Hi Simon,
PLEASE DON'T DO THIS, unless you know what you are doing! Reason: If you
use the various boilerplate polynomial ring constructors directly, you
might break the cache and create several distinct instances of "the
same" polynomial ring, which has a high probability of confusing the
coercion framework and thus compromising the Sage session.
It was more like a (not so good apparently) example of thing that could
be done in the PolynomialRing constructor, to handle this case. I was
not aware of the possibility you mentioned:
sage: R.<t> = PolynomialRing(QQ, 1, order='neglex')
Would it make sense to return a libsingular multivariate polynomial ring
whenever the number of variables is explicitly prescribed OR an ordering
is prescribed OR an implementation is explicitly chosen?
It would be relatively easy to refactor the polynomial ring constructor
so that it only returns something when the chosen implementation
supports all given arguments (such as order).
It would definitely make sense to me to have a simpler way to obtain the
same result as above, for instance with the simpler invocation:
sage: R.<t> = PolynomialRing(QQ, order='neglex')
To me it would make sense to return a libsingular multivariate
polynomial ring whenever an ordering is prescribed or an implementation
is explicitly chosen. But I think I've seen quite often people writing
sage: R.<t> = PolynomialRing(QQ, 1)
and I do not think they wanted to get a Multivariate 1-variable
Polynomial Ring. While whenever a user writes "order=..." or
"implementation=singluar", it seems quite clear that s/he knows what
s/he wants!
Cheers,
Bruno
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