next | previous | forward | backward | up | top | index | toc | Macaulay2 website
IntegralClosure :: integralClosure(...,Verbosity=>...)

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

Synopsis

Description

When the computation takes a considerable time, this function can be used to decide if it will ever finish, or to get a feel for what is happening during 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 .000675423 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use minprimes) .00388719 seconds
      idlizer1:  .0111101 seconds
      idlizer2:  .0214621 seconds
      minpres:   .0142924 seconds
  time .111073 sec  #fractions 4]
 [step 1: 
      radical (use minprimes) .0029498 seconds
      idlizer1:  .0190053 seconds
      idlizer2:  .0342691 seconds
      minpres:   .0217032 seconds
  time .102115 sec  #fractions 4]
 [step 2: 
      radical (use minprimes) .00260082 seconds
      idlizer1:  .0202475 seconds
      idlizer2:  .0389433 seconds
      minpres:   .0177467 seconds
  time .148434 sec  #fractions 5]
 [step 3: 
      radical (use minprimes) .00395418 seconds
      idlizer1:  .0214098 seconds
      idlizer2:  .0586006 seconds
      minpres:   .0442956 seconds
  time .161656 sec  #fractions 5]
 [step 4: 
      radical (use minprimes) .00401352 seconds
      idlizer1:  .066085 seconds
      idlizer2:  .108174 seconds
      minpres:   .0213945 seconds
  time .233396 sec  #fractions 5]
 [step 5: 
      radical (use minprimes) .00398109 seconds
      idlizer1:  .0163363 seconds
  time .0336898 sec  #fractions 5]
     -- used 0.796269 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..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

Further information

Caveat

The exact information displayed may change.

Functions with optional argument named Verbosity :