Calculate a big determinant of the matrix 6 * 6 ?

Questions
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1

Hello, Community!
I’m seeking the determinant of the square matrix 6 * 6 (all members are nonzero & big polynoms of 6 variables):

Print[Det[a]]

Mathematica 9.0 writes

Expand::lrgexp: Exponent is out of bounds for function Expand. >>

(no command Expand in my program, only - Print[Det[a]]) and continues without result for several hours (after i abort it).
GroebnerBasis - no result.
Are some methods to solve this problem?

2

If the 6*6 matrix contains big polynomials then the determinant will be very big:

vars = Table[Unique[], {36}]
Det[Partition[vars, 6]]

If you look replace those variables afterwards it will certainly be a huge expression. Analytic substitution is possible but I’m wondering why you would want an analytic expression for such a thing… numerical evaluation before calculating the Det is way faster.

3

Hello, Sander!

Thanks for the answer - it helps me to understand what i really need.

Numerical evaluation & number as a result can’t be an answer here - need formula for former analyse.

Suddenly it counts - more then 1 mln members, 100 MB (=oi-oi-oi).

So, i recombined the problem and now work with determinant 4 * 4.