On Saturday 07 February 2009, Florent Hivert wrote:
>       Dear All,
>
>    I'm preparing a patch which allows one to use generic_power (computing
> a^n) for monoids and even semi groups. So I had to change the handling of
> particular cases (a=0 or n=0). After this change all tests passes except
> for one in matrix_mod2_dense:
> **********************************************************************
> File
> "/usr/local/sage/devel/sage-combinat/sage/matrix/matrix_mod2_dense.pyx",
> line 755: sage: A^(-1)
> Expected:
>     Traceback (most recent call last):
>     ...
>     ZeroDivisionError
> Got:
>     []
> **********************************************************************
> Here is the corresponding code
>     TESTS:
>         sage: A = matrix(GF(2),0,0)
>         sage: A^(-1)
>         Traceback (most recent call last):
>         ...
>         ZeroDivisionError
>
> Note that with my patch it answers without touching the matrix code the
> empty matrix "[]". Even if the set of 0x0 matrix seems to be a strange ring
> (I think a ring has to contains at least two *different* elements 0 and 1),
> it is a perfectly acceptable multiplicative group. From this point of view,
> the empty matrix seems to be the correct answer. So I'm tempted to replace
> this test by testing the 1x1 zero matrix.
>
> So my question is the following: is there a specific reason why this test
> has been written ?

I wrote that doctest, because that behaviour is consistent with other 
matrices.

sage: A = random_matrix(GF(127),0,0)
sage: A^(-1)
Traceback (most recent call last)
...
ZeroDivisionError:

sage: A = random_matrix(QQ,0,0)
sage: A^(-1)
---------------------------------------------------------------------------
Traceback (most recent call last)
...
ZeroDivisionError:


I have no strong feelings about how things should behave as long as it is 
consistent. I suggest, to add doctests to catch these for the various matrix 
types while you're changing the behaviour. 

Martin

-- 
name: Martin Albrecht
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