Apparently, this is caused by a problem in degree() which is used in
polynomial(). In your example:

sage: pol2.degree(q)
0
sage: pol2.degree(p)
3

You get the expected behavior if you bring q into pol2.parent()
explicitly:

sage: q=pol2.parent()(q)
sage: pol2.degree(q),pol2.polynomial(q)
(3, 4*q^3 + 3*q + 2)

So, this seems like an error to me. In the implementation of degree()
the line reading

return singular_polynomial_deg(p, (<MPolynomial_libsingular>x)._poly, r)

should probably be changed (x is the generator passed to the method).
But maybe somebody who knows more about the singular/sage connection can
say more about this.

cheers,
julian


* rafaeldleon <rafaeldl...@gmail.com> [2011-07-25 12:31:29 -0700]:

> Hello all,
> 
> I don´t know if the following is an error in the implementation of the
> method polynomial
> or if I am using it in a way that is not intended, but it seems that
> the use of the method
> polynomial changes when I am in a polynomial ring with 2 or with 3
> variables.
> 
> pol and pol2 are the "same" polynomial in rings with 3 or 2 variables
> resp. and
> the method pol.polynomial(q) and pol2.polynomial(q) return different
> answers.
> 
> 
> sage: R.<p,q,t>=ZZ[]
> sage: pol=2+3*q+4*q^3;pol
> 4*q^3 + 3*q + 2
> sage: parent(pol)
> Multivariate Polynomial Ring in p, q, t over Integer Ring
> sage: pol2=pol.polynomial(t).coefficients()[0];pol2
> 4*q^3 + 3*q + 2
> sage: parent(pol2)
> Multivariate Polynomial Ring in p, q over Integer Ring
> sage: pol2.polynomial(q)
> 2
> sage: pol.polynomial(q)
> 4*q^3 + 3*q + 2
> 
> Can anyone give me some insight about why I am getting these
> different answers?
> 
> Thanks!
> 
> Rafael
> 
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