Chris, I'm having trouble posting a reply here. Here's the essence of what I wanted to show you. Perhaps more in just a minute.
sage: m=matrix(QQ, [[3/2, 4/3], [1/7, 5/11]) sage: m._clear_denoms() ([693 616] [ 66 210], 462) Rob On Mar 19, 8:13 pm, Mike Hansen <mhan...@gmail.com> wrote: > On Mar 19, 6:54 pm, Chris Godsil <cgod...@uwaterloo.ca> wrote: > > > What algorithm(s) does sage use to compute determinants over QQ[t] or > > QQ[t,u]? > > For both of these, it is computing them using minors, which is awful > when the matrices are not tiny. > > > Does they work over the ring of definition, or over the field of > > fractions? > > These work over the ring of definition. If you work over the field of > fractions, then you can get some speedup since you can put then matrix > in Hessenberg form and read the determinant off from the > characteristic polynomial. For the CycleGraph(9): > > sage: m.change_ring(R.fraction_field()).det() > t^9 - 9*t^7 + 27*t^5 - 30*t^3 + 9*t - 2 > CPU time: 0.54 s, Wall time: 0.57 s > > > over QQ[t] is not polynomial time. As the Reference Manual suggests, I > > entered > > M.determinant? to see what algorithm was being used, but did not get > > any useful information. > > In this case, doing M.determinant?? to see the actual source code > gives you everything it's doing. > > --Mike --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
