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2010-08-26 04:14:24 +0200	commented answer	Multivariate Polynomials over Rational Function Fields Thanks, that works perfectly. Now my quest for the Elimination ideal I2 = I.elimination_ideal([x]) fails with TypeError: Cannot call Singular function 'eliminate' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.mpolynomialring_polydict_do\="" main'="">'
2010-08-26 03:12:25 +0200	asked a question	Multivariate Polynomials over Rational Function Fields Is it possible to define multivariate polynomials where the coefficients lie in a rational function field and do Groebner basis computations on them? Maple, Reduce and Axiom support this. For example I would like to be able to compute the Groebner basis of the polynomials `{v * x^2 + y, u* x * y + y^2}` where the polynomials belong to the ring Q(u,v)[x,y]. I tried the following `B.<u,v> = PolynomialRing(QQ, 'u', 'v') R.<x,y> = PolynomialRing(B, 'x', 'y') I = R.ideal(v * x^2 + y, u* x * y + y^2) g = I.groebner_basis()` This fails with the error `TypeError: Can only reduce polynomials over fields.`