学習環境
- Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
- Windows 10 Pro (OS)
- 数式入力ソフト(TeX, MathML): MathType
- MathML対応ブラウザ: Firefox、Safari
- MathML非対応ブラウザ(Internet Explorer, Microsoft Edge, Google Chrome...)用JavaScript Library: MathJax
- 参考書籍
解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第2部(微分と基本的な関数)、第6章(曲線をえがくこと)、4(極座標)、練習問題22、23、24、25、26.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from sympy import pprint, symbols, solve, sqrt, plot, asin
x, y = symbols('x y', real=True)
eqs = [(x ** 2 + y ** 2) * sqrt(x ** 2 + y ** 2) - 4 * y ** 2,
(x ** 2 + y ** 2) * sqrt(x ** 2 + y ** 2) -
2 * (x ** 2 + y ** 2) - 2 * x * y,
(x ** 2 + y ** 2) * sqrt(x ** 2 + y ** 2) - x,
(x ** 2 + y ** 2) * sqrt(x ** 2 + y ** 2) - y,
sqrt(x ** 2 + y ** 2) * asin(y / sqrt(x ** 2 + y ** 2)) - 1]
for i, eq in enumerate(eqs, 22):
try:
print(f'{i}.')
s = solve(eq, y)
pprint(s)
p = plot(*s, show=False, legend=True)
p.save(f'sample{i}.png')
except Exception as err:
print(type(err), err)
print()
入出力結果(Terminal, IPython)
$ ./sample22.py
22.
⎡ ________________________________________________________________
⎢ ╱
⎢ ╱ 2
⎢ ╱ 2 48⋅x
⎢-√3⋅ ╱ - 3⋅x + ──────────────────────────────────────────────────────
⎢ ╱ __________________________________________________
⎢ ╱ ╱ ____________
⎢ ╱ 3 ╱ 4 2 ╱ 2 2
⎢ ╲╱ ╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x -
⎢─────────────────────────────────────────────────────────────────────────────
⎢
⎢
⎢
⎣
______________________________________________________________________________
______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
──── - 2⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 16 - ───
____
3 ╱
512 ╲╱
──────────────────────────────────────────────────────────────────────────────
3
________________________________________________________ _______
╱
╱
128 ╱ 2
─────────────────────────────────────────────────────── √3⋅ ╱ - 3⋅x
______________________________________________________ ╱
╱ ____________ ╱
4 2 ╱ 2 2 ╱
- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 ╲╱
─────────────────────────────────────────────────────────, ───────────────────
______________________________________________________________________________
________
2 ╱
48⋅x 3 ╱ 4
+ ────────────────────────────────────────────────────────── - 2⋅╲╱ - 27⋅x
______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
______________________________________________________________________________
______________________________________________
____________
2 ╱ 2 2
+ 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 16 - ────────────────────────
____________________
╱
3 ╱ 4 2
╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲
──────────────────────────────────────────────────────────────────────────────
3
___________________________________
128
────────────────────────────────── ______________________________
__________________________________ ╱
____________ ╱
╱ 2 2 ╱
╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 ╱
───────────────────────────────────, - ╱ ─────────────────────────────
╱ _____________________
╱ ╱
╱ 3 ╱ 4 2
╲╱ - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱
______________________________________________________________________________
______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
3⋅x ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
_________________________________ _______________________________
____________ ╱ _________
╱ 2 2 3 ╱ 4 2 ╱ 2
27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x -
______________________________________________________________________________
_______
╱
2 3 ╱
3⋅√3⋅ⅈ⋅x ⋅╲╱ - 27⋅x
─────────────────────── - ────────────────────────────────────────────────────
_______________________ ____________________________________________
___ ╱ ____________
2 3 ╱ 4 2 ╱ 2
64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288
______________________________________________________________________________
_______________________________________________
____________
4 2 ╱ 2 2
+ 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
__________ ______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
______________________________________________________________________________
2
96⋅x
+ ───────────────────────────────────────────────────────────────────────────
______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2 3 ╱
- 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱
______________________________________________________________________________
─────────────────────────────────────────────────────── + ────────────────────
______________________________________________________ ____________
╱ ____________ ╱
4 2 ╱ 2 2 3 ╱ 4
- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3
______________________________________________________________________________
2/3
⎛ ____________ ⎞
⎜ 4 2 ╱ 2 2 ⎟
2⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
──────────────────────────────────────────────────────────────────────────────
__________________________________________ ______________________
____________ ╱
2 ╱ 2 2 3 ╱ 4 2 ╱
⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱
______________________________________________________________________________
⎛
⎜
2⋅√3⋅ⅈ⋅⎝-
──────────────────────────────── + ───────────────────────────────────────────
________________________________ ___________________________________
____________ ╱ ____________
2 2 3 ╱ 4 2 ╱ 2
27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅
______________________________________________________________________________
2/3
____________ ⎞
4 2 ╱ 2 2 ⎟
27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
