#10625: Generic smith form of a matrix fails on integer matrix
-----------------------+----------------------------------------------------
Reporter: rbeezer | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.2
Component: algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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The generic Smith Form routine fails for integer matrices, making me
suspicious it needs some attention. The specialized version for integer
matrices seems fine, so this is not a problem per se, just evidence
something is amiss. Here's the evidence, obtained by shipping in a sparse
matrix - this should soon be fixed by sending sparse matrices to the
working dense version. So if you test this ''use something like 4.6.1 or
earlier''.
{{{
sage: A = matrix(2,range(4), sparse=True)
sage: A.smith_form()
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/sage/sage-4.6.1.alpha2/<ipython console> in <module>()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.smith_form
(sage/matrix/matrix2.c:37477)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2._smith_onestep
(sage/matrix/matrix2.c:42366)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2._smith_onestep
(sage/matrix/matrix2.c:42181)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in
sage.matrix.matrix2._generic_clear_column (sage/matrix/matrix2.c:41049)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/rings/integer.so in sage.rings.integer.Integer.inverse_mod
(sage/rings/integer.c:28740)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/rings/integer.so in sage.rings.integer.as_Integer
(sage/rings/integer.c:6052)()
/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-
packages/sage/rings/integer.so in sage.rings.integer.Integer.__init__
(sage/rings/integer.c:7312)()
TypeError: unable to coerce <class 'sage.rings.ideal.Ideal_pid'> to an
integer
}}}
On the input above, I think the failure is in
`sage.matrix.matrix2._generic_clear_column` at the line:
{{{
c = R(a[0,0] / B).inverse_mod(R.ideal(a[k,0] / B))
}}}
which would be
{{{
ZZ(2/1).inverse_mod(ZZ.ideal(3/1))
}}}
which by itself fails in a similar fashion.
Can you place an ideal inside `Integer.inverse_mod`?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10625>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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