Dear developers,
I implemented "Symmetric Polynomial Rings" -- these are polynomial
rings with countably many variables plus a permutation action on the
variables. Now I'd like to implement the algorithms of Aschenbrenner
and Hillar for computing Gröbner bases of Symmetric Ideals (i.e.,
ideals that are set-wise fixed by the permutation action).
I guess that my class ``SymmetricIdeal`` should inherit from
``Ideal_generic``.
``Ideal_generic`` requires that the underlying ring R has the property
is_CommutativeRing(R), which just checks that R is an instance of
``CommutativeRing``. In my applications, the Symmetric Polynomial
Rings will be commutative, so, I could indeed inherit from
CommutativeRing.
Nevertheless, out of curiosity: Why is there this restriction to the
commutative case?
I mean, there are non-commutative Gröbner bases -- wouldn't it be
better to deal with commutativity only in the classes that inherit
from Ideal_generic, rather than in Ideal_generic itself? Being in a
commutative ring is not a generic property of ideals.
Cheers,
Simon
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