学習環境
- Surface Go、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(iOS))
- 参考書籍
ラング線形代数学(下)(S.ラング (著)、芹沢 正三 (翻訳)、ちくま学芸文庫)の12章(多項式と素因子分解)、2(最大公約因子)、練習問題1.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3
from sympy import pprint, symbols, summation
print('1.')
t = symbols('t')
n, k = symbols('n, k', integer=True)
eq = t ** n - 1
for m in range(10):
eqm = eq.subs({n: m})
eq1 = (t - 1) * summation(t ** k, (k, 0, m - 1))
for s in [eqm, eqm.factor(), eq1, eq1.expand()]:
pprint(s)
print()
入出力結果(Terminal, Jupyter(IPython))
$ ./sample1.py
1.
0
0
0
0
t - 1
t - 1
t - 1
t - 1
2
t - 1
(t - 1)⋅(t + 1)
(t - 1)⋅(t + 1)
2
t - 1
3
t - 1
⎛ 2 ⎞
(t - 1)⋅⎝t + t + 1⎠
⎛ 2 ⎞
(t - 1)⋅⎝t + t + 1⎠
3
t - 1
4
t - 1
⎛ 2 ⎞
(t - 1)⋅(t + 1)⋅⎝t + 1⎠
⎛ 3 2 ⎞
(t - 1)⋅⎝t + t + t + 1⎠
4
t - 1
5
t - 1
⎛ 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + 1⎠
⎛ 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + 1⎠
5
t - 1
6
t - 1
⎛ 2 ⎞ ⎛ 2 ⎞
(t - 1)⋅(t + 1)⋅⎝t - t + 1⎠⋅⎝t + t + 1⎠
⎛ 5 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + t + 1⎠
6
t - 1
7
t - 1
⎛ 6 5 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + t + t + 1⎠
⎛ 6 5 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + t + t + 1⎠
7
t - 1
8
t - 1
⎛ 2 ⎞ ⎛ 4 ⎞
(t - 1)⋅(t + 1)⋅⎝t + 1⎠⋅⎝t + 1⎠
⎛ 7 6 5 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + t + t + t + 1⎠
8
t - 1
9
t - 1
⎛ 2 ⎞ ⎛ 6 3 ⎞
(t - 1)⋅⎝t + t + 1⎠⋅⎝t + t + 1⎠
⎛ 8 7 6 5 4 3 2 ⎞
(t - 1)⋅⎝t + t + t + t + t + t + t + t + 1⎠
9
t - 1
$
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="1"> <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="-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"> <br> <label for="n0">n = </label> <input id="n0" type="number" min="0" step="1" value="1"> <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="sample1.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_a1 = document.querySelector('#a1'),
input_b1 = document.querySelector('#b1'),
input_a2 = document.querySelector('#a2'),
input_b2 = document.querySelector('#b2'),
input_n0 = document.querySelector('#n0'),
inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2,
input_n0],
p = (x) => pre0.textContent += x + '\n';
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),
n0 = parseInt(input_n0.value, 10);
if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
return;
}
let points = [],
fns = [[(x) => x ** n0 - 1, 'green']],
lines = [[1, y1, 1, y2, 'red']];
fns
.forEach((o) => {
let [f, color] = o;
for (let x0 = x1; x0 <= x2; x0 += dx) {
points.push([x0, f(x0), 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);
p(fns.join('\n'));
};
inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();
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