──────────────────────────────────────────────────────────────────────────────
___________________ _____________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2
│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅
______________________________________________________________________________
_________________________
╱ ___
3 ╱ 4 2 ╱
16⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27
───────── - ──────────────────────────────────────────────────────────────────
_________ ______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3
______________________________________________________________________________
_____________________________
_________
2 2
⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────── + ───────────
______________________________________________________ ___
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ -
______________________________________________________________________________
_____________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2
16⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅
──────────────────────────────────────────────────────────────────────────────
___________________________________________________ _____________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅
______________________________________________________________________________
_________
2
x - 512
───────────────────────────────────────── - ──────────────────────────────────
_________________________________________ __________________________
____________ ╱ ____
2 ╱ 2 2 3 ╱ 4 2 ╱
√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅
______________________________________________________________________________
256
──────────────────────────────────────────────────────────────────────────────
____________________________ ____________________________________
________ ╱ ____________
2 2 3 ╱ 4 2 ╱ 2
x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│
___________________ _______________________________________________
╱ ____
╱ ╱
╱ 2 3 ╱
╱ 3⋅x ⋅╲╱ - 2
────────────────── , ╱ ──────────────────────────────────────────────
__________________ ╱ ______________________________________
╱ ╱ ____________
2 ╱ 3 ╱ 4 2 ╱ 2
x│ + 288⋅x - 512 ╲╱ - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│
______________________________________________________________________________
__________________________________________________
____________
4 2 ╱ 2 2
7⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
________________ ________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
+ 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x
______________________________________________________________________________
________________________
╱ __
2 3 ╱ 4 2 ╱
3⋅√3⋅ⅈ⋅x ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 2
────── - ─────────────────────────────────────────────────────────────────────
______ ______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
- 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3
______________________________________________________________________________
______________________________
__________
2 2
7⋅x - 64 ⋅│x│ + 288⋅x - 512
───────────────────────────────────────────────────────────── + ──────────────
______________________________________________________ ______
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅
______________________________________________________________________________
2
96⋅x
──────────────────────────────────────────────────────────────────────────────
________________________________________________ ________________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅
______________________________________________________________________________
2⋅
────────────────────────────────────── + ─────────────────────────────────────
______________________________________ _____________________________
____________ ╱ _______
2 ╱ 2 2 3 ╱ 4 2 ╱ 2
x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x
______________________________________________________________________________
2/3
⎛ ____________ ⎞
⎜ 4 2 ╱ 2 2 ⎟
⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
──────────────────────────────────────────────────────────────────────────────
_________________________ _______________________________________
_____ ╱ ____________
2 3 ╱ 4 2 ╱ 2
- 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│
______________________________________________________________________________
⎛
⎜ 4 2
2⋅√3⋅ⅈ⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲
─────────────── + ────────────────────────────────────────────────────────────
_______________ ____________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
+ 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 51
______________________________________________________________________________
2/3
____________ ⎞
╱ 2 2 ⎟
╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
────────────────────────────────────────────────────────────────────── - ─────
__ ______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2 3
2 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲
______________________________________________________________________________
__________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2
16⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 2
──────────────────────────────────────────────────────────────────────────────
______________________________________________________ _______
╱ ____________ ╱
╱ 4 2 ╱ 2 2 3 ╱
╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x
______________________________________________________________________________
____________
2
88⋅x - 512
