On Mar 28, 4:18 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > On 3/28/07, Michel <[EMAIL PROTECTED]> wrote: > > > I have repeatedly read on this list that sage has now optimized > > routines for > > linear algebra mod p. Does this extend to linear algebra mod m with m > > not prime? > > > I am mainly thinking about solving a system of linear equations (with > > presumably > > a unique solution). > > What is m? What is the system of equations like? Ax=b where A is a matrix over Z/mZ, b is a column vector over Z/mZ and x is an unknown column vector over Z/mZ. m is composite. In the discrete log example we were discussing I think A was a 14000x14000 sparse matrix over p-1. Here p was a number with 128bits. (That's what I gathered from the debug output). > > > I know that one can reduce this problem to the prime case (if one > > knows > > the factorization of m) but I wonder if this now already built in. > > No, this is not built in. > > And our optimized mod-p linear algebra is only for p fairly small > (e.g., less than 46000). > > William Hmm, sorry I had misunderstood. Michel --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
