paizaでsympy その２

概要

sympyが、魔法なので、paizaで、やってみた。
練習問題、やってみた。

問題1

8x – 4 = 9x + 1
4x^2 = 100
3x^2 - 7x + 4 = 0
2x^2 + 4x = 48
5x^2 - 2x - 3 = 0
5x^2 - 3 = 0
(x - 3) ^ 2 = 3(x - 3）

import sympy as sym

x = sym.symbols('x')
print ("solve - 式を解く")
print (sym.solve(8 * x - 4 - 9 * x - 1))
print (sym.solve(4 * x * x - 100))
print (sym.solve(3 * x * x - 7 * x + 4))
print (sym.solve(2 * x * x + 4 * x - 48))
print (sym.solve(5 * x * x - 2 * x - 3))
print (sym.solve(5 * x * x - 3))
print (sym.solve((x - 3) * (x - 3) - 3 * (x -3)))
print (sym.solve(2 * x * x + 3 * x - 5))

問題2

xyz = -234
x + y + z = 20
5x – y + 2z = 85

import sympy as sym

x, y, z = sym.symbols('x y z')
f0 = x * y * z + 234
f1 = x + y + z - 20
f2 = 5 * x - y + 2 * z - 85
print ("solve - 式を解く")
print (sym.solve((f0, f1, f2)))

問題3

2 * x + 3 * y = 6
1 * x + 2 * y = 3

import sympy as sym

x, y = sym.symbols('x y')
f0 = 2 * x + 3 * y - 6
f1 = 1 * x + 2 * y - 3
print ("solve - 式を解く")
print (sym.solve((f0, f1)))

問題4

x^2 - 10x + 24 = 0 のとき、xを求めよ。

import sympy as sym

x = sym.symbols('x')
f = x ** 2 - 10 * x + 24
print ("expand - 展開")
# print (sym.expand(f))
print ("factor - 因数分解")
print (sym.factor(f))
print ("simplify - 簡約")
# print (sym.simplify(f))
print ("limit - 極限")
# print (sym.limit(f, x, sym.oo))
print (sym.limit(f, x, 0))
print ("diff - 微分")
# print (sym.diff(f))
print ("integrate - 積分")
# print (sym.integrate(f))
print ("solve - 式を解く")
print (sym.solve(f))

問題5

2 * x + 2 * y + 6 * z + 3 = 0
x + y - 2 * z - 7 = 0
5 * x - 9 * y + 2 * z - 15 = 0

import sympy as sym

x, y, z = sym.symbols('x y z')
fuc1 = 2 * x + 2 * y + 6 * z + 3
fuc2 = x + y - 2 * z - 7
fuc3 = 5 * x - 9 * y + 2 * z - 15
print (sym.solve([fuc1, fuc2, fuc3], [x, y, z]))

以上。