─────────────────────────────────────────────── + ────────────────────────────
_______________________________________________ ____________________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4 2
+ 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲
______________________________________________________________________________
______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
16⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
__________________________________ ______________________________
____________ ╱ ________
╱ 2 2 3 ╱ 4 2 ╱ 2
╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x -
______________________________________________________________________________
──────────────────────── - ───────────────────────────────────────────────────
________________________ ___________________________________________
____ ╱ ____________
2 3 ╱ 4 2 ╱ 2
64 ⋅│x│ + 288⋅x - 512 - 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 28
______________________________________________________________________________
256
──────────────────────────────────────────────────────────────────────────────
___________ _____________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
8⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
__ _______________________________________________________________
╱ ___________________
╱ ╱
╱ 2 3 ╱ 4 2
╱ 3⋅x ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅
─ , - ╱ - ────────────────────────────────────────────────────────────
_ ╱ ______________________________________________________
╱ ╱ ____________
╱ 3 ╱ 4 2 ╱ 2 2
╲╱ 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
______________________________________________________________________________
___________________________________
____________
╱ 2 2
╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────── - ───────
______________________________________________________ _
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
+ 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱
______________________________________________________________________________
_________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2
3⋅√3⋅ⅈ⋅x ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ +
──────────────────────────────────────────────────────────────────────────────
_____________________________________________________ ___________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x +
______________________________________________________________________________
_____________
2
288⋅x - 512
─────────────────────────────────────────── - ────────────────────────────────
___________________________________________ __________________________
____________ ╱ ____
2 ╱ 2 2 3 ╱ 4 2 ╱
3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅
______________________________________________________________________________
2
96⋅x
──────────────────────────────────────────────────────────────────────────────
____________________________ ____________________________________
________ ╱ ____________
2 2 3 ╱ 4 2 ╱ 2
x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│
______________________________________________________________________________
⎛
⎜ 4 2
2⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱
────────────────── - ─────────────────────────────────────────────────────────
__________________ ___________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 5
______________________________________________________________________________
2/3
____________ ⎞
╱ 2 2 ⎟
27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
─────────────────────────────────────────────────────────────────────── + ────
___ ______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2 3
12 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱
______________________________________________________________________________
⎛ ____________
⎜ 4 2 ╱ 2
2⋅√3⋅ⅈ⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 28
──────────────────────────────────────────────────────────────────────────────
______________________________________________________ ________
╱ ____________ ╱
╱ 4 2 ╱ 2 2 3 ╱ 4
- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x
______________________________________________________________________________
2/3
⎞
2 ⎟
8⋅x - 512⎠
────────────────────────────────────────────── + ─────────────────────────────
______________________________________________ _______________________
____________ ╱ _
2 ╱ 2 2 3 ╱ 4 2 ╱
+ 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱
______________________________________________________________________________
______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
16⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
_______________________________ _________________________________
___________ ╱ ___________
2 2 3 ╱ 4 2 ╱ 2
27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64
______________________________________________________________________________
___________
╱
3 ╱ 4
16⋅√3⋅ⅈ⋅╲╱ - 27⋅x +
───────────────────── + ──────────────────────────────────────────────────────
_____________________ ________________________________________________
_ ╱ ____________
2 3 ╱ 4 2 ╱ 2 2
⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x
______________________________________________________________________________
___________________________________________
____________
2 ╱ 2 2
3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
────────────────────────────────────────────────────────────────────────── + ─
______ ______________________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2 2
- 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3
