2018年10月27日土曜日

学習環境

数学読本〈1〉数・式の計算/方程式/不等式 (松坂 和夫(著)、岩波書店)の第3章(数学の威力を発揮する - 方程式)、3.1(方程式とその解法)、2次方程式の解法の問4.を取り組んでみる。



    1. x = - 5 ± 25 + 96 8 = - 5 ± 121 8 = - 5 ± 11 8 = - 2 , 3 4

    2. x = 2 ± 4 + 16 2 = 2 1 ± 1 + 4 2 = 1 ± 5

    3. x = - 8 ± 8 2 + 4 · 16 2 = 2 - 4 ± 2 4 + 16 2 = - 4 ± 2 5

    4. x = 11 ± 121 - 76 2 = 11 ± 45 2 = 11 ± 3 5 2

    5. x = - 17 ± 1 7 2 - 24 · 12 12 = - 17 ± 289 - 288 12 = - 3 2 , - 4 3

    6. x = 4 ± 4 2 - 4 · 3 · - 2 2 · 3 = 2 2 ± 4 + 6 2 - 3 = 2 ± 10 3

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, solve, plot

print('4.')

x = symbols('x', real=True)

eqs = [(4, 5, -6),
       (1, -2, -4),
       (1, 8, -16),
       (1, -11, 19),
       (6, 17, 12),
       (3, -4, -2)]

for i, (a, b, c) in enumerate(eqs, 1):
    print(f'({i})')
    pprint(solve(a * x ** 2 + b * x + c, dict=True))
    print()

p = plot(*[a * x ** 2 + b * x + c for a, b, c in eqs], show=False, legend=True)
colors = ['red', 'green', 'blue', 'orange', 'brown', 'purple']
for i, color in enumerate(colors):
    p[i].line_color = color
p.save('sample4.svg')

入出力結果(Terminal, Jupyter(IPython))

$ ./sample4.py
4.
(1)
[{x: -2}, {x: 3/4}]

(2)
[{x: 1 + √5}, {x: -√5 + 1}]

(3)
[{x: -4 + 4⋅√2}, {x: -4⋅√2 - 4}]

(4)
⎡⎧     3⋅√5   11⎫  ⎧   3⋅√5   11⎫⎤
⎢⎨x: - ──── + ──⎬, ⎨x: ──── + ──⎬⎥
⎣⎩      2     2 ⎭  ⎩    2     2 ⎭⎦

(5)
[{x: -3/2}, {x: -4/3}]

(6)
⎡⎧   2   √10⎫  ⎧     √10   2⎫⎤
⎢⎨x: ─ + ───⎬, ⎨x: - ─── + ─⎬⎥
⎣⎩   3    3 ⎭  ⎩      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="0.001">
<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="sample4.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';

let fns = [[x => 4 * x ** 2 + 5 * x - 6, 'red']];
    
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 = [[-2, y1, -2, y2, 'green'],
                 [3 / 4, y1, 3 / 4, y2, 'blue']];

    fns
        .forEach((o) => {
            let [f, color] = o;
            for (let x = x1; x <= x2; x += dx) {
                let y = f(x);

                points.push([x, y, 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].forEach((fs) => p(fs.join('\n')));
};

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();







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