Nils Bruin wrote:
> I think the only choice (if any) is to match the occurrence of a name
> in the smallest ring.
>
> If your generic code is relying on coercion in a setting where name
> matching like this is relevant, I suspect it's almost certainly the
> wrong choice.
I think we agree. To clarify, what I was trying to say is that
(1) Forbidding polynomial ring towers with repeated variables breaks
essentially all code that creates polynomial rings for its private use
over base rings provided by the caller, even code that doesn't use
coercion, say
def foo(a):
Pol = PolynomialRing(a.parent(), 'x')
return Pol([a, 1]).roots()
(Everyone in this thread probably agrees on that part.)
(2) Disallowing conversions from R to R[x] when R already contains a
variable called x doesn't sound great to me either. Indeed, converting
constants into polynomials is a pretty common operation, it is quite
idiomatic to use parent-call syntax for that, and it may not be obvious
on first sight that it could fail in some cases. Whereas I can only
think of rather contrived examples where one would write Pol(p) in a
situation where ambiguity may occur and expect it to map the variable of
the polynomial p to that of the ring Pol. (Not only the pitfall is more
evident, but also there are often other natural tools to do the job,
e.g. change_ring() methods.)
--
Marc
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