On Feb 1, 12:46 pm, William Stein <[email protected]> wrote: > On Sun, Feb 1, 2009 at 11:21 AM, Roman Pearce <[email protected]> wrote: > > > I just want to point out the Maple's linear algebra is not quite as > > bad as old Linbox times imply. The linalg package has been obsolete > > for some time now. > > It should print a deprecation warning so I would know. Could you suggest > that?
I can ask but it was deprecated in Maple 6 so I don't think they'll change it now. > Does A := LinearAlgebra:-RandomMatrix(n); > create a random matrix with entries uniformly distributed between -99 and 99? Yes. > What algorithm is maple using to compute the determinants of integer > matrices? I'm curious if it is the same one as Sage uses, but Maple > is just slower because of a worse implementation. Based on the timing > discrepancies above, though, it appears that Maple is using a much > much worse O complexity algorithm. It's using chinese remaindering, which is bad for large matrices and large determinant. It also has code to identify structured systems. The linear solver uses p-adic lifting for dense systems (and a bunch of methods for sparse systems) which is fine. > By the way, most of the work for Sage computing dets uses IML, > not Linbox. IML is very good. The algorithms are good :) I'm not sure what Magma is doing, but if I had to guess, I'd say they are solving a system AX=B mod p where p is 23 bits using SSE floating point and using p- adic lifting and rational reconstruction to recover the determinant. I can't help thinking that in another year or two all this stuff will be done ten times faster on GPUs. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
