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, 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4章(正弦と余弦)、3(加法公式)、練習問題7、8.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, sin, cos, plot, solve, Rational
import random
x = symbols('x')
n, m = symbols('n m', integer=True)
eqs = [
sin(m * x) * sin(n * x) - Rational(1, 2) *
(cos((m - n) * x) - cos((m + n) * x)),
sin(m * x) * cos(n * x) - Rational(1, 2) *
(sin((m + n) * x) + sin((m - n) * x)),
cos(m * x) * cos(n * x) - Rational(1, 2) *
(cos((m + n) * x) + cos((m - n) * x))
]
for eq in eqs:
pprint(eq == 0)
m0 = random.randrange(1, 10)
n0 = random.randrange(1, 10)
p = plot(*map(lambda f: f.subs({m: m0, n: n0}), eqs), show=False, legend=True)
for i, color in enumerate(['red', 'green', 'blue']):
p[i].line_color = color
p.save('sample7.svg')
入出力結果(Terminal, IPython)
$ ./sample7.py False False False $
0になって欲しいところが、SymPyの問題で誤差で上手くいってないかも？
JavaScriptではグラフ上で0になった。(計算結果の出力では誤差有り。)
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="-2"> <label for="x2">x2 = </label> <input id="x2" type="number" value="2"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-2"> <label for="y2">y2 = </label> <input id="y2" type="number" value="2"> <br> <label for="n0">n = </label> <input id="n0" type="number" min="0" step="1" value="5"> <label for="m0">m = </label> <input id="m0" type="number" min="0" step="1" 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="sample7.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_n0 = document.querySelector('#n0'),
input_m0 = document.querySelector('#m0'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2,
input_n0, input_m0],
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 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),
n = parseInt(input_n0.value, 10),
m = parseInt(input_m0.value, 10);
if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
return;n
}
let points = [],
lines = [],
f1 = (x) => Math.sin(m * x) * Math.sin(n * x),
f2 = (x) => 1 / 2 * (Math.cos((m - n) * x) - Math.cos((m + n) * x)),
f = (x) => f1(x) - f2(x),
g1 = (x) => Math.sin(m * x) * Math.cos(n * x),
g2 = (x) => 1 / 2 * (Math.sin((m + n) * x) + Math.sin((m - n) * x)),
g = (x) => g1(x) - g2(x),
h1 = (x) => Math.cos(m * x) * Math.cos(n * x),
h2 = (x) => 1 / 2 * (Math.cos((m + n) * x) + Math.cos((m - n) * x)),
h = (x) => h1(x) - h2(x);
for (let x = x1; x <= x2; x += dx) {
let y = f1(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
let t1 = points.length;
for (let x = x1; x <= x2; x += dx) {
let y = g1(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
let t2 = points.length;
for (let x = x1; x <= x2; x += dx) {
let y = h1(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
let t3 = points.length;
for (let x = x1; x <= x2; x += dx) {
let y = f(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
for (let x = x1; x <= x2; x += dx) {
let y = g(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
for (let x = x1; x <= x2; x += dx) {
let y = h(x);
if (Math.abs(y) < Infinity) {
points.push([x, y]);
}
}
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', '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, i) =>
i < t1 ? 'red' :
i < t2 ? 'green' :
i < t3 ? 'blue' : 'brown');
svg.append('g')
.attr('transform', `translate(0, ${height - padding})`)
.call(xaxis);
svg.append('g')
.attr('transform', `translate(${padding}, 0)`)
.call(yaxis);
[f, g, h].forEach((fn) => p(fn(Math.random())));
};
inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();
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