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

Now how do I compute polynomials g0, g1, g2, g3, such that g = g0*f0
+ ... + g3*f3? In other words, I just want to execute the division
algorithm with respect to whatever groebner basis is being used
internally, and then get the answer expressed in terms of my original
choice of generators f0, f1, f2, f3. Is there a function that will do
this for me?

thanks

david

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