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

 [step 0: 
      radical (use decompose) .009795 seconds
      idlizer1:  .079529 seconds
      idlizer2:  .029598 seconds
      minpres:   .019657 seconds
  time .158109 sec  #fractions 4]
 [step 1: 
      radical (use decompose) .009545 seconds
      idlizer1:  .009514 seconds
      idlizer2:  .057222 seconds
      minpres:   .098855 seconds
  time .204067 sec  #fractions 4]
 [step 2: 
      radical (use decompose) .009904 seconds
      idlizer1:  .019712 seconds
      idlizer2:  .059423 seconds
      minpres:   .089434 seconds
  time .208085 sec  #fractions 5]
 [step 3: 
      radical (use decompose) 0 seconds
      idlizer1:  .019725 seconds
      idlizer2:  .07931 seconds
      minpres:   .069456 seconds
  time .297559 sec  #fractions 5]
 [step 4: 
      radical (use decompose) .00989 seconds
      idlizer1:  .099246 seconds
      idlizer2:  .228062 seconds
      minpres:   .029659 seconds
  time .416306 sec  #fractions 5]
 [step 5: 
      radical (use decompose) .009942 seconds
      idlizer1:  .029594 seconds
  time .049329 sec  #fractions 5]
     -- used 1.34313 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