Hi!
My impression is that relatively often questions on sage-support are
about people accidentally mixing symbolics and polynomials. For
example
sage: z = var('z')
sage: R = QQ[z]
and then believing that z is the generator of R.
I think it would avoid trouble if one would print a big warning
message in those cases.
For example:
sage: z = var('z')
sage: R = QQ[z]
WARNING: The globally defined symbolic expression z is *not* a
generator of Univariate Polynomial Ring in z over Rational Field
I think such warning would be useful.
If you agree, we should think about some details.
* Should the polynomial ring constructor check for any given variable
name whether there is a symbolic variable of that name in globals()?
That might be too slow, and it would be annoying to always get a
warning for ZZ['x'].
* Should the warning only be given when a symbolic variable is passed
as an argument to the polynomial ring constructor? Hence, R=QQ[z]
would trigger the warning, but R.<z>=QQ[] would be without warning,
because here only the string 'z' is passed to the ring constructor. In
that case, the warning might better read "WARNING: The given argument
'z' is a symbolic expression; this is not the same as a generator of
Univariate Polynomial Ring in z over Rational Field".
I am in favour of the second scenario: It would be a quick test and
should prevent some typical misuses.
Best regards,
Simon
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