______________________________________________________________________________
256
──────────────────────────────────────────────────────────────────────────────
______________________________________________________ _____
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27
__________________________________________________ ________________
╱
╱
╱
╱
───────────────────────────────────────────────── , ╱ - ─────────────
_________________________________________________ ╱ _______
____________ ╱ ╱
4 2 ╱ 2 2 ╱ 3 ╱
⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 ╲╱ 3⋅╲╱ - 27⋅x
______________________________________________________________________________
__________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
3⋅x ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x -
──────────────────────────────────────────────────────────────────────────────
_______________________________________________ _________________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
+ 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x
______________________________________________________________________________
____
512 3⋅√3⋅ⅈ⋅x
───────────────────────────────────── - ──────────────────────────────────────
_____________________________________ ________________________________
____________ ╱ __________
2 ╱ 2 2 3 ╱ 4 2 ╱ 2
⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 6
______________________________________________________________________________
______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────────────────
______________________ __________________________________________
__ ╱ ____________
2 3 ╱ 4 2 ╱ 2
4 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 2
______________________________________________________________________________
96
──────────── - ───────────────────────────────────────────────────────────────
____________ ______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
88⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 +
______________________________________________________________________________
2
⋅x
───────────────────────────────────────────────────────────────── - ──────────
______________________________________________________ ____
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 2
______________________________________________________________________________
⎛ ____________
⎜ 4 2 ╱ 2 2
2⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 51
──────────────────────────────────────────────────────────────────────────────
__________________________________________________ ______________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
7⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√
______________________________________________________________________________
2/3
⎞
⎟
2⎠ 2⋅√
──────────────────────────────────────── + ───────────────────────────────────
________________________________________ _____________________________
____________ ╱ _______
2 ╱ 2 2 3 ╱ 4 2 ╱ 2
3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x
______________________________________________________________________________
2/3
⎛ ____________ ⎞
⎜ 4 2 ╱ 2 2 ⎟
3⋅ⅈ⋅⎝- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512⎠
──────────────────────────────────────────────────────────────────────────────
_________________________ _______________________________________
_____ ╱ ____________
2 3 ╱ 4 2 ╱ 2
- 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│
______________________________________________________________________________
____________________
╱
3 ╱ 4 2
16⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲
─────────────── + ────────────────────────────────────────────────────────────
_______________ ______________________________________________________
╱ ____________
2 3 ╱ 4 2 ╱ 2 2
+ 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
______________________________________________________________________________
__________________________________
____________
╱ 2 2
╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512
──────────────────────────────────────────────────────────────────── + ───────
______________________________________________________ _
╱ ____________ ╱
3 ╱ 4 2 ╱ 2 2 3 ╱
+ 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱
______________________________________________________________________________
__________________________________________
╱ ____________
3 ╱ 4 2 ╱ 2
16⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 2
──────────────────────────────────────────────────────────────────────────────
_____________________________________________________ ___________
____________ ╱
4 2 ╱ 2 2 3 ╱ 4
- 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x +
______________________________________________________________________________
____________
2
88⋅x - 512
─────────────────────────────────────────── + ────────────────────────────────
___________________________________________ __________________________
____________ ╱ ____
2 ╱ 2 2 3 ╱ 4 2 ╱
3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│x│ + 288⋅x - 512 3⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅
______________________________________________________________________________
256
──────────────────────────────────────────────────────────────────────────────
____________________________ ____________________________________
________ ╱ ____________
2 2 3 ╱ 4 2 ╱ 2
x - 64 ⋅│x│ + 288⋅x - 512 + 3⋅√3⋅ⅈ⋅╲╱ - 27⋅x + 3⋅√3⋅x ⋅╲╱ 27⋅x - 64 ⋅│
⎤
⎥
⎥
⎥
___________________⎥
⎥
⎥
⎥
⎥
────────────────── ⎥
__________________ ⎥
⎥
2 ⎥
x│ + 288⋅x - 512 ⎦
23.
[]
<class 'IndexError'> list index out of range
24.
[]
<class 'IndexError'> list index out of range
25.
