Python 如何在辛方程中计算矩阵的幂?
我有一个来自于Python 如何在辛方程中计算矩阵的幂?,python,sympy,factorization,Python,Sympy,Factorization,我有一个来自于 from sympy.physics.quantum import Commutator as cmm x, t, A, V, W, D = sp.symbols('x t A V W D', commutative = False) Q = sp.Function('Q', commutative = False) F = (sp.diff(Q(x,t),x)+ cmm(W,Q(x,t)).doit() - sp.I*cmm(A,Q(x,t)+ cmm
from sympy.physics.quantum import Commutator as cmm
x, t, A, V, W, D = sp.symbols('x t A V W D', commutative = False)
Q = sp.Function('Q', commutative = False)
F = (sp.diff(Q(x,t),x)+ cmm(W,Q(x,t)).doit() - sp.I*cmm(A,Q(x,t)+ cmm(W,Q(x,t)).doit()).doit())*(sp.diff(Q(x,t),x)+ cmm(W,Q(x,t)).doit() - sp.I*cmm(A,Q(x,t)+ cmm(W,Q(x,t)).doit()).doit())
F.expand()
这给了我一个表达式,其中的元素在W中为零级,在W中为一级,在W中为二级。我只想要第一份W的。我尝试了因子分解过程,但由于没有交换的事实,它似乎不承认W的幂,它总是给我0。有什么简单的方法可以做到这一点吗?当然我可以用手做,但这不是我的目标
谢谢您可以在遍历F的参数时收集W中一阶的所有术语:
>>> from sympy import Add
>>> first_order_terms = []
>>> for i in Add.make_args(F.expand()):
... if i == W or i.is_Mul and i.has(W) and i.subs(W,y).as_independent(y)[1] == y:
... first_order_terms.append(i)
...
>>> Add(*first_order_terms)
-A*W*Q(x, t)*A*Q(x, t) - I*A*W*Q(x, t)*Derivative(Q(x, t), x) + A*W*Q(x, t)**2*A -
A*Q(x, t)*A*W*Q(x, t) + A*Q(x, t)*A*Q(x, t)*W + A*Q(x, t)*W*A*Q(x, t) - I*A*Q(x,
t)*W*Q(x, t) + I*A*Q(x, t)*W*Derivative(Q(x, t), x) + I*A*Q(x, t)**2*W - A*Q(x,
t)**2*W*A - I*W*Q(x, t)*A*Q(x, t) - W*Q(x, t)*A*Q(x, t)*A + I*W*Q(x,
t)*A*Derivative(Q(x, t), x) + W*Q(x, t)*A**2*Q(x, t) + W*Q(x, t)*Derivative(Q(x, t),
x) + I*W*Q(x, t)**2*A + I*Q(x, t)*A*W*Q(x, t) - Q(x, t)*A*W*Q(x, t)*A - I*Q(x,
t)*A*Q(x, t)*W + Q(x, t)*A*Q(x, t)*W*A + Q(x, t)*A**2*W*Q(x, t) - Q(x, t)*A**2*Q(x,
t)*W + I*Q(x, t)*W*A*Q(x, t) + Q(x, t)*W*A*Q(x, t)*A - I*Q(x, t)*W*A*Derivative(Q(x,
t), x) - Q(x, t)*W*A**2*Q(x, t) - I*Q(x, t)*W*Q(x, t)*A - Q(x, t)*W*Derivative(Q(x,
t), x) - I*Derivative(Q(x, t), x)*A*W*Q(x, t) + I*Derivative(Q(x, t), x)*A*Q(x, t)*W +
Derivative(Q(x, t), x)*W*Q(x, t) + I*Derivative(Q(x, t), x)*W*Q(x, t)*A -
Derivative(Q(x, t), x)*Q(x, t)*W - I*Derivative(Q(x, t), x)*Q(x, t)*W*A