2020年5月29日金曜日

学習環境

代数への出発 (新装版 数学入門シリーズ) (松坂 和夫(著)、岩波書店)の第6章(1次方程式、2次方程式)、4(2次関数のグラフ)の問9、10の解答を求めてみる。


  1. y = 0 - 2 2 - 1 = 3 0 = x - 2 2 - 1 x - 2 + 1 x - 2 - 1 = 0 x - 1 x - 3 = 0 x = 1 , 3


    1. 軸の方程式。

      x = 0

      頂点。

      0 , - 2

    2. x = - 1 - 1 , 0

    3. x = - 2 - 2 , 1

    4. x = 3 3 , 4

コード

#!/usr/bin/env python3
from unittest import TestCase, main
from sympy import symbols, plot

print('9, 10.')
x = symbols('x')
ys = [x ** 2 / 2 - 2,
      -2 * (x + 2) ** 2,
      (x + 2) ** 2 + 1,
      -(x - 3) ** 2 / 2 + 4]


class Test(TestCase):
    def test9(self):
        y = (x - 2) ** 2 - 1
        self.assertEqual(y.subs({x: 0}), 3)
        self.assertEqual(y.subs({x: 1}), 0)
        self.assertEqual(y.subs({x: 3}), 0)


p = plot(*ys,
         (x, -10, 10),
         ylim=(-10, 10),
         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.show()
p.save('sample10.png')

if __name__ == "__main__":
    main()

入出力結果(Zsh、PowerShell、Terminal、Jupyter(IPython))

% ./sample9.py -v
9, 10.
/opt/local/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/sympy/plotting/plot.py:1065: MatplotlibDeprecationWarning: 
The set_smart_bounds function was deprecated in Matplotlib 3.2 and will be removed two minor releases later.
  self.ax[i].spines['left'].set_smart_bounds(True)
/opt/local/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/sympy/plotting/plot.py:1066: MatplotlibDeprecationWarning: 
The set_smart_bounds function was deprecated in Matplotlib 3.2 and will be removed two minor releases later.
  self.ax[i].spines['bottom'].set_smart_bounds(False)
test9 (__main__.Test) ... ok

----------------------------------------------------------------------
Ran 1 test in 0.002s

OK
%

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