⎡ ________________________________________________________________
⎢ ╱ __________________________
⎢ ╱ ╱ ___________
⎢ ╱ 2 2/3 3 ___ 3 ╱ 2 ╱ 4 2
⎢-√6⋅ ╱ - 6⋅x - 2 ⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - ──────────
⎢ ╱ ______
⎢ ╱ ╱
⎢ ╱ 3 ╱ 2
⎢ ╲╱ ╲╱ 9⋅x
⎢─────────────────────────────────────────────────────────────────────────────
⎢ 6
⎢
⎢
⎣
_____________________ __________________________________________
╱ _________________
3 ___ 2/3 ╱ ╱ ___
⋅╲╱ 2 ⋅3 ╱ 2 2/3 3 ___ 3 ╱ 2 ╱
──────────────────── √6⋅ ╱ - 6⋅x - 2 ⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27
____________________ ╱
___________ ╱
╱ 4 ╱
+ √3⋅╲╱ 27⋅x - 4 ╲╱
──────────────────────, ──────────────────────────────────────────────────────
6
___________________________________________
_________
________ 3 ___ 2/3
4 2⋅╲╱ 2 ⋅3
⋅x - 4 - ────────────────────────────── ______________________
__________________________ ╱
╱ ___________ ╱
3 ╱ 2 ╱ 4 ╱
╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 ╱
───────────────────────────────────────────, - ╱ - ───────────────────
╱ _______
╱ ╱
╱ 3 ___ 3 ╱ 2
╲╱ 6⋅╲╱ 3 ⋅╲╱ 9⋅x +
______________________________________________________________________________
__________________________
╱ ___________
3 ___ 2 3 ╱ 2 ╱ 4
6⋅╲╱ 3 ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
───────────────────────────────────────────────────────────── + ──────────────
___________________ __________________________ __
___________ ╱ ___________ ╱
╱ 4 5/6 3 ╱ 2 ╱ 4 3 ___ 3 ╱
√3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9
______________________________________________________________________________
__________________________
╱ ___________
5/6 2 3 ╱ 2 ╱ 4
6⋅3 ⋅ⅈ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
────────────────────────────────────────────────────────────────── - ─────────
________________________ __________________________
___________ ╱ ___________
2 ╱ 4 5/6 3 ╱ 2 ╱ 4 3 ___ 3
⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲
______________________________________________________________________________
2/3
⎛ ___________⎞
2/3 ⎜ 2 ╱ 4 ⎟
6 ⋅⎝9⋅x + √3⋅╲╱ 27⋅x - 4 ⎠
─────────────────────────────────────────────────────────────────────── - ────
__________________________ __________________________
╱ ___________ ╱ ___________
╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4 3
╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱
______________________________________________________________________________
2/3
⎛ ___________⎞
2/3 6 ___ ⎜ 2 ╱ 4 ⎟
3⋅2 ⋅╲╱ 3 ⋅ⅈ⋅⎝9⋅x + √3⋅╲╱ 27⋅x - 4 ⎠
──────────────────────────────────────────────────────────────────────────── +
__________________________ __________________________
╱ ___________ ╱ ___________
___ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4
3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
______________________________________________________________________________
3 ___
12⋅╲╱ 2
─────────────────────────────────────────────────────────────────────────────
__________________________ _______________________
╱ ___________ ╱ _________
3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4
6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x -
____ ______________________________________________________________
╱ _________________________
╱ ╱ ___________
╱ 3 ___ 2 3 ╱ 2 ╱ 4
╱ 6⋅╲╱ 3 ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
─── , ╱ - ───────────────────────────────────────────────────────────
___ ╱ __________________________ _____
__ ╱ ╱ ___________ ╱
╱ 3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2
4 ╲╱ 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x
______________________________________________________________________________
_ ___________________
╱ _____
5/6 2 3 ╱ 2 ╱
6⋅3 ⋅ⅈ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x
───────────────────── + ──────────────────────────────────────────────────────
_____________________ __________________________
___________ ╱ ___________ ╱
╱ 4 3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱
