Hi Urs,

On 20 Okt., 13:08, Urs Hackstein <urs.hackst...@googlemail.com> wrote:
> f.parent() gives indeed "Symbolic Ring".  But at the beginning I defined
>
> P.<s> = CC[]
> P.fraction_field()

Then we really need to know how you define f.

Recall that in the other thread on that subject, I pointed out how
easy it is to start with a polynomial and end with a symbolic
expression: The symbol "I" is a symbolic expression. It is recognised
as an element of CC, but nevertheless its parent is the symbolic ring:

 sage: I in CC
 True
 sage: I.parent()
 Symbolic Ring

Hence, when you add the generator s of the polynomial ring with I,
then you obtain a symbolic expression, not a polynomial, even though
the sum is recognised as an element of the polynomial ring:
  sage: P.<s> = CC[]
  sage: s.parent()
  Univariate Polynomial Ring in s over Complex Field with 53 bits of
precision
  sage: (s+I).parent()
  Symbolic Ring
  sage: s+I in P
  True

This can be avoided by explicitly defining "I" to be the generator of
CC:
  sage: I = CC.0
  sage: I
  1.00000000000000*I
  sage: (s+I).parent()
  Univariate Polynomial Ring in s over Complex Field with 53 bits of
precision

Best regards,
Simon

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