Sympy从表达式中得到二次项和线性项

Question

在x的函数中，我有一个任意的表达式E，我想从这个表达式中得到二次项、线性项和常数项。我该怎么做？

import sympy
from sympy import sin, cos
def separate(expression, var):
# ...
return Q, L, C
x, a, b, c = sympy.symbols("x a b c")
separate(a*x**2 + b*x + c)   # Q = a, L = b, C = c
separate(cos(x), x)    # Q = 0, L = 0, C = cos(x)
separate(x*cos(x), x)  # Q = 0, L = cos(x), C = 0
separate(sin(x), x)    # Q = 0, L = 0, C = sin(x)
separate(x*sin(x), x)  # Q = 0, L = sin(x), C = 0

我尝试过导数，但当我有cos、sin、exp等函数时，我的函数就坏了。

Answer 1

也许使用.coeff()？

def separate(expression, var):
Q = expression.coeff(var**2)
L = expression.coeff(var)
C = (expression - (Q * var + L) * var).simplify()
print(expression,' t -->', [Q, L, C])
return Q, L, C

结果：

a*x**2 + b*x + c     --> [a, b, c]
cos(x)       --> [0, 0, cos(x)]
x*cos(x)     --> [0, cos(x), 0]
sin(x)       --> [0, 0, sin(x)]