#6178: [with patch, needs review] Hermite normal form over PID's
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Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-4.0.2
Component: linear algebra | Keywords: echelon form
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Changes (by davidloeffler):
* cc: was (added)
* owner: was => davidloeffler
* status: new => assigned
Comment:
Here's a patch, which adds echelon form (= Hermite normal form) over
PID's. I've also added a simple routine for kernel finding over PID's
using Smith form (since the algorithm we had before silently assumed that
the base ring was a field).
With this installed, I've done some playing around with free modules over
the ring of integers of Q(sqrt(-7)), and it seems to be quite usable.
There are unresolved uniqueness issues, because I don't know how to pick a
canonical generator for an ideal or a canonical representative for an
element modulo an ideal (even in the particular case of number field
orders), but I haven't yet found an example where this is a problem :-)
William: I'm CCing you on this, because you seemed interested in the Smith
form stuff. In conjunction with your work at #5882 this will mean we can
handle all sorts of new kinds of modules.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6178#comment:1>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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