Hello, I'm using the current developer version of sage and noticed that when computing determinants of matrices over polynomial rings and rational functions, cases where the determinant is easily seen to be zero due to zero rows or columns can take an unreasonable long time to compute. I compared the timings with the same computation over other domains.
sage: L.<x>=PolynomialRing(QQ) sage: MS=MatrixSpace(L,100) sage: time _=MS.zero().determinant() CPU times: user 13.4 s, sys: 19.6 ms, total: 13.5 s Wall time: 13.5 s sage: MS=MatrixSpace(L.fraction_field(),100) sage: time _=MS.zero().determinant() CPU times: user 200 ms, sys: 0 ns, total: 200 ms Wall time: 200 ms sage: MS=MatrixSpace(ZZ,100) sage: time _=MS.zero().determinant() CPU times: user 563 µs, sys: 5 µs, total: 568 µs Wall time: 573 µs sage: MS=MatrixSpace(L,40) sage: M=MS.random_element(3) sage: M=M.with_rescaled_row(0,0) sage: M.rows()[0]==0 True sage: time _=M.determinant() CPU times: user 35.2 s, sys: 8.06 ms, total: 35.2 s Wall time: 35.2 s sage: MS=MatrixSpace(L.fraction_field(),10) sage: M=MS.random_element(3) sage: M=M.with_rescaled_row(0,0) sage: M.rows()[0]==0 True sage: time _=M.determinant() CPU times: user 1min 56s, sys: 300 ms, total: 1min 56s Wall time: 1min 56s sage: MS=MatrixSpace(ZZ,500) sage: M=MS.random_element(2^40) sage: M=M.with_rescaled_row(0,0) sage: M.rows()[0]==0 True sage: time _=M.determinant() CPU times: user 67.6 ms, sys: 0 ns, total: 67.6 ms Wall time: 67.9 ms sage: Probably a preprocessing step could help that looks for zero rows or columns before running the actual algorithm. Best, Maximilian -- 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 post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
