学習環境
- Surface
- Windows 10 Pro (OS)
- Nebo(Windows アプリ)
- iPad
- MyScript Nebo - MyScript(iPad アプリ(iOS))
- 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Ⅵ部(多変数の関数)、第18章(ベクトルの微分)、2(曲線の長さ)の練習問題1、2の解答を求めてみる。
コード
#!/usr/bin/env python3
from unittest import TestCase, main
from sympy import symbols, Matrix, Derivative, sin, cos, Integral, sqrt
from sympy.plotting import plot3d_parametric_line
print('1, 2.')
t = symbols('t')
x1 = Matrix([cos(t), sin(t), t])
x2 = Matrix([cos(2 * t), sin(2 * t), 3 * t])
tss = [(0, 1),
(1, 3)]
class MyTestCase(TestCase):
def test1(self):
l = Integral(sqrt(sum([Derivative(f, t, 1).doit() ** 2 for f in x1])),
(t, *tss[0])).doit().simplify()
self.assertEqual(l, sqrt(2))
def test2(self):
l = Integral(sqrt(sum([Derivative(f, t, 1).doit() ** 2 for f in x2])),
(t, *tss[1])).doit().simplify()
self.assertEqual(l, 2 * sqrt(13))
colors = ['red', 'green', 'blue', 'brown', 'orange',
'purple', 'pink', 'gray', 'skyblue', 'yellow']
p = plot3d_parametric_line(*[(*x1, (t, t1, t2))
for t1, t2 in [(-10, 0), tss[0], (1, 10)]],
legend=True,
show=False)
for o, color in zip(p, colors):
o.line_color = color
p.save('sample1.png')
p = plot3d_parametric_line(*[(*x2, (t, t1, t2))
for t1, t2 in [(-10, 1), tss[1], (3, 10)]],
legend=True,
show=False)
for o, color in zip(p, colors):
o.line_color = color
p.show()
p.save('sample2.png')
if __name__ == "__main__":
main()
入出力結果(Zsh、PowerShell、Terminal、Jupyter(IPython))
% ./sample1.py -v
1, 2.
test1 (__main__.MyTestCase) ... ok
test2 (__main__.MyTestCase) ... ok
----------------------------------------------------------------------
Ran 2 tests in 1.271s
OK
%
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