Thanx Rob, you guys are damn fast in replying! On 12 fév, 00:41, Robert Bradshaw <[email protected]> wrote: > 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 > > ratinalfunctionfield 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 overfunctionfields. 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 withfunctionfields. It might be > > the problem with NTL though. > > > I knew that Magma/Kash are far ahead sage infunctionfield > > 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
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