Hello forum,
I'm looking to do some computations with binary relations in GAP. There
is a connection with the finite dimensional matrix algebras over the
Boolean Semiring (i.e. {0,1} with *Minimum* and *Maximum* as *** and *+*
respectively).
The standard output when computing a BinaryRelation in GAP is
Binary Relation on 2 points
or similar. This is essentially without any sort of information, so I'd
like to change the output slightly, to something more visual -
explicitly presenting the output data in said matrix algebra even if not
explicitly doing computations in that representation.
How would I go about getting GAP to "recognize" the Boolean structure as
that of a semiring (/i.e. a GAP /*AdditiveMagma*/with a distributive
multiplication on it/) and thereafter construct its matrix algebra?
I'd ideally like to do the former in a categorical manner (/in the sense
of GAP categories, not in the technical sense/) since I'll probably use
other semirings for related work, and so that I can, for instance,
define the variable '*a*' to be 1 regarded as an element of this
semiring, so evaluating that '*a+a*' returns 1 instead of 2 (akin, I'd
imagine, to the way that GAP differentiates *LieMatrix*es from
*OrdinaryMatrix*es).
I've implicitly assumed that the construction
*FullMatrixAlgebra(<R>,<n>)* defined over a ring is defined in such a
way that it would scale in its current form to accommodating what I've
detailed; please correct me if this is not the case.
Many thanks in advance,
Nick Loughlin
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