2020年3月7日土曜日

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4章(1次方程式, 2次方程式 )、5(解の係数の関係、2次式の因数分解)、2数を解にもつ2次方程式、問33の解答を求めてみる。



    1. α + β = - - 5 2 = 5 2 α β = - 4 2 = - 2 x - α + 3 x - β + 3 = 0 x 2 - α + β + 6 x + α β + 3 α + β + 9 = 0 x 2 - 5 2 + 6 x - 2 + 15 2 + 9 = 0 2 x 2 - 17 x + 29 = 0

    2. x - 4 α x - 4 β = 0 x 2 - 4 α + β x + 16 α β = 0 x 2 - 10 x - 32 = 0

    3. x - α 2 x - β 2 = 0 x 2 - α 2 + β 2 x + α 2 β 2 = 0 x 2 - α + β 2 - 2 α β x + α β 2 = 0 x 2 - 25 4 + 4 x + 4 = 0 4 x 2 - 41 x + 16 = 0

    4. x - α + β x - α β = 0 x - 5 2 x + 2 = 0 x 2 - 1 2 x - 5 = 0 2 x 2 - x - 10 = 0

    5. x - 1 α - 1 x - 1 β - 1 = 0 x 2 - 1 α - 1 + 1 β - 1 x + 1 α - 1 β - 1 = 0 x 2 - α + β - 2 α β - α + β + 1 x + 1 α β - α + β + 1 = 0 x 2 - 1 2 · - 2 7 x - 2 7 = 0 7 x 2 + x - 2 = 0

コード

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

print('33.')

x = symbols('x')
f = 2 * x ** 2 - 5 * x - 4
abcs = [(2, -17, 29),
        (1, -10, -32),
        (4, -41, 16),
        (2, -1, -10),
        (7, 1, -2)]
gs = [a * x ** 2 + b * x + c for a, b, c in abcs]
a, b = solveset(f)


class MyTestCase(TestCase):
    def test1(self):
        self.assertEqual({a + 3, b + 3}, solveset(gs[0]))

    def test2(self):
        self.assertEqual({4 * a, 4 * b}, solveset(gs[1]))

    def test3(self):
        self.assertEqual(
            {x0.expand() for x0 in [a ** 2, b ** 2]},
            solveset(gs[2]))

    def test4(self):
        self.assertEqual({x0.expand()
                          for x0 in [a + b, a * b]},
                         solveset(gs[3]))

    def test5(self):
        self.assertEqual({x0.simplify()
                          for x0 in [1 / (a - 1), 1 / (b - 1)]},
                         solveset(gs[4]))


p = plot(f, *gs,
         (x, -20, 20),
         ylim=(-20, 20),
         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(f'sample33.png')

if __name__ == "__main__":
    main()

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

% ./sample33.py -v
33.
test1 (__main__.MyTestCase) ... ok
test2 (__main__.MyTestCase) ... ok
test3 (__main__.MyTestCase) ... ok
test4 (__main__.MyTestCase) ... ok
test5 (__main__.MyTestCase) ... ok

----------------------------------------------------------------------
Ran 5 tests in 0.451s

OK
%

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