integralClosure(...,Verbosity=>...) -- display a certain amount of detail about the computation

i1 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);

i2 : time R' = integralClosure(R, Verbosity => 2)
 [jacobian time .000606057 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use minprimes) .0560377 seconds
      idlizer1:  .00920049 seconds
      idlizer2:  .0172122 seconds
      minpres:   .0117357 seconds
  time .112427 sec  #fractions 4]
 [step 1: 
      radical (use minprimes) .00302538 seconds
      idlizer1:  .0146819 seconds
      idlizer2:  .029856 seconds
      minpres:   .017956 seconds
  time .0845186 sec  #fractions 4]
 [step 2: 
      radical (use minprimes) .00284699 seconds
      idlizer1:  .0149222 seconds
      idlizer2:  .0315637 seconds
      minpres:   .0140225 seconds
  time .106567 sec  #fractions 5]
 [step 3: 
      radical (use minprimes) .00280971 seconds
      idlizer1:  .0151859 seconds
      idlizer2:  .0464662 seconds
      minpres:   .0360944 seconds
  time .126654 sec  #fractions 5]
 [step 4: 
      radical (use minprimes) .00286785 seconds
      idlizer1:  .0458744 seconds
      idlizer2:  .104363 seconds
      minpres:   .0201312 seconds
  time .200934 sec  #fractions 5]
 [step 5: 
      radical (use minprimes) .00331829 seconds
      idlizer1:  .0124338 seconds
  time .0271454 sec  #fractions 5]
     -- used 0.663326 seconds

o2 = R'

o2 : QuotientRing

i3 : trim ideal R'

                     3   2                     2 2    4           4                      2 2     2 3    2   3      2   3 2  
o3 = ideal (w   z - x , w   x - w   , w   x - y z  - z  - z, w   x  - w   z, w   w    - x y z - x z  - x , w    + w   x y  -
             4,0         4,0     1,1   1,1                    4,0      1,1    4,0 1,1                       4,0    4,0      
     ----------------------------------------------------------------------------------------------------------------------------
        4 2      2 4       2       3           3    2      6 2    6 2
     x*y z  - x*y z  - 2x*y z - x*z  - x, w   x  - w    + x y  + x z )
                                           4,0      1,1

o3 : Ideal of QQ[w   , w   , x..z]
                  4,0   1,1

i4 : icFractions R

       3   2 2    4
      x   y z  + z  + z
o4 = {--, -------------, x, y, z}
       z        x

o4 : List