+ √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ⋅╲╱
______________________________________________________________________________
_______
______ ⎛ _______
4 2/3 ⎜ 2 ╱ 4
- 4 6 ⋅⎝9⋅x + √3⋅╲╱ 27⋅x
────────────────────────── - ─────────────────────────────────────────────────
__________________________ __________________________
___________ ╱ ___________
2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4 5/6
9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3 ⋅ⅈ
______________________________________________________________________________
2/3
____⎞ ⎛
⎟ 2/3 6 ___ ⎜ 2
- 4 ⎠ 3⋅2 ⋅╲╱ 3 ⋅ⅈ⋅⎝9⋅x + √3⋅
─────────────────────────────── - ────────────────────────────────────────────
__________________________ __________________________
╱ ___________ ╱ ___________
3 ╱ 2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4
⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 - 6⋅3
______________________________________________________________________________
2/3
___________⎞
╱ 4 ⎟
╲╱ 27⋅x - 4 ⎠ 12⋅
──────────────────────────────────── + ───────────────────────────────────────
__________________________ __________________________
╱ ___________ ╱ ___________
5/6 3 ╱ 2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4
⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
__________________________________________ _______________________
╱
╱
3 ___ ╱
╲╱ 2 ╱ 6
───────────────────────────────────────── , - ╱ - ────────────────────
__________________________ ╱ ________
╱ ___________ ╱ ╱
5/6 3 ╱ 2 ╱ 4 ╱ 3 ___ 3 ╱ 2
- 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 ╲╱ 6⋅╲╱ 3 ⋅╲╱ 9⋅x +
______________________________________________________________________________
__________________________
╱ ___________
3 ___ 2 3 ╱ 2 ╱ 4
⋅╲╱ 3 ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
──────────────────────────────────────────────────────────── - ───────────────
__________________ __________________________ ___
___________ ╱ ___________ ╱
╱ 4 5/6 3 ╱ 2 ╱ 4 3 ___ 3 ╱
√3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅
______________________________________________________________________________
__________________________
╱ ___________
5/6 2 3 ╱ 2 ╱ 4
6⋅3 ⋅ⅈ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
───────────────────────────────────────────────────────────────── - ──────────
_______________________ __________________________
___________ ╱ ___________
2 ╱ 4 5/6 3 ╱ 2 ╱ 4 3 ___ 3
x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱
______________________________________________________________________________
2/3
⎛ ___________⎞
2/3 ⎜ 2 ╱ 4 ⎟
6 ⋅⎝9⋅x + √3⋅╲╱ 27⋅x - 4 ⎠
────────────────────────────────────────────────────────────────────── + ─────
__________________________ __________________________
╱ ___________ ╱ ___________
╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4 3 _
9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱
______________________________________________________________________________
2/3
⎛ ___________⎞
2/3 6 ___ ⎜ 2 ╱ 4 ⎟
3⋅2 ⋅╲╱ 3 ⋅ⅈ⋅⎝9⋅x + √3⋅╲╱ 27⋅x - 4 ⎠
─────────────────────────────────────────────────────────────────────────── +
__________________________ __________________________
╱ ___________ ╱ ___________
__ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4
3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
______________________________________________________________________________
3 ___
12⋅╲╱ 2
──────────────────────────────────────────────────────────────────────────────
__________________________ ________________________
╱ ___________ ╱ __________
3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2 ╱ 4
6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
___ _______________________________________________________________
╱ __________________________
╱ ╱ ___________
╱ 3 ___ 2 3 ╱ 2 ╱ 4
╱ 6⋅╲╱ 3 ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4
── , ╱ - ────────────────────────────────────────────────────────────
__ ╱ __________________________ ______
_ ╱ ╱ ___________ ╱
