#9502: Basis parent bug in FreeModule
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Reporter: novoselt | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.5
Component: algebra | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* status: new => needs_review
* author: => Andrey Novoseltsev
Old description:
> There is an inconsistency in the example below for the echelonized basis
> of submodules with basis:
> {{{
> sage: F = FreeModule(ZZ, 3)
> sage: S = F.submodule_with_basis([(1,2,3),(3,2,1)])
> sage: parent(S.basis()[0])
> Free module of degree 3 and rank 2 over Integer Ring
> User basis matrix:
> [1 2 3]
> [3 2 1]
> sage: parent(S.echelonized_basis()[0])
> Ambient free module of rank 3 over the principal ideal domain Integer
> Ring
> }}}
>
> For automatic bases everything is OK:
> {{{
> sage: S = F.submodule([(1,2,3),(3,2,1)])
> sage: parent(S.echelonized_basis()[0])
> Free module of degree 3 and rank 2 over Integer Ring
> Echelon basis matrix:
> [1 2 3]
> [0 4 8]
> sage: parent(S.basis()[0])
> Free module of degree 3 and rank 2 over Integer Ring
> Echelon basis matrix:
> [1 2 3]
> [0 4 8]
> }}}
>
> I am working on a patch to fix this.
New description:
There is an inconsistency in the example below for the echelonized basis
of submodules with basis:
{{{
sage: F = FreeModule(ZZ, 3)
sage: S = F.submodule_with_basis([(1,2,3),(3,2,1)])
sage: parent(S.basis()[0])
Free module of degree 3 and rank 2 over Integer Ring
User basis matrix:
[1 2 3]
[3 2 1]
sage: parent(S.echelonized_basis()[0])
Ambient free module of rank 3 over the principal ideal domain Integer Ring
}}}
For automatic bases everything is OK:
{{{
sage: S = F.submodule([(1,2,3),(3,2,1)])
sage: parent(S.echelonized_basis()[0])
Free module of degree 3 and rank 2 over Integer Ring
Echelon basis matrix:
[1 2 3]
[0 4 8]
sage: parent(S.basis()[0])
Free module of degree 3 and rank 2 over Integer Ring
Echelon basis matrix:
[1 2 3]
[0 4 8]
}}}
While I was working on this patch, I expanded documentation for
`FreeModule_submodule_with_basis_pid` and rewrote its constructor to fix
the issue on this ticket and make its logic more clear.
I have also discovered that it avoids calling the base constructor which
checks that the base ring is indeed a PID. I tried to fix, got errors,
fixed one of them (thanks to Mike Hansen), but there are more with number
fields and since it was not the main issue on this ticket I delegated it
to #9503.
Current patch passed all tests on 4.5.alpha1.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9502#comment:1>
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