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Determinant function in Mathematica


I wonder if someone in this group could shed some light on why
the Det[] function in Mathematica requires as much time as it does.

I have been trying to compute the symbolic determinant of a 4x4
matrix and Mma has been running for about 18 hours with no answer.

This seems like a large amount of time for such a simple problem.
I talked to another person doing similar calculations and he ran into
the exact same problem with both Mma and Maple.

Has anybody out there found a fix for this problem? I would like to
hear from people who have perhaps written Determinant functions that
take full advantage of sparse matrices.

The problem I am looking at is that of computing saddle-node and Hopf
bifurcations in nonlinear ordinary differential equations. I need to
be able to take the determinant of the Jacobian with the fixed point
and parameter values left unspecified.

Thanks for your help
	Tony Varghese





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