multiply matrix of matrices by a scalar: boom

[jhpalmieri]

From  stackoverflow: Define a to be a matrix whose entries are matrices, and multiply a by a scalar:

a = matrix([[matrix([[ 1,  2], [ 3,  4]]),
             matrix([[ 5,  6], [ 7,  8]])],
            [matrix([[ 9, 10], [11, 12]]),
             matrix([[13, 14], [15, 16]])]])
3 * a

This results in the following error message:

TypeError: unsupported operand parent(s) for '*':
           'Full MatrixSpace of 2 by 2 dense matrices over Integer Ring' and
           'Full MatrixSpace of 2 by 2 dense matrices over Integer Ring'

which is clearly nonsense. Multiplying a by, for example, 3 * identity_matrix(2) works, by the way.

Apply only 12964-fix-mul.patch .

[mhansen]

This happens because matrices don't really use _mul_. The end result is less efficient than it could be (since you're doing matrix multiplications for each entry); however, I think this would be for another ticket.

[mhansen]

Another option would be to define _mul_ on matrices to do _matrix_times_matrix_.

[robertwb]

apply just this patch

[robertwb]

My first thought when reading this patch (before even reading your comments) was also to add a _mul_ method on matrices. _rmul_ should always be safe to call with identical ring elements, and this assumption is used in many other places.

[jhpalmieri]

Robert: after your patch, regarding __mul__ and _mul_ for matrices in element.pyx: what are their roles? In what order do they get called?

[mhansen]

The matrix code (changed in the first patch) assumed that you can always call _mul_ on the entries of the matrix in order to do multiplication. However, this is not the case if the entries of the matrix are in fact matrices themselves since they bypass the coercion system, implement __mul__ directly (which calls _matrix_times_matrix_), and don't implement _mul_. Robert's patch just implements _mul_ to do "what it should" in case there are other places that assume that you can always use _mul_ directly.

Positive review for Robert's patch.

Apply only 12964-fix-mul.patch .

[robertwb]

Thanks, Mike, for revewing this.

Replying to jhpalmieri:

Robert: after your patch, regarding __mul__ and _mul_ for matrices in element.pyx: what are their roles? In what order do they get called?

To close the loop on this, a.__mul__(b) is called by Python when a * b is encountered. a._mul_(b) is called by the coercion model when parent(a) is parent(b) to actually do the arithmetic. Full details at http://www.sagemath.org/doc/reference/coercion.html