I opened a ticket on trac regarding this problem:

http://trac.sagemath.org/sage_trac/ticket/11652

* rafaeldleon <[email protected]> [2011-07-28 18:00:25 -0700]:

> Dear Julian,
> 
> Thank you very much for your help. It seems like an error to me too.
> I am using your solution in my code and is working nicely.
> 
> Should we report this error in any other place?
> 
> Thank you again,
> 
> Rafael
> 
> On Jul 25, 4:42 pm, Julian Rüth <[email protected]> wrote:
> > 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 <[email protected]> [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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