Hi Ralf,

On 2018-02-28, Ralf Stephan <gtrw...@gmail.com> wrote:
> The reason is apparently that the polynomial ring was not created by the 
> user on the command line but by the charpoly() code.

The parent of the pre-defined variable x wasn't created by the user
either, so, please don't blame polynomial rings or the
minpoly()/charpoly() code for it.

 sage: QQbar(sqrt(2)).minpoly().parent()
 Univariate Polynomial Ring in x over Rational Field
 sage: x.parent()
 Symbolic Ring


> i would consider this a high priority bug. Is there a ticket?

Not in the way you think, IMHO.

One problem that I see is the fact that it is possible to create rings
in which one variable name occurs twice, such as here:
  sage: RR['x']['x']
  Univariate Polynomial Ring in x over Univariate Polynomial Ring in x
  over Real Field with 53 bits of precision
  sage: RR['x'].gen()-RR['x']['x'].gen()
  -x + x
  sage: _==0
  False

So, we have two x with different roles. It would make sense to disallow
the creation of such rings.

Also, I belive it is a bug that x is pre-defined as a symbolic variable;
we should finally drop that pseudo-courtesy. Users mistake FAR too often
symbolics with polynomials; by pre-defining x, we let the users believe
that x is good for *all* computations. So, I believe it would be better
to let the user create x him/herself, for the specific application that
he/she has in mind. However, I am aware that I belong to a minority with
that opinion.

Best regards,
Simon

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