2018年8月29日水曜日

学習環境

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。


  1. t n - 1 = t - 1 t n - 1 + t n - 2 + t n - 3 + + t n - n - 1 + 1

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();








0 コメント:

コメントを投稿

関連コンテンツ