#11579: Free module equality, comparisons
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Reporter: rbeezer | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: linear algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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On #11553, mmarco gives an example that can be distilled to:
{{{
sage: R = PolynomialRing(QQ, 'a')
sage: x = vector(R, [1, 0])
sage: y = vector(R, [0, 1])
sage: z = vector(R, [0,-1])
sage: A = (R^2).span([x, y])
sage: B = (R^2).span([x, z])
sage: A == B
False
sage: A.is_submodule(B)
True
sage: B.is_submodule(A)
True
}}}
Root cause looks like an assumption that echelon form (Hermite form) over
PIDs is unique, which may be insurmountable in general.
{{{
sage: S = matrix([x, y])
sage: S._echelon_form_PID()[1]
[1 0]
[0 1]
sage: T = matrix([x, z])
sage: T._echelon_form_PID()[1]
[ 1 0]
[ 0 -1]
}}}
This also affects the ordering of free modules via the {{{__cmp__}}}
method.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11579>
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