╱ 3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱ 2
╲╱ 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱ 9⋅x
______________________________________________________________________________
____________________
╱ ______
5/6 2 3 ╱ 2 ╱ 4
6⋅3 ⋅ⅈ⋅x ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x
──────────────────── - ───────────────────────────────────────────────────────
____________________ __________________________ _
___________ ╱ ___________ ╱
╱ 4 3 ___ 3 ╱ 2 ╱ 4 5/6 3 ╱
+ √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅╲╱
______________________________________________________________________________
______
_____ ⎛ ________
2/3 ⎜ 2 ╱ 4
- 4 6 ⋅⎝9⋅x + √3⋅╲╱ 27⋅x -
───────────────────────── - ──────────────────────────────────────────────────
_________________________ __________________________
___________ ╱ ___________
2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4 5/6
9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3 ⋅ⅈ⋅
______________________________________________________________________________
2/3
___⎞ ⎛
⎟ 2/3 6 ___ ⎜ 2
4 ⎠ 3⋅2 ⋅╲╱ 3 ⋅ⅈ⋅⎝9⋅x + √3⋅╲
────────────────────────────── + ─────────────────────────────────────────────
__________________________ __________________________
╱ ___________ ╱ ___________
3 ╱ 2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4 5
╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 + 6⋅3
______________________________________________________________________________
2/3
___________⎞
╱ 4 ⎟ 3
╱ 27⋅x - 4 ⎠ 12⋅╲
─────────────────────────────────── + ────────────────────────────────────────
__________________________ __________________________
╱ ___________ ╱ ___________
/6 3 ╱ 2 ╱ 4 3 ___ 3 ╱ 2 ╱ 4
⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 6⋅╲╱ 3 ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 +
⎤
⎥
⎥
⎥
_________________________________________⎥
⎥
⎥
___ ⎥
╱ 2 ⎥
──────────────────────────────────────── ⎥
__________________________ ⎥
╱ ___________ ⎥
5/6 3 ╱ 2 ╱ 4 ⎥
6⋅3 ⋅ⅈ⋅╲╱ 9⋅x + √3⋅╲╱ 27⋅x - 4 ⎦
26.
<class 'NotImplementedError'> multiple generators [asin(y/sqrt(x**2 + y**2)), sqrt(x**2 + y**2)]
No algorithms are implemented to solve equation sqrt(x**2 + y**2)*asin(y/sqrt(x**2 + y**2)) - 1
$
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="dΘ">dΘ = </label> <input id="dΘ" type="number" min="0" step="0.0001" 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="sample22.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_dΘ = document.querySelector('#dΘ'),
input_x1 = document.querySelector('#x1'),
input_x2 = document.querySelector('#x2'),
input_y1 = document.querySelector('#y1'),
input_y2 = document.querySelector('#y2'),
inputs = [input_r, input_dΘ, input_x1, input_x2, input_y1, input_y2],
p = (x) => pre0.textContent += x + '\n',
range = (start, end, step=1) => {
let res = [];
for (let i = start; i < end; i += step) {
res.push(i);
}
return res;
};
let f23 = (Θ) => 2 + Math.sin(2 * Θ),
f241 = (Θ) => Math.sqrt(Math.cos(Θ)),
f242 = (Θ) => -f241(Θ),
f26 = (Θ) => 1 / Θ;
let draw = () => {
pre0.textContent = '';
let r = parseFloat(input_r.value),
dΘ = parseFloat(input_dΘ.value),
x1 = parseFloat(input_x1.value),
x2 = parseFloat(input_x2.value),
y1 = parseFloat(input_y1.value),
y2 = parseFloat(input_y2.value);
if (r === 0 || dΘ === 0 || x1 > x2 || y1 > y2) {
return;
}
let points = [],
lines = [],
f16_1 = (Θ) => Math.sqrt(2 * a0 ** 2 * Math.cos(2 * Θ)),
f16_2 = (Θ) => -f16_1(Θ),
fns = [[f23, 'red'],
[f241, 'green'],
[f242, 'green'],
[f26, 'blue']],
fns1 = [],
fns2 = [];
fns
.forEach((o) => {
let [f, color] = o;
for (let Θ = 0; Θ <= 2 * Math.PI; Θ += dΘ) {
let r = f(Θ),
x = r * Math.cos(Θ),
y = r * Math.sin(Θ);
points.push([x, y, color]);
}
});
fns2
.forEach((o) => {
let [f, color] = o;
for (let x = x1; x <= x2; x += dx0) {
let g = f(x);
lines.push([x1, g(x1), x2, g(x2), 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, fns1, fns2].forEach((fs) => p(fs.join('\n')));
};
inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();
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