 ⎛ -2⋅x ⎞ ⎜0, ─────⎟ ⎝ 3 ⎠ ⎛ -x ⎞ ⎜x, ───⎟ ⎝ 5 ⎠ (2⋅x - 5, -5/7) ⎛ 5⋅x 4⎞ ⎜-3⋅x + 4, ─── - ─⎟ ⎝ 3 3⎠ $
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="0.001" value="0.005"> <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"> <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="sample17.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'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2], 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 f1 = (x) => 0, g1 = (x) => -2 / 3 * x, f2 = (x) => x, g2 = (x) => -1 / 5 * x, f3 = (x) => 2 * x - 5, g3 = (x) => - 7 / 5, f4 = (x) => -3 * x + 4, g4 = (x) => 5 / 3 * x - 4; 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); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [], fns = [[f1, 'red'], [g1, 'green'], [f2, 'blue'], [g2, 'orange'], [f3, 'brown'], [g3, 'pink'], [f4, 'purple'], [g4, 'yellow']], 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]); } }); fns1 .forEach((o) => { let [f, color] = o; lines.push([x1, f(x1), x2, f(x2), 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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