Serious restriction: It is assumed that this ring R[1/f H] is an endomorphism ring of an ideal in R. This means that the Groebner basis, in a product order, will have lead terms all quadratic monomials in the new variables, together with other elements which are degree 0 or 1 in the new variables.
i1 : R = QQ[x,y]/(y^2-x^3)
o1 = R
o1 : QuotientRing
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i2 : H = (y * ideal(x,y)) : ideal(x,y)
2
o2 = ideal (y, x )
o2 : Ideal of R
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i3 : (F,G) = ringFromFractions(((gens H)_{1}), H_0);
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i4 : S = target F
o4 = S
o4 : QuotientRing
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i5 : F
o5 = map(S,R,{x, y})
o5 : RingMap S <--- R
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i6 : G
y
o6 = map(frac(R),frac(S),{-, x, y})
x
o6 : RingMap frac(R) <--- frac(S)
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