On Feb 11, 2010, at 11:36 PM, [email protected] wrote:
Hi Alex, The only way I know to do so is throw defining polynomial ring over ratinal function field and taking quotient. sage: R.<x> = FiniteField(3)['x'] sage: K = R.fraction_field() sage: print K Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 sage: K.<T> = K['T'] sage: MinPoly = T^5+2*T+1 sage: MinPolyTest = x^5 + 2*x+1 sage: print MinPolyTest.is_irreducible() True sage: F.<z> = K.extension(MinPoly, 'z') sage: print F Univariate Quotient Polynomial Ring in z over Univariate Polynomial Ring in T over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 with modulus z^5 + 2*z + 1 sage: 1/z Traceback (most recent call last): ... AttributeError: 'sage.rings.polynomial.polynomial_element.Polynomia' object has no attribute 'xgcd' First of all, I needed to do that trick to find a irreducible polynomial, because checking irreduciblity apparently not implemented for polynomials over function fields. The second problem, as you see, sage see F as a ring and not a field, so as you see it's semi-useless and you can't benefit much out of it. I hope somebody tells us, a reasonable way of construct and work with function fields. It might be the problem with NTL though. I knew that Magma/Kash are far ahead sage in function field computation, but one expects that elementary computations, such as algebraic extensions should be possible in comperhensive tool such as sage. So SOS help us!
People only started looking at this in Sage very recently and very little has been done to date. I'm very hopeful things will be looking a lot better come May (and shortly thereafter, as people finish up what they started/talked about there).
- Robert -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
