Dear SAGE community,
I am trying to compute characters for some finite fields.
With "small" fields, everything is fine:
sage: K=CyclotomicField(10);
sage: p=10151;
sage: Character=DirichletGroup(p,K);
sage: Khi=Character.0;
sage: Khi(7)
zeta10
However, with slightly larger
Carl Witty wrote:
>
> I've opened a couple of bug reports for this example,
> http://trac.sagemath.org/sage_trac/ticket/3329 and
> http://trac.sagemath.org/sage_trac/ticket/3330; the first just says
> there should be a better error message, and the second requests an
> actual implementation.
>
>
Carl Witty wrote :
> >
> > For instance:
> > R. = NumberField(x^2-3,'g')[]
> > S. = R.fraction_field()[]
> > xgcd(y^2, a*y+b)
> >
> > returns the error: (more below)
> > : unsupported operand type(s) for %:
> > 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_qua
Carl Witty wrote:
> You need to explicitly use the field of fractions of R:
>
> sage: R. = QQ[]
> sage: S. = R.fraction_field()[]
> sage: xgcd(x^2, a*x+b)
> (b^2/a^2, 1, ((-1)/a)*x + b/a^2)
Thanks. Is it possible to do the same computation over a number field
(instead of QQ)?
For instance:
R.
Gaetan Bisson wrote:
> Here is a short example:
> sage: R.=PolynomialRing(RationalField(),2);
> sage: S.=PolynomialRing(R);
> sage: xgcd(x^2,a+x*b)
>
> : cannot coerce nonconstant polynomial
I've forgotten to mention which versions of SAGE I'm using:
SAGE Version 3.0, Release Date: 200
Dear SAGE community,
I would like to do some symbolic computation using SAGE, namely, to
compute the extended GCD of two polynomials, one of them having symbolic
coefficients.
Here is a short example:
sage: R.=PolynomialRing(RationalField(),2);
sage: S.=PolynomialRing(R);
sage: xgcd(x^2,
