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IntegralClosure :: ringFromFractions

ringFromFractions -- find presentation for f.g. ring

Synopsis

Description

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
i2 : H = (y * ideal(x,y)) : ideal(x,y)

                2
o2 = ideal (y, x )

o2 : Ideal of R
i3 : (F,G) = ringFromFractions(((gens H)_{1}), H_0);
i4 : S = target F

o4 = S

o4 : QuotientRing
i5 : F

o5 = map(S,R,{x, y})

o5 : RingMap S <--- R
i6 : G

                        y
o6 = map(frac R,frac S,{-, x, y})
                        x

o6 : RingMap frac R <--- frac S

Ways to use ringFromFractions :