#12693: bug in jordan_form(transformation=true) for integer matrices
---------------------------------------+------------------------------------
Reporter: hthomas | Owner: jason, was
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.1
Component: linear algebra | Resolution:
Keywords: jordan form, sd40.5 | Work issues:
Report Upstream: N/A | Reviewers: Rob Beezer
Authors: Douglas McNeil | Merged in:
Dependencies: | Stopgaps: todo
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Changes (by {'newvalue': u'Douglas McNeil', 'oldvalue': ''}):
* status: new => needs_review
* reviewer: => Rob Beezer
* author: => Douglas McNeil
Old description:
> {{{
> sage: M=matrix(((2,2,2),(0,0,0),(-2,-2,-2)))
> sage: M.jordan_form(transformation=true)
> (
> [0 1|0]
> [0 0|0] [ 2 1 1]
> [---+-] [ 0 0 0]
> [0 0|0], [-2 0 -1]
> )
> }}}
>
> If the output from M.jordan_form(transformation=true) is J,P, then we are
> supposed to have J=P^-1^ M P. The output here is obviously wrong, since
> P is not invertible (having a zero row).
>
> If you change the 2's to 1's and the -2's to -1's it works properly.
>
> This behaviour exists in 4.8 and 5.0beta5.
New description:
{{{
sage: M=matrix(((2,2,2),(0,0,0),(-2,-2,-2)))
sage: M.jordan_form(transformation=true)
(
[0 1|0]
[0 0|0] [ 2 1 1]
[---+-] [ 0 0 0]
[0 0|0], [-2 0 -1]
)
}}}
If the output from M.jordan_form(transformation=true) is J,P, then we are
supposed to have J=P^-1^ M P. The output here is obviously wrong, since P
is not invertible (having a zero row).
If you change the 2's to 1's and the -2's to -1's it works properly.
This behaviour exists in 4.8 and 5.0beta5.
'''Apply:'''
1. [attachment:trac_12693_fix_jordan_form_bug.3.patch]
1. [attachment:trac_12693_fix_jordan_form_reviewer.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12693#comment:9>
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