coherent handling of trivial matrices (depend on #5244, #5242).

[hivert]

There where a lot of inconsistency and bugs in the handling of trivial matrices. The following patch aims to solve these and to check systematicly the coherence. Here is a selection of weirdness:

• plain wrong answers

sage: m = matrix(SR, 1,1, [1])
sage: m.inverse()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

sage: m = matrix(RDF, 0,2)
sage: m.inverse()
[]

• Inconsistencies in the answers depending on the base ring

sage: m = matrix(RDF, 1,1)
sage: m.inverse()
---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)

whereas

sage: m = matrix(QQ, 1,1)
sage: m.inverse()
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)

Aside rewriting some error messages, changing some exception and working around several bug in particular in maxima's handling of matrix over SR, the main contribution of this patch lies in the function test_trivial_matrices_inverse in sage/matrix/matrix_space.py and its associated doctests. Trough a bunch of assertions this function indirectly checks the behavior of matrix spaces. Any new implementation of a kind of matrices should be checked be this function.

Patch Author: Florent Hivert

CC: @sagetrac-sage-combinat

Component: linear algebra

Keywords: matrices, invert, determinant

Issue created by migration from https://trac.sagemath.org/ticket/5256

[jasongrout]

comment:2

I'm really happy you did all this. I'll look at this soon, unless someone else gets to it before me.

It'd be great to have a system-wide function that tested different Sage types for consistency on things like this. That way, all someone would have to remember to do is add their new sage type to a doctest like:

sage: check_consistency(MY_NEW_TYPE)
True

That function would automatically call things like the function in this patch and other functions for vectors, polynomials, etc.

[hivert]

comment:3

In his category framework, Nicolas Thiery wrote a very handy feature that allows one to add some plug in function to test properties on a parent object. For example in the category of groups there are among other the following methods (some are inherited from higher categories):

• test_some_elements
• test_associativity
• test_unity
• test_inverse Then once you have a group G you can ask for G.check() which lauch automatically all those tests. Unfortunately this is buried in the category framework and cannot be used right now. (see [sage-devel] Generic tests and categories 6 Feb 2009). In the mean time I do this by hands.

[hivert]

New version with a corrected typo (thanks Jason)

[malb]

comment:4

Attachment: empty_matrix_inverse-fh.patch.gz

Review patch looks good except

• typo: "seld" -> "self" (2402)
• docstring INPUT block of test_trivial_matrices_inverse does not conform to Sage's conventions
• "TODO: must be adapted to Nicolas check framework (see trac FIXME)." The FIXME should probably be addressed

i.e. all issues are trivial.

I didn't run doctests yet, will do now.

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:5

I have doctested this patch on top of #5242 and #5244 in my current Sage 3.3.rc1 merge tree and:

All tests passed!

Cheers,

Michael

[hivert]

comment:6

Replying to @malb: Done ! See the new patch.

Note that I currently didn't had time to check it. It's currently being done on my machine but it takes times. I only change docs from the first version but who knows...

[hivert]

Reupped after malb request on irc.

[mwhansen]

comment:7

Attachment: trivial_matrices_inverse-5256-submitted.patch.gz

Positive review on trivial_matrices_inverse-5256-submitted.patch.

[mwhansen]

comment:8

Note that there is #5274 for the TODO/FIXME.

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:9

Merged trivial_matrices_inverse-5256-submitted.patch in Sage 3.3.rc1.

Cheers,

Michael