2017年5月14日日曜日

学習環境

数学読本〈4〉数列の極限,順列/順列・組合せ/確率/関数の極限と微分法(松坂 和夫(著)、岩波書店)の第17章(関数の変化をとらえる - 関数の極限と微分法)、17.1(関数と極限)、極限の応用問題、問11.を取り組んでみる。


  1. P h :( 0,p ) x 2 + ( yp ) 2 = r 2 p 2 = r 2 h 2 + ( h 2 p ) 2 = r 2 p 2 2 h 2 p+ h 4 + h 2 = p 2 p= 1+ h 2 2 h0 P h ( 0, 1 2 )

コード(Emacs)

Python 3

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from sympy import Symbol, solve, Limit, pprint

x = Symbol('x')
y = Symbol('y')
p = Symbol('p')
h = Symbol('h', nonzero=True)
r = Symbol('r', positive=True)

circle = x ** 2 + (y - p) ** 2 - r ** 2
expr1 = circle.subs({x: h, y: h**2})
expr2 = circle.subs({x: -h, y: h**2})
expr3 = circle.subs({x: 0, y: 0})

pprint(Limit(solve((expr1, expr2, expr3), p, r, dict=True)[0][p], h, 0).doit())

入出力結果(Terminal, IPython)

$ ./sample11.py
1/2
$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="x1">ε = </label>
<input id="e0" type="number" min="0.001" value="0.001">
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-2">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="2">
<label for="h0">h = </label>
<input id="h0" type="number" step="0.01"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="sample11.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_e = document.querySelector('#e0'),
    input_x1 = document.querySelector('#x1'),
    input_x2 = document.querySelector('#x2'),
    input_h = document.querySelector('#h0'),
    inputs = [input_e, input_x1, input_x2, input_h],
    p = (x) => pre0.textContent += x + '\n';

let draw = () => {
    pre0.textContent = '';

    let epsilon = parseFloat(input_e.value),
        x1 = parseFloat(input_x1.value),
        x2 = parseFloat(input_x2.value),
        h = parseFloat(input_h.value);

    if (h === 0) {
        return;
    }
    let points = [[0, (1 + h ** 2) / 2]];

    for (let x = x1; x <= x2; x += epsilon) {
        points.push([x, x ** 2]);
    }
    
    let xscale = d3.scaleLinear()
        .domain([x1, x2])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([x1, x2])
        .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('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', (d, i) => i === 0 ? xscale(d[1]) - xscale(0) : 1)
        .attr('fill', (d, i) => i === 0 ? 'rgba(0, 255, 0, 0)' : 'blue')
        .attr('stroke', (d, i) => i === 0 ? 'green' : 'blue');

    svg.append('g')
        .attr('transform', `translate(0, ${yscale(0)})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${xscale(0)}, 0)`)
        .call(yaxis);
}

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























 
						

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