-- -*- M2-comint -*- {* hash: 1769253071 *}

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4-z^3);

i2 : R' = integralClosure R

o2 = R'

o2 : QuotientRing

i3 : gens R'

o3 = {w   , x, y, z}
       3,0

o3 : List

i4 : icFractions R

       2
      x
o4 = {--, x, y, z}
       z

o4 : List

i5 : icMap R

o5 = map(R',R,{x, y, z})

o5 : RingMap R' <--- R

i6 : I = trim ideal R'

                     2   3      2     3
o6 = ideal (w   z - x , w    - y z - z  - 1)
             3,0         3,0

o6 : Ideal of QQ[w   , x, y, z]
                  3,0

i7 : S = ZZ/101[a..d]/ideal(a*(b-c),c*(b-d),b*(c-d));

i8 : C = decompose ideal S

o8 = {ideal (b - c, - c + d), ideal (b, d, a), ideal (c, b), ideal (c, d, a)}

o8 : List

i9 : Rs = apply(C, I -> (ring I)/I);

i10 : Rs/integralClosure

         ZZ               ZZ               ZZ               ZZ
        ---[a, b, c, d]  ---[a, b, c, d]  ---[a, b, c, d]  ---[a, b, c, d]
        101              101              101              101
o10 = {----------------, ---------------, ---------------, ---------------}
       (b - c, - c + d)     (b, d, a)          (c, b)         (c, d, a)

o10 : List

i11 : oo/prune

        ZZ         ZZ      ZZ         ZZ
o11 = {---[a, d], ---[c], ---[a, d], ---[b]}
       101        101     101        101

o11 : List

i12 :