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
続 解析入門 (原書第2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章(ベクトルの微分)、1(微分係数)の練習問題8の解答を求めてみる。
コード
#!/usr/bin/env python3
from unittest import TestCase, main
from sympy import Matrix, Derivative, sin, cos, pi
from sympy.plotting import plot_parametric
from sympy.abc import t
print('8.')
a = Matrix([cos(t), sin(t)])
b = Matrix([cos(3 * t), sin(3 * t)])
class Test(TestCase):
def test3(self):
self.assertEqual(
Derivative(a, t, 1).doit().dot(a), 0
)
def test4(self):
self.assertEqual(
Derivative(b, t, 1).doit().dot(b), 0
)
p = plot_parametric(
(cos(t), sin(t), (t, 0, 2 * pi)),
(cos(pi / 3) + t * -sin(pi / 3),
sin(pi / 3) + t * cos(pi / 3),
(t, 0, 1)),
(t * cos(pi / 3), t * sin(pi / 3), (t, -1, 1)),
legend=True,
show=False
)
colors = ['red', 'green', 'blue', 'brown', 'orange',
'purple', 'pink', 'gray', 'skyblue', 'yellow']
for o, color in zip(p, colors):
o.line_color = color
p.save('sample8_3.png')
p = plot_parametric(
(cos(3 * t), sin(3 * t), (t, 0, 2 * pi / 3)),
(cos(3 * pi / 3) + t * -3 * sin(3 * pi / 3),
sin(3 * pi / 3) + t * 3 * cos(3 * pi / 3),
(t, 0, 1)),
(-1 * t, 0, (t, -1, 1)),
legend=True,
show=False
)
colors = ['red', 'green', 'blue', 'brown', 'orange',
'purple', 'pink', 'gray', 'skyblue', 'yellow']
for o, color in zip(p, colors):
o.line_color = color
p.save('sample8_4.png')
p.show()
if __name__ == "__main__":
main()
入出力結果(Zsh、PowerShell、Terminal、Jupyter(IPython))
% ./sample8.py -v
8.
test3 (__main__.Test) ... ok
test4 (__main__.Test) ... ok
----------------------------------------------------------------------
Ran 2 tests in 0.006s
OK
%
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