## 2018年11月18日日曜日

### 数学 – Python - JavaScript - 数学はここから始まる - 数 – 2次方程式と複素数 – 2数を解とする方程式(対称式)

1. $\begin{array}{}\alpha +\beta =-\frac{4}{2}=2\\ \alpha \beta =\frac{5}{2}\\ \left(\alpha +3\right)+\left(\beta +3\right)\\ =\alpha +\beta +6\\ =2+6\\ =8\\ \left(\alpha +3\right)\left(\beta +3\right)\\ =\alpha \beta +9+3\left(\alpha +\beta \right)\\ =\frac{5}{2}+9+6\\ =\frac{35}{2}\\ 2{x}^{2}-16x+35=0\end{array}$

2. $\begin{array}{}{\alpha }^{2}+{\beta }^{2}\\ ={\left(\alpha +\beta \right)}^{2}-2\alpha \beta \\ =4-5\\ =-1\\ {\alpha }^{2}{\beta }^{2}=\frac{25}{4}\\ 4{x}^{2}+4x+25=0\end{array}$

3. $\begin{array}{}\frac{1}{2\alpha -1}+\frac{1}{2\beta -1}\\ =\frac{2\left(\alpha +\beta \right)-2}{4\alpha \beta +1-2\left(\alpha +\beta \right)}\\ =\frac{4-2}{10+1-4}\\ =\frac{2}{7}\\ \frac{1}{2\alpha -1}·\frac{1}{2\beta -1}\\ =\frac{1}{4\alpha \beta -2\left(\alpha +\beta \right)+1}\\ =\frac{1}{10-4+1}\\ =\frac{1}{7}\\ 7{x}^{2}-2x+1=0\end{array}$

コード(Emacs)

Python 3

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

print('14.')

x = symbols('x')
alpha, beta = solve(2 * x ** 2 - 4 * x + 5, x)
ts = [(2, alpha + 3, beta + 3),
(4, alpha ** 2, beta ** 2),
(7, 1 / (2 * alpha - 1), 1 / (2 * beta - 1))]

for i, (a, alpha0, beta0) in enumerate(ts, 1):
print(f'({i})')
pprint((a * (x - alpha0) * (x - beta0)).simplify())


$./sample14.py 14. (1) 2 2⋅x - 16⋅x + 35 (2) 2 4⋅x + 4⋅x + 25 (3) 2 7⋅x - 2⋅x + 1$


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="0.01">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-25">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="25">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-25">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="25">

<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="sample14.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 => 2 * x ** 2 - 16 * x + 35, 'red'],
[x => 4 * x ** 2 + 4 * x + 25, 'green'],
[x => 7 * x ** 2 - 2 * x + 1, '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 = [],
lines = [];

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();