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 .000315867 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use decompose) .00241534 seconds
      idlizer1:  .00449986 seconds
      idlizer2:  .00931312 seconds
      minpres:   .00661569 seconds
  time .0326381 sec  #fractions 4]
 [step 1: 
      radical (use decompose) .00291229 seconds
      idlizer1:  .00537263 seconds
      idlizer2:  .016475 seconds
      minpres:   .00985167 seconds
  time .0460336 sec  #fractions 4]
 [step 2: 
      radical (use decompose) .00293417 seconds
      idlizer1:  .00749485 seconds
      idlizer2:  .0189077 seconds
      minpres:   .00812461 seconds
  time .0882493 sec  #fractions 5]
 [step 3: 
      radical (use decompose) .00277508 seconds
      idlizer1:  .00648158 seconds
      idlizer2:  .0283757 seconds
      minpres:   .0218489 seconds
  time .0762653 sec  #fractions 5]
 [step 4: 
      radical (use decompose) .00283028 seconds
      idlizer1:  .0122881 seconds
      idlizer2:  .0580772 seconds
      minpres:   .00989328 seconds
  time .0990601 sec  #fractions 5]
 [step 5: 
      radical (use decompose) .00263075 seconds
      idlizer1:  .00768436 seconds
  time .0152817 sec  #fractions 5]
     -- used 0.360111 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