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

Usage:

integralClosure(R, Verbosity => n)
Inputs:
- n, an integer, The higher the number, the more information is displayed. A value of 0 means: keep quiet.

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 .000623394 sec #minors 3]
integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2

 [step 0: 
      radical (use minprimes) .00277756 seconds
      idlizer1:  .00950372 seconds
      idlizer2:  .0111854 seconds
      minpres:   .0109933 seconds
  time .0484081 sec  #fractions 4]
 [step 1: 
      radical (use minprimes) .00311947 seconds
      idlizer1:  .0152507 seconds
      idlizer2:  .0125321 seconds
      minpres:   .0141907 seconds
  time .0589129 sec  #fractions 4]
 [step 2: 
      radical (use minprimes) .0029006 seconds
      idlizer1:  .0904164 seconds
      idlizer2:  .012059 seconds
      minpres:   .0124966 seconds
  time .132369 sec  #fractions 5]
 [step 3: 
      radical (use minprimes) .00325488 seconds
      idlizer1:  .0157211 seconds
      idlizer2:  .0173828 seconds
      minpres:   .0207322 seconds
  time .0735015 sec  #fractions 5]
 [step 4: 
      radical (use minprimes) .00314184 seconds
      idlizer1:  .012174 seconds
      idlizer2:  .0202387 seconds
      minpres:   .0138198 seconds
  time .0652462 sec  #fractions 5]
 [step 5: 
      radical (use minprimes) .00282661 seconds
      idlizer1:  .0101262 seconds
  time .0208982 sec  #fractions 5]
 -- used 0.4039s (cpu); 0.373545s (thread); 0s (gc)

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

Caveat

The exact information displayed may change.

Functions with optional argument named Verbosity:

icFracP(...,Verbosity=>...) -- Prints out the conductor element and the number of intermediate modules it computed.
idealizer(...,Verbosity=>...) -- see idealizer -- compute Hom(I,I) as a quotient ring
integralClosure(...,Verbosity=>...) -- display a certain amount of detail about the computation
isPrime(Ideal,Verbosity=>...) -- see isPrime(Ideal) -- whether an ideal is prime
makeS2(...,Verbosity=>...) -- see makeS2 -- compute the S2ification of a reduced ring
decompose(Ideal,Verbosity=>...) -- see minimalPrimes -- minimal primes of an