#16893: Free modules over PIDs
-------------------------------------+-------------------------------------
Reporter: aly.deines | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: linear algebra | Resolution:
Keywords: free modules, PID | Merged in:
Authors: aly.deines | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/aly.deines/free_modules_over_pids| 867b1507389a0b3f3c4be024bffb0c8a1f1a2cb8
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'aly.deines', 'oldvalue': ''}):
* status: new => needs_review
* author: => aly.deines
* component: PLEASE CHANGE => linear algebra
* keywords: => free modules, PID
* commit: => 867b1507389a0b3f3c4be024bffb0c8a1f1a2cb8
* type: PLEASE CHANGE => defect
Old description:
New description:
{{{
sage: F.<a> = NumberField(x^2-x-1)
sage: ZF = F.ring_of_integers()
sage: A = matrix(ZF,[[1,0,0,0],[0,-1,0,0],[0,0,1,0],[0,0,0,1]])
sage: B = identity_matrix(ZF,4)
sage: VA = (ZF^4).span(A)
sage: VB = (ZF^4).span(B)
sage: VB == VA
False
}}}
This should return true. As Sage is only checking the echelon form, it is
not catching this.
To fix this I used the wrapped pseudo basis nfhnf and compute the Hermite
normal form and the pseudo basis ideal list as _pseudo_hermite_matrix.
--
Comment:
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=5b40230340a931a2a7d5dd56215d4023e6100b15
5b40230]||{{{Added _pseudo_hermite_matrix so we can check equality of free
modules over rings of integers of number fields.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=867b1507389a0b3f3c4be024bffb0c8a1f1a2cb8
867b150]||{{{Added a _pseudo_basis_matrix method to modules/free_module.py
and}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/16893#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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