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 .000936 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use decompose) .007806 seconds
      idlizer1:  .012735 seconds
      idlizer2:  .027016 seconds
      minpres:   .017987 seconds
  time .090698 sec  #fractions 4]
 [step 1: 
      radical (use decompose) .007589 seconds
      idlizer1:  .015104 seconds
      idlizer2:  .096366 seconds
      minpres:   .028518 seconds
  time .177531 sec  #fractions 4]
 [step 2: 
      radical (use decompose) .00687 seconds
      idlizer1:  .021068 seconds
      idlizer2:  .103608 seconds
      minpres:   .023569 seconds
  time .184457 sec  #fractions 5]
 [step 3: 
      radical (use decompose) .007853 seconds
      idlizer1:  .018474 seconds
      idlizer2:  .079456 seconds
      minpres:   .112728 seconds
  time .262577 sec  #fractions 5]
 [step 4: 
      radical (use decompose) .007851 seconds
      idlizer1:  .033368 seconds
      idlizer2:  .212797 seconds
      minpres:   .028506 seconds
  time .326771 sec  #fractions 5]
 [step 5: 
      radical (use decompose) .007852 seconds
      idlizer1:  .020597 seconds
  time .044117 sec  #fractions 5]
     -- used 1.13834 seconds

o2 = R'

o2 : QuotientRing

i3 : trim ideal R'

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

o3 : Ideal of QQ[w   , w   , x, y, 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