From perspective of calculation time of matrix multiplications Infix operators
is a reasonable solution to define a subset of your own.
https://doc.sagemath.org/html/en/reference/misc/sage/misc/decorators.html#sage.misc.decorators.infix_operator
The problem is that if one implements it, there has to be a substitution at the
expense of loosing a default operator. In scientific libraries this isn't great
as all existing operators tend to be used.
What I would alternatively propose is to introduce a couple of (meaningless
operators), so that library developers can make use of them as they wish. What
characters aren't used? “$, ?, `” (or are they?).
A $pow$ 3 - meh
A ?pow? 3 - looks ok. The question mark is appropriately marking
ambiguous/implementation dependent meaning.
A `pow` 3 - looks good
A @@ 3 - doesn’t look too great...
A.pow(3) - nice
If I was lacking just one operator (especially in such case where different
algorithms can be used), A.pow(-1, inv_type=‘LU') feels most convenient given
flexibility of arguments.
If I was to go heavy on operators in matrix algebra or defining some sort of
new syntax, then @@ wouldn’t help anyways - it’s just one (and fairly awful
looking).
> On 5 Jul 2023, at 13:02, ha...@interia.pl wrote:
>
>
> Python has the "star" ("*") operator for multiplication. In the context of
> collections it is supposed to mean element-wise multiplication. Its
> associated operator is __mul__. It also has the double star ("**") operator
> for exponentiation, which is repeated multiplication. Its associated operator
> is __exp__.
>
> In addition to that Python has the "at" ("@") operator for multiplication. In
> the context of collections it should mean linear product, like matrix times a
> matrix, or matrix times vector. Its associated method is __matmul__.
>
> For completeness we should now have the exponentiation operator meaning
> repeated application of the "at" operator. Its method could me __matexp__.
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