Dear Team,
the impression that I got from this thread is the following:
-------
Commutative:
1. If f is a *commutative* polynomial in x,y,z,..., then everybody
would at least correctly guess that f(1,2,3,...) has the intended
meaning "evalutation of f at x=1, y=2, z=3,..."
2. Some people would actually *expect* (not just accept) that this
meaning is intended.
=>
It is ok that multivariate polynomials in Sage are callable in the
sense described above. Currently, symbolic variables commute with each
other, and thus it is acceptable that they are callable as well.
Hence, no need to change!
Do we agree on this?
---------
Non-Commutative:
Several people gave evidence that calling a non-commutative
polynomial should be different from the above. It makes sense to
consider non-commutative multiplication as a functional composition
(e.g., if differentials are involved). Therefore my suggestion: f(a,b)
for non-commutative bivariate polynomial f should require that a and b
are functions, and the nc-monomials in f give rise to functional
compositions of a and b. However, this suggestion would only work if f
is freely non-commutative.
=>
The people who are currently implementing non-commutative
polynomials (Burcin, Michael B., William?) should speak up, what
meaning they want to give to their __call__ methods.
Regards
Simon
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