How to simplify matrix expressions in SymPy?

Question

Consider the following example

import sympy as sy
n = sy.symbols('n')
A = sy.MatrixSymbol("A",n,n)
B = sy.MatrixSymbol("B",n,n)
C = sy.MatrixSymbol("C",n,n)
M = A.inverse()*B.inverse() - A.inverse()*C*B.inverse()
B.inverse()*M.inverse()*A.inverse()

The example prints out B^-1*(A^-1*B^-1 - A^-1*C*B^-1)^-1*A^-1.

Can SymPy simplify the expression to (I-C)^-1? If not, how about any of the intermediate results, like collecting common factors in M?

Answer 1

The work around for this is using string converting on expression:

from sympy import *

n = symbols('n')
A = MatrixSymbol("A",n,n)
B = MatrixSymbol("B",n,n)
C = MatrixSymbol("C",n,n)
M = A.inverse()*B.inverse() - A.inverse()*C*B.inverse()
expression = B.inverse()*M.inverse()*A.inverse()

# convert expression to string then simplify
simplify_expression = simplify(str(expression))

pprint(simplify_expression)

Output:

 -1  
─────
C - 1