How compute a big determinant?

I have the following problem:

I need to compute the determinant of a n*n matrix M (with n "not small", n=10, 15,21 for instance) the coefficients of which are formal expression in u,v,log(u), log(v), log(1-u), log(1-v),.... and two inderterminate dU and dV.

The result is a homogeneous polynomial P in dU and dV, with coefficients in u,v,etc... I know that the solutions of P=0 are very simple expressions in u,v,etc.. I need to know these solutions!

But even in some simple cases, Maple 10 can not achieves the computation of det(M).

Is there a way in Maple (or Is exists an other soft than Maple) to make this kind of computations?

Thanks in advance for any Help!

A geometer (who want to compute!)
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