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IntegralClosure :: idealizer

idealizer -- compute Hom(I,I) as a quotient ring

Synopsis

Description

The idealizer of I, computed as target F, is the largest subring of the fraction field of ring I in which I is still an ideal. Note that this is NOT the common use of the term in commutative algebra.

This is a key subroutine used in the computation of integral closures.

i1 : R = QQ[x,y]/(y^3-x^7)

o1 = R

o1 : QuotientRing
i2 : I = ideal(x^2,y^2)

             2   2
o2 = ideal (x , y )

o2 : Ideal of R
i3 : (F,G) = idealizer(I,x^2);
i4 : target F

                 QQ[w   , x, y]
                     0,0
o4 = -------------------------------------
           2    2   2      3            5
     (w   x  - y , w    - x y, w   y - x )
       0,0          0,0         0,0

o4 : QuotientRing
i5 : first entries G.matrix

       2
      y
o5 = {--, x, y}
       2
      x

o5 : List

See also

Ways to use idealizer :