SymPy

Installation

# 記得先切到 virtualenv 裡面
$ pip install sympy

Example

Example 1

# var(names, **args)
#     Create symbols and inject them into the global namespace.
#
#     This calls :func:`symbols` with the same arguments and puts the results
#     into the *global* namespace. It's recommended not to use :func:`var` in
#     library code, where :func:`symbols` has to be used::

>>> from sympy import var
>>> var('x y')
(x, y)
>>> z = x + y
>>> z
x + y

>>> from sympy import symbols
>>> x, y = symbols('x y')
>>> z = x + y
>>> z
x + y
>>> z - x
y
>>> z + x
2⋅x + y
>>> z ** 2
       2
(x + y)
>>> (z ** 2).expand()
 2            2
x  + 2⋅x⋅y + y
# 把其他值代入原本的方程式
>>> z
x + y
>>> z.subs(x, 3)
y + 3
>>> z.subs({x: 3, y: 4})
7
>>> z.subs([(x, 3), (y, 4)])
7
# symbol 名稱跟變數名稱可以不同
>>> m, n = symbols('n m')
>>> m
n
>>> n
m
>>> from sympy import init_printing
>>> from sympy import Integral
>>> init_printing()
>>> a = Integral(z, x)
>>> a
⌠
⎮ (x + y) dx
⌡
>>> from sympy import pi
>>> pi
π
# .evalf(100) : 計算 formula 實際的值，精準度指定為 100 位 (包含整數部份)
>>> pi.evalf(100)
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
# .evalf(100, subs=...) : 計算 formula 實際的值 (代入其他值)，精準度為 100 位 (包含整數部份)
>>> z.evalf(100, subs={x: pi, y: 1})
4.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

Example 2

>>> from sympy import Symbol
>>> from sympy.solvers import solve
>>> x = Symbol('x')
>>> y = x**2 - 1
# 解出方程式 (x**2 - 1 = 0) 裡的 x
>>> solve(y, x)
[-1, 1]