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 .00108458 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use decompose) .00920782 seconds
      idlizer1:  .0173605 seconds
      idlizer2:  .0315163 seconds
      minpres:   .0215568 seconds
  time .111099 sec  #fractions 4]
 [step 1: 
      radical (use decompose) .0095831 seconds
      idlizer1:  .0197475 seconds
      idlizer2:  .0539994 seconds
      minpres:   .0334728 seconds
  time .151768 sec  #fractions 4]
 [step 2: 
      radical (use decompose) .00944154 seconds
      idlizer1:  .078811 seconds
      idlizer2:  .0621735 seconds
      minpres:   .0276267 seconds
  time .214346 sec  #fractions 5]
 [step 3: 
      radical (use decompose) .0102268 seconds
      idlizer1:  .0237144 seconds
      idlizer2:  .0978393 seconds
      minpres:   .0743825 seconds
  time .26049 sec  #fractions 5]
 [step 4: 
      radical (use decompose) .0100106 seconds
      idlizer1:  .0960996 seconds
      idlizer2:  .194373 seconds
      minpres:   .0347551 seconds
  time .387825 sec  #fractions 5]
 [step 5: 
      radical (use decompose) .0101434 seconds
      idlizer1:  .0279458 seconds
  time .0564824 sec  #fractions 5]
     -- used 1.19062 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