I stumbled on some odd behavior today which I think I have isolated to characteristic polynomials. I've not been following linear algebra development very closely for a few months, so maybe this is known, or maybe I'm confused about something. But if it this is a bug, it seems like it could be serious. On 6.2.beta7.
n=31 J = jordan_block(0, n).change_ring(QQ) [(J^m).characteristic_polynomial() for m in range(1, n+1)] [x^31, x^16, x^21, x^23, x^25, x^26, x^26, x^27, x^27, x^28, x^28, x^28, x^28, x^28, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^29, x^31, x^31] It gets a bit weirder. For n=59, output is [x^59, x^59, x^59, x^59, x^51, x^59, x^59, x^59, x^53, x^53, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59, x^59] n = 31 is the smallest value where I see trouble. I think the 0 diagonal is necessary. The n=31 output is "typical", as the second power seems to have about half the expected degree, and eventually higher powers get the degree right. The matrices themselves look to be OK. I can make a ticket if that seems warranted. Rob -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
