This might be opening a can of worms, but...
Currently the callable symbolic ring (i.e., what we get when we do
something like f(x)=x^2) blissfully ignores the infrastructure in Sage
for defining maps. Instead, (to the best of my knowledge) callable
symbolic elements are just simple sugar over a symbolic expressions
which prints a bit differently and makes __call__ invocations have a
default variable order. This is nice and simple, but it isn't really
"pure", in the sense that Sage has functionality for defining maps
between rings or vector spaces of rings.
So for those of you that did all of that hard, long, tedious,
under-appreciated work on the category system: is there a
straightforward way to represent functions like:
f(x)=x^2 (SR --> SR)
f(x,y,z)=x*y (SR^3 --> SR)
f(x,y,z)=[x*y,y+z] (SR^3 --> SR^2)
using the category framework?
Thanks,
Jason
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