## 2019年2月3日日曜日

### 数学 - Python - JavaScript - 大小関係を見る - 不等式 – 不等式の解法 – 2次不等式(2つの2次不等式、共通部分)

1. $\begin{array}{}\left(x-3\right)\left(x+2\right)>0\\ x<-2,3

よって、 求める x の値の範囲は、

$-\frac{5}{2}

2. $\begin{array}{}{x}^{2}-1>1\\ x<-1,1

3. $\begin{array}{}\left(x-2\right)\left(x-5\right)\ge 0\\ x\le 2,5\le x\\ \left(x-3\right)\left(2x+1\right)>0\\ x<-\frac{1}{2},3

4. $\begin{array}{}\left(x+2\right)\left(3x-2\right)<0\\ -2

5. $\begin{array}{}\left(x-5\right)\left(x+7\right)\ge 0\\ x\le -7,5\le x\\ -10

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, plot, factor
from sympy.solvers.inequalities import reduce_inequalities

print('10.')

x = symbols('x')
ts = [(x ** 2 - x - 6 > 0, 2 * x ** 2 + 3 * x - 5 < 0),
(x ** 2 > 1, x ** 2 - 2 * x - 8 <= 0),
(x ** 2 - 7 * x + 10 >= 0, 2 * x ** 2 - 5 * x - 3 > 0),
(3 * x ** 2 + 4 * x - 4 < 0, 2 * x ** 2 + 9 * x - 5 <= 0),
(x ** 2 + 2 * x - 35 >= 0, abs(x - 2) < 10)]

for i, (a, b) in enumerate(ts, 1):
print(f'({i})')
pprint(reduce_inequalities(a) & reduce_inequalities(b))
print()

p = plot(x ** 2 + 2 * x - 35, abs(x - 2), 10,
(x, -9, 13), legend=True, show=False)
colors = ['red', 'green', 'blue']
for i, _ in enumerate(p):
p[i].line_color = colors[i]

p.save('sample10.png')


$python3 sample10.py 10. (1) ((-∞ < x ∧ x < -2) ∨ (3 < x ∧ x < ∞)) ∧ -5/2 < x ∧ x < 1 (2) -2 ≤ x ∧ x ≤ 4 ∧ ((-∞ < x ∧ x < -1) ∨ (1 < x ∧ x < ∞)) (3) ((5 ≤ x ∧ x < ∞) ∨ (x ≤ 2 ∧ -∞ < x)) ∧ ((-∞ < x ∧ x < -1/2) ∨ (3 < x ∧ x < ∞)) (4) -5 ≤ x ∧ x ≤ 1/2 ∧ -2 < x ∧ x < 2/3 (5) ((5 ≤ x ∧ x < ∞) ∨ (x ≤ -7 ∧ -∞ < x)) ∧ -8 < x ∧ x < 12$


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="-10">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="15">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-10">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="15">

<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="sample10.js"></script>


JavaScript

let div0 = document.querySelector('#graph0'),
pre0 = document.querySelector('#output0'),
width = 600,
height = 600,
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 => x ** 2 + 2 * x - 35, 'red'],
[x => Math.abs(x - 2), 'green'],
[x => 10, 'blue']];

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 = [],
x0 = 10,
y0 = 12,
lines = [[-8, y1, -8, y2, 'orange'],
[-7, y1, -7, y2, 'brown'],
[5, y1, 5, y2, 'purple'],
[12, y1, 12, y2, 'pink']];

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])
let yscale = d3.scaleLinear()
.domain([y1, y2])

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();