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)
- 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, Microsoft Edge, Google Chrome...)用JavaScript Library: MathJax
- 参考書籍
解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第2部(微分と基本的な関数)、第6章(曲線をえがくこと)、4(極座標)、練習問題19、20、21.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3 # -*- coding: utf-8 -*- from sympy import pprint, symbols, solve, sqrt, plot, Rational x, y = symbols('x y', real=True) a = symbols('a', positive=True) eqs = [2 * sqrt(x ** 2 + y ** 2) - x - 2, x ** 2 + y ** 2 - abs(sqrt(x ** 2 + y ** 2) + 2 * x)] for i, eq in enumerate(eqs, 20): print(f'{i}.') s = solve(eq, y) pprint(s) try: p = plot(*s, show=False, legend=True) p.save(f'sample{i}.svg') except Exception as err: print(type(err), err) print()
入出力結果(Terminal, IPython)
$ ./sample19.py 20. ⎡ ____________________ ____________________⎤ ⎢-╲╱ -(x - 2)⋅(3⋅x + 2) ╲╱ -(x - 2)⋅(3⋅x + 2) ⎥ ⎢────────────────────────, ──────────────────────⎥ ⎣ 2 2 ⎦ 21. ⎡ ___________________________________ ________________________________ ⎢ ╱ 2 __________ ╱ 2 __________ ⎢-╲╱ - 4⋅x - 8⋅x - 2⋅╲╱ -8⋅x + 1 + 2 ╲╱ - 4⋅x - 8⋅x - 2⋅╲╱ -8⋅x + 1 + ⎢────────────────────────────────────────, ─────────────────────────────────── ⎢ 2 2 ⎢ ⎣ ___ ___________________________________ ____________________________ ╱ 2 __________ ╱ 2 ________ 2 -╲╱ - 4⋅x - 8⋅x + 2⋅╲╱ -8⋅x + 1 + 2 ╲╱ - 4⋅x - 8⋅x + 2⋅╲╱ -8⋅x + ───, ────────────────────────────────────────, ─────────────────────────────── 2 2 _______ ⎧ __________________________________ ______________ __ ⎪ ╱ 2 _________ ╱ ___ 1 + 2 ⎪-╲╱ - 4⋅x + 8⋅x - 2⋅╲╱ 8⋅x + 1 + 2 ╲╱ 8⋅x - 2⋅╲╱ 8⋅ ───────, ⎨─────────────────────────────────────── for 2⋅x + ───────────────── ⎪ 2 2 ⎪ ⎩ nan otherwise ___________ ⎧ __________________________________ ________ ______ ⎪ ╱ 2 _________ ╱ x + 1 + 2 ⎪╲╱ - 4⋅x + 8⋅x - 2⋅╲╱ 8⋅x + 1 + 2 ╲╱ 8⋅x - 2 ─────────── ≥ 0, ⎨───────────────────────────────────── for 2⋅x + ─────────── ⎪ 2 ⎪ ⎩ nan other _________________ ⎧ __________________________________ _________ ⎪ ╱ 2 _________ ╱ ⋅╲╱ 8⋅x + 1 + 2 ⎪-╲╱ - 4⋅x + 8⋅x + 2⋅╲╱ 8⋅x + 1 + 2 ╲╱ ───────────────── ≥ 0, ⎨─────────────────────────────────────── for 2⋅x + ─── 2 ⎪ 2 ⎪ wise ⎩ nan _________________________ ⎧ __________________________________ _________ ⎪ ╱ 2 _________ 8⋅x + 2⋅╲╱ 8⋅x + 1 + 2 ⎪╲╱ - 4⋅x + 8⋅x + 2⋅╲╱ 8⋅x + 1 + 2 ───────────────────────── ≥ 0, ⎨───────────────────────────────────── for 2⋅x 2 ⎪ 2 ⎪ otherwise ⎩ nan _________________________ ⎤ ╱ _________ ⎥ ╲╱ 8⋅x + 2⋅╲╱ 8⋅x + 1 + 2 ⎥ + ──────────────────────────── ≥ 0⎥ 2 ⎥ ⎥ otherwise ⎦ <class 'TypeError'> Invalid comparison of complex -19.5 - 4.44409720865779*I $
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="dΘ">dΘ = </label> <input id="dΘ" type="number" min="0" step="0.0001" value="0.001"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-5"> <label for="x2">x2 = </label> <input id="x2" type="number" value="5"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-5"> <label for="y2">y2 = </label> <input id="y2" type="number" value="5"> <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="sample19.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_dΘ = document.querySelector('#dΘ'), input_x1 = document.querySelector('#x1'), input_x2 = document.querySelector('#x2'), input_y1 = document.querySelector('#y1'), input_y2 = document.querySelector('#y2'), inputs = [input_r, input_dΘ, 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 f19 = (Θ) => 3 / Math.cos(Θ), f20 = (Θ) => 2 / (2 - Math.cos(Θ)), f21 = (Θ) => Math.abs(1 + 2 * Math.cos(Θ)); let draw = () => { pre0.textContent = ''; let r = parseFloat(input_r.value), dΘ = parseFloat(input_dΘ.value), x1 = parseFloat(input_x1.value), x2 = parseFloat(input_x2.value), y1 = parseFloat(input_y1.value), y2 = parseFloat(input_y2.value); if (r === 0 || dΘ === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [], f16_1 = (Θ) => Math.sqrt(2 * a0 ** 2 * Math.cos(2 * Θ)), f16_2 = (Θ) => -f16_1(Θ), fns = [[f19, 'red'], [f20, 'green'], [f21, 'blue']], fns1 = [], fns2 = []; fns .forEach((o) => { let [f, color] = o; for (let Θ = 0; Θ <= 2 * Math.PI; Θ += dΘ) { let r = f(Θ), x = r * Math.cos(Θ), y = r * Math.sin(Θ); 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();
0 コメント:
コメントを投稿