SymPy,使用已知模式或子表达式的简化/替换 [英] SymPy, simplification / substitution using known patterns or sub-expressions
问题描述
我有以下表达式:
from sympy import pi, sin, cos, var, simplify
var('j,u,v,w,vt,wt,a2,t,phi')
u0 = v*a2*sin(pi*j/2 + pi*j*t*phi**(-1)/2) + pi*vt*a2*cos(pi*j/2 + pi*j*t*phi**(-1)/2)*j*phi**(-1)/2 + pi*w*a2*cos(pi*j/2 + pi*j*t*phi**(-1)/2)*j*phi**(-1)
可以简化:
print simplify(u0)
#a2*(pi*j*vt*cos(pi*j*(phi + t)/(2*phi)) + 2*pi*j*w*cos(pi*j*(phi + t)/(2*phi)) + 2*phi*v*sin(pi*j*(phi + t)/(2*phi)))/(2*phi)
给出子表达式:
bj = pi*j*(phi + t)/(2*phi)
cj = j*pi/(2*phi)
目前,我在简化的u0
表达式中手动替换了bj
和cj
以获得:
Currently I substitute manually bj
and cj
in the simplified u0
expression to get:
u0 = a2*(v*sin(bj) + cj*vt*cos(bj) + 2*cj*w*cos(bj))
是否可以使用SymPy来实现这一目标,而避免手动替换?
Is it possible to use SymPy to achieve that, avoiding the manual substitution?
推荐答案
我想您缺少的是subs
将替换任意表达式,而不仅仅是符号
I guess what you are missing is that subs
will replace arbitrary expressions, not just symbols
>>> print simplify(u0).subs({pi*j*(phi + t)/(2*phi): bj, j*pi/(2*phi): cj})
a2*(pi*j*vt*cos(bj) + 2*pi*j*w*cos(bj) + 2*phi*v*sin(bj))/(2*phi)
(我使用了simplify
,因为这是pi*j*(phi + t)/(2*phi)
而不是pi*j/2 + pi*j*t/(2*phi)
的结果,但并非必须如此)
(I used simplify
because that is what results in the pi*j*(phi + t)/(2*phi)
instead of pi*j/2 + pi*j*t/(2*phi)
, but it's not otherwise required)
阅读 http://docs.sympy.org/0.7.3/tutorial/basic_operations. html#substitution 了解有关替换和替换的更多信息.如果要进行更高级的替换,请查看
Read http://docs.sympy.org/0.7.3/tutorial/basic_operations.html#substitution for more information about substitution and replacement. If you want to do more advanced replacement, take a look at the replace
method.
这篇关于SymPy,使用已知模式或子表达式的简化/替换的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持IT屋!