There is no universal answer, it depends on the matrix. For some, Gauss-Bareiss will perform well, for some others Lagrange interpolation will, you can guess that with total degree and partial degree bounds. For some matrices (sparse ones) minor expansion will perform better (compute first all minors with columns 0 and 1, then all minors with columns 0 to 2 using previously computed minors and so on)..
On Sunday, August 20, 2023 at 2:16:45 PM UTC+2 Dima Pasechnik wrote: > a standard way to compute the determinant in such cases is interpolation > at random points. > > you won't need much more memory than the space for the coefficients of the > corresponding polynomial. > > > > On Sun, 20 Aug 2023, 13:53 ETAL, <amals...@gmail.com> wrote: > >> Dear all , >> I'm seeking advice on how to speed up the computation of the determinant >> for large symbolic matrices. Are there alternative approaches, >> optimizations, or libraries that could help me achieve faster results? I'm >> particularly interested in any insights that might help me handle a 20x20 >> matrix with 5 variables efficiently. >> Additionally, I suspect that memory allocation might be contributing to >> the issue. Could anyone provide guidance on how much memory I should >> allocate for these computations? This information could be crucial in >> tackling the memory-related challenges I'm facing, as it was one of the >> issues i ran into while trying to run the code on super computer. >> I greatly appreciate your help! >> Best, >> Amal >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-devel" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-devel+...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-devel/0e98d9c9-b211-464d-be18-061fb060e81fn%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sage-devel/0e98d9c9-b211-464d-be18-061fb060e81fn%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/67be5db5-b3af-4ba3-8730-5ac60a00066en%40googlegroups.com.
