#5882: [with patch; not ready for review] implement general package for finitely
generated not-necessarily free R-modules
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Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0
Component: linear algebra | Keywords:
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Comment(by was):
It turns out there is a bug in 5882 still. In the following example,
computing the kernel of f is wrong, because f somehow gets defined by a
map on free modules V-->V that doesn't preserve the W's that we're
quotienting out by. Trac 5882 is basically the ultimate generalization
of that round2 problem everybody was confused by in 583 last quarter --
it's hard to get right!
{{{
sage: V = span([[1/14,3/14],[0,1/2]],ZZ); W = ZZ^2
sage: Q = V/W
sage: f = Q.hom([Q([1,11]), Q([1,3])])
sage: f
Morphism from module over Integer Ring with invariants (2, 14) to module
with invariants (2, 14) that sends the generators to [(1, 11), (1, 3)]
sage: f.kernel()
Finitely generated module V/W over Integer Ring with invariants (14)
sage: f.image()
Finitely generated module V/W over Integer Ring with invariants (14)
sage: f._phi
Free module morphism defined by the matrix
[ 11 -10]
[ 3 -2]
Domain: Free module of degree 2 and rank 2 over Integer Ring
User basis ...
Codomain: Free module of degree 2 and rank 2 over Integer Ring
Echelon ...
sage: R = Q.optimized()[0]; R
Finitely generated module V/W over Integer Ring with invariants (2, 14)
sage: f._phi(R.W()).is_submodule(W)
False
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5882#comment:12>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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