On Wed, Feb 11, 2009 at 7:16 AM, Greg Kuperberg <[email protected]> wrote: > > On Feb 11, 2:11 am, daveloeffler <[email protected]> wrote: >> Yes, as William points out, I wrote a generic Smith normal form >> implementation which has been in Sage since version 3.2.2 a couple of >> months back. > > Oh okay, cool. Yes, my matrices would be sparse. > >> I didn't 100% follow what it was that you wanted to do, so I'm not >> quite sure if this answers your question. Did you just want Smith form >> of one matrix, or were you after some sort of simultaneous Smith form >> of multiple matrices? > > I am generating a Lie algebra inside 14 x 14 matrices, and I want to > know its dimension for different specializations of the ground ring's > variable d. So one way to do this is to flatten matrices in the Lie > algebra so that they become vectors of length 196. Then you can stack > these vectors to make a matrix which is 196 x (something), and then > find the SNF of that matrix. 196 x 196 is a lot though. > > Actually even better than SNF, or good in addition to SNF, would be > echelon form.
By echelon form do you mean Hermite Normal Form over that base ring, or do you mean echelon form over the fraction field? If you just want the dimension, is their any chance you can specialize one of the variables and compute the rank there -- if you do this for enough values it's likely to give you the correct rank, and of course is very fast. William --~--~---------~--~----~------------~-------~--~----~ 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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
