Comment #6 on issue 1441 by mattpap: integrate takes forever
http://code.google.com/p/sympy/issues/detail?id=1441

Perhaps fixing issue 1850 would help. I don't know much about matrix algorithms. Can rref be made more efficient for sparse matrices (the average equation has
about 4 variables)?

The solution is pretty simple: rewrite linear algebra module (and linear solvers) the same way as polynomials manipulation module was rewritten (take advantage of specific ground types (e.g. gmpy), ...). This is a lot of work, but in the end we will arrive
with fast linear algebra in SymPy.

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