2020年6月30日火曜日

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7章(不等式)、2(2次不等式)の問6の解答を求めてみる。



    1. x < - 3 2 , 1 < x

    2. x < - 5 3 , 4 < x

    3. ( x - 4 ) ( x + 1 ) 0 x - 1 , 4 x

    4. ( x - 6 ) ( x + 4 ) < 0 - 4 < x < 6

    5. 2 x 2 - x - 6 < 0 ( x - 2 ) ( 2 x + 3 ) < 0 - 3 2 < x < 2

    6. 3 x 2 + x - 10 > 0 ( 3 x - 5 ) ( x + 2 ) > 0 x < - 2 , 5 3 < x

    7. ( x + 4 ) 2 > 0 \ { - 4 }

    8. x 2 0 x = 0

    9. D 4 = 9 - 20 < 0 ϕ

    10. ( 2 x + 3 ) 2 - 4 2 0 ( 2 x + 3 + 4 ) ( 2 x + 3 - 4 ) 0 ( 2 x + 7 ) ( 2 x - 1 ) 0 - 7 2 x 1 2

    11. 10 x 2 - 5 x + 2 > 0 D = 25 - 80 < 0

    12. 3 x 2 - 4 x - 3 < 0 3 x 2 - 4 x - 3 = 0 x = 2 ± 13 3 2 - 13 3 < x < 2 + 13 3

    13. x 2 + 2 x - 35 0 ( x + 7 ) ( x - 5 ) 0 x < - 7 , 5 < x

    14. x 2 - 3 x + 2 + x 2 - 6 x + 8 < 12 x - 30 2 x 2 - 21 x + 40 < 0 ( x - 8 ) ( 2 x - 5 ) < 0 5 2 < x < 8

コード

#!/usr/bin/env python3
from sympy import pprint
from sympy.solvers.inequalities import solve_univariate_inequality
from sympy.abc import x

print('6.')

exprs = [(x - 1) * (2 * x + 3) > 0,
         (4 - x) * (3 + 5 * x) < 0,
         x ** 2 - 3 * x - 4 >= 0,
         x ** 2 - 2 * x - 24 < 0,
         x + 6 - 2 * x ** 2 > 0,
         10 - 3 * x ** 2 < x,
         x ** 2 + 8 * x + 16 > 0,
         -2 * x ** 2 >= 0,
         4 * x ** 2 + 6 * x + 5 < 0,
         (2 * x + 3) ** 2 <= 16,
         5 * x - 10 * x ** 2 < 2,
         4 * x > 3 * (x ** 2 - 1),
         2 * x ** 2 + 3 * x - 10 >= x ** 2 + x + 25,
         (x - 1) * (x - 2) + (x - 2) * (x - 4) < 6 * (2 * x - 5)]

for i, expr in enumerate(exprs, 1):
    print(f'({i})')
    pprint(solve_univariate_inequality(expr, x))

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

% ./sample6.py
6.
(1)
(-∞ < x ∧ x < -3/2) ∨ (1 < x ∧ x < ∞)
(2)
(-∞ < x ∧ x < -3/5) ∨ (4 < x ∧ x < ∞)
(3)
(4 ≤ x ∧ x < ∞) ∨ (x ≤ -1 ∧ -∞ < x)
(4)
-4 < x ∧ x < 6
(5)
-3/2 < x ∧ x < 2
(6)
(-∞ < x ∧ x < -2) ∨ (5/3 < x ∧ x < ∞)
(7)
x > -∞ ∧ x < ∞ ∧ x ≠ -4
(8)
x = 0
(9)
False
(10)
-7/2 ≤ x ∧ x ≤ 1/2
(11)
-∞ < x ∧ x < ∞
(12)
    2   √13   2   √13    
x < ─ + ─── ∧ ─ - ─── < x
    3    3    3    3     
(13)
(5 ≤ x ∧ x < ∞) ∨ (x ≤ -7 ∧ -∞ < x)
(14)
5/2 < x ∧ x < 8
%

0 コメント:

コメントを投稿