Determinant probably is aimed at
symbolic determinant entries. There
is also a program called newdet.
expansion by minors is actually faster
for some inputs (not numbers).
A good purely numerical version
is worth doing, I think.
RJF
Fabrizio Caruso wrote:
> Hi!
>
> While implementing my package on
> real algebraic geometry I have
> discovered how slow the commmands
> "Determinant" and "Triangularize" are.
>
> Then I reimplemented "the wheel"
> and with my surprise my implementation
> is much much faster. The main reason being
> that I used arrays instead of lists.
>
> "Triagularize" is moderately slow
> but "Determinant" is pathologically
> slow. It looks like it doesn't even use
> Gaussian elimination. Maybe it uses
> Laplace rule.
>
> Some timings:
> (%i22) Triangularize(apply(matrix,Hilbert(100)))$
> Evaluation took 248.75 seconds (250.41 elapsed) using 6807858.430 KB.
> (%i23) gaussElim(Hilbert(100))$
> Evaluation took 72.27 seconds (72.28 elapsed) using 1152581.820 KB.
>
> "Determinant" cannot compute
> determinants of even small sizes
> like 30.
>
> Fabrizio
>
>
>
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