next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 .000598832 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use minprimes) .00784161 seconds
      idlizer1:  .0113766 seconds
      idlizer2:  .0878736 seconds
      minpres:   .00785249 seconds
  time .198269 sec  #fractions 4]
 [step 1: 
      radical (use minprimes) .00425758 seconds
      idlizer1:  .00636851 seconds
      idlizer2:  .244665 seconds
      minpres:   .0545438 seconds
  time .395416 sec  #fractions 4]
 [step 2: 
      radical (use minprimes) .00818124 seconds
      idlizer1:  .0510824 seconds
      idlizer2:  .137447 seconds
      minpres:   .0502063 seconds
  time .453991 sec  #fractions 5]
 [step 3: 
      radical (use minprimes) .0445743 seconds
      idlizer1:  .0459355 seconds
      idlizer2:  .156444 seconds
      minpres:   .143333 seconds
  time .63746 sec  #fractions 5]
 [step 4: 
      radical (use minprimes) .0421228 seconds
      idlizer1:  .0927 seconds
      idlizer2:  .455656 seconds
      minpres:   .0539921 seconds
  time .706165 sec  #fractions 5]
 [step 5: 
      radical (use minprimes) .0104408 seconds
      idlizer1:  .0855818 seconds
  time .140862 sec  #fractions 5]
     -- used 2.5376 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

Further information

Caveat

The exact information displayed may change.