#4681: [with new patch, needs review] General Smith normal form implementation
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Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.2.2
Component: linear algebra | Resolution:
Keywords: matrix, smith normal form |
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Changes (by davidloeffler):
* cc: ncalexan (added)
* summary: [with patch, needs work] General Smith normal form
implementation => [with new patch, needs
review] General Smith normal form
implementation
Comment:
(cc'ed to ncalexan as symplectic_basis is his territory)
Nobody's objected violently to the change yet on sage-devel, so the
following patch changes SNF over ZZ, to put 1's first and 0's last. (Also,
when M is non-square it puts the nonzero entries in the [i,i] diagonal,
not on some shifted diagonal ending in the bottom corner like the previous
code did -- I found that rather inconvenient.)
As I suggested above, I've changed the call syntax over a general ring to
be consistent with the existing code over ZZ, so I got rid of the
"transformation=True" argument and added an extra function
"elementary_divisors" which returns the diagonal entries of M. This can be
overridden later, if anyone feels like implementing a fast algorithm for
elementary divisors for more general rings.
I've also fixed up "symplectic_basis" to be consistent with the new
"smith_form"; it doesn't explicitly use smith_form, but the conventions
for the output are chosen for consistency with smith_form, so I've changed
them in tandem. (ncalexan: is this OK with you?)
I didn't actually make it choose ideal representatives that compare as >=
0 -- I decided I couldn't bear to fix such a horrible convention. This
means that if R is a general PID, coercing integer matrices from ZZ to R
doesn't quite commute with Smith form, but I don't see why one should
expect it to.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4681#comment:9>
Sage <http://sagemath.org/>
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