On Tuesday, June 9, 2015 at 5:36:01 PM UTC+2, black...@gmx.de wrote: > > Thank you, > > and i already tried this. In this case it obiously does work but in case i > have denominators, can u explain me how to solve it? > for example: K(s/(s+t),s^2*t^2) then i have to calculate the elimination > ideal of ((a0-s,a1-s^2t^2):(s+t)^\inf) where (I:J^\inf) is the saturation > of I with respect to J? > > You should look for elimination theory, If you have a subfield K(f1/g1,...,fr/gr) in K(x1,...,xn) han have an element h,
You should construct the Ideal I = Ideal ( g1*a1-f1, ...., gr*ar-fr, h-b) Where a1,...,ar, b are new variables. You saturate with respect to g1*g2*...*gr. For efficiency reasons, it might be faster to succesively saturate with respect to each gi Then eliminate the variables x1,...,xn, I0 = I.elimination_ideal([x1,...,xn]) Now you have to check if there is a polynomial in I0 of degree exactly 1 in b. You can obtain this from a Grobner basis with respect to an appropriate order. In general, if every generator of I0 has degree 0 in b, then h is transcendent over K(f1/g1,...fr/gr) otherwise, the polynomial with minimal degree in b is in fact (a multiple of) the minimal polynomial of h over K(f1/g1,...,fr/gr) I think that if you can factor and compute gcd of multivariate polynomials, you can also approach the problem using resultants. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
