#18365: Definition of LU descomposition of a matrix depends on the base ring
------------------------------+----------------------------
Reporter: tmonteil | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.7
Component: linear algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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As reported on [http://ask.sagemath.org/question/26713/lu-descomposition-
for-a-matrix/ this ask question], there is an inconsistency in the
definition of the LU decomposition of a matrix depending on its base ring.
If a matrix `A` belongs to `ZZ`, `QQ`, `AA`, `QQbar`, `A.LU()` returns a
triple `(P,L,U)` such that `A=PLU`. If a matrix `A` belongs to `RDF`,
`A.LU()` returns a triple `(P,L,U)` such that `PA=LU`. For example:
{{{
sage: A = random_matrix(ZZ,4)
sage: A.LU()
(
[0 1 0 0] [ 1 0 0 0] [ 72 -4 -38 0]
[0 0 1 0] [ 0 1 0 0] [ 0 -1 -2 10]
[1 0 0 0] [ 1/36 8/9 1 0] [ 0 0 17/6 -80/9]
[0 0 0 1], [-1/36 1/9 -1 1], [ 0 0 0 -17]
)
sage: B = A.change_ring(RDF)
sage: B.LU()
(
[0.0 0.0 1.0 0.0]
[1.0 0.0 0.0 0.0]
[0.0 1.0 0.0 0.0]
[0.0 0.0 0.0 1.0],
[ 1.0 0.0 0.0 0.0]
[ 0.0 1.0 0.0 0.0]
[ 0.0277777777778 0.888888888889 1.0 0.0]
[-0.0277777777778 0.111111111111 -1.0 1.0],
[ 72.0 -4.0 -38.0 0.0]
[ 0.0 -1.0 -2.0 10.0]
[ 0.0 0.0 2.83333333333 -8.88888888889]
[ 0.0 0.0 0.0 -17.0]
)
sage: B.LU()[0] == A.LU()[0]
False
sage: B.LU()[0] == A.LU()[0].transpose()
True
sage:
}}}
The aim of this ticket is to fix this inconsistency and choose a common
definition for all rings.
--
Ticket URL: <http://trac.sagemath.org/ticket/18365>
Sage <http://www.sagemath.org>
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