On Sunday 27 February 2011, dmharvey wrote: > Hi, > > sage: R.<x0,x1,x2,x3> = PolynomialRing(QQ) > sage: f = x0^2*x1 + x1^2*x2 + x2^2*x3 + x3^2*x0 > sage: (f0, f1, f2, f3) = [f.derivative(v) for v in [x0, x1, x2, x3]] > sage: I = R.ideal(f0, f1, f2, f3) > sage: h = x0^5 > sage: h in I > sage: True
Hi David, sage: R.<x0,x1,x2,x3> = PolynomialRing(QQ) sage: f = x0^2*x1 + x1^2*x2 + x2^2*x3 + x3^2*x0 sage: (f0, f1, f2, f3) = [f.derivative(v) for v in [x0, x1, x2, x3]] sage: I = R.ideal(f0, f1, f2, f3) sage: h = x0^5 sage: h.lift(I) [-x0^2*x2 - 4/15*x0*x1*x3, x0^3 + 8/15*x1^2*x3 + x2*x3^2, -16/15*x1*x2*x3, 2/15*x1*x3^2] sage: h.lift(I.gens()) [-x0^2*x2 - 4/15*x0*x1*x3, x0^3 + 8/15*x1^2*x3 + x2*x3^2, -16/15*x1*x2*x3, 2/15*x1*x3^2] sage: h.lift(I.groebner_basis()) [0, 0, 0, 0, x0*x2, x0^3, -2*x0^2*x2, 0, 0] sage: sum(map(prod,zip(I.groebner_basis(),h.lift(I.groebner_basis())))) x0^5 Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://martinralbrecht.wordpress.com/ _jab: martinralbre...@jabber.ccc.de -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
