Le Fri, 14 May 2010 08:52:33 +0200, Martin Rubey <martin.ru...@math.uni-hannover.de> a écrit :
> Is the following close to what you have in mind? (two problems: you > need to know the extension in advance, and I don't see a way to factor > over extensions of degree higher than one right now. Possibly Waldek > knows.) > > > (1) -> SAEs5 := SAE(FRAC INT,UP(s5,FRAC INT),s5^2-5) > > (1) > SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(s5,Fra > ction(Integer)),s5^2+-5) > Type: Type > (2) -> p:UP(x,SAEs5) :=(x^5-1)*(x^2-1)*(x-1) > > 8 7 6 5 3 2 > (2) x - x - x + x - x + x + x - 1 > Type: > > UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(s5,Fraction(Integer)),s5^2+-5)) > (3) -> factor p > > 3 2 1 1 2 1 1 > (3) (x - 1) (x + 1)(x + (- - s5 + -)x + 1)(x + (- s5 + -)x + 1) > 2 2 2 2 > Type: > > Factored(UnivariatePolynomial(x,SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(s5,Fraction(Integer)),s5^2+-5))) > (4) -> partialFraction(1/p, x) > > (4) > 13 2 9 27 1 1 1 1 1 > -- x - -- x + -- - (- -- s5 - --)x + -- s5 - -- > 40 10 40 8 50 10 50 10 > ----------------- - ----- + ---------------------------- > 3 x + 1 2 1 1 > (x - 1) x + (- - s5 + -)x + 1 > 2 2 > + > 1 1 1 1 > (-- s5 - --)x - -- s5 - -- > 50 10 50 10 > -------------------------- > 2 1 1 > x + (- s5 + -)x + 1 > 2 2 > Type: > > PartialFraction(UnivariatePolynomial(x,Fraction(Polynomial(SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(s5,Fraction(Integer)),s5^2+-5))))) Yeah, definitely closer ! I'll have to investigate all this. Thanks. \bye -- Nicolas FRANCOIS | /\ http://nicolas.francois.free.fr | |__| X--/\\ We are the Micro$oft. _\_V Resistance is futile. You will be assimilated. darthvader penguin _______________________________________________ Axiom-math mailing list Axiom-math@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-math
