On Dec 8, 5:11 pm, Nick Alexander <[EMAIL PROTECTED]> wrote: > David, could I ask for some examples over > some other rings or doctests explaining why that doesn't work? I > think QQ[x] should work, and maybe ZZ / n ZZ (depending on how much > care you take to make it work).
It works in QQ[x] and there is a doctest, although somehow it ended up being put in the _smith_onestep docstring rather than the one for smith_form (because I was trying to nail down a bug which that matrix exposed). Over ZZ / n ZZ for n composite it isn't expected to work as the ring isn't a domain, but for n prime it should work. For some strange reason Integers(p) and GF(p) aren't the same. In the former it fails, as creating ideals in that ring breaks. Over the latter it does work, but the answers look a bit strange: sage: m = matrix(GF(23), 3,3,[15,9,22,11,13,15,7,9,15]); m.smith_form () ([15 0 0] [ 0 11 0] [ 0 0 19], [ 1 0 0] [10 1 0] [ 2 5 1], [ 1 4 14] [ 0 1 10] [ 0 0 1]) One would probably want Smith form over fields to give a diagonal matrix with first some 1's and then some 0's, but it doesn't. This is because the code doesn't try and pick "canonical generators" of ideals, since in general there isn't any good way of doing that. But there is a canonical generator of the unit ideal of any ring, namely 1, and perhaps I should make it pick this generator whenever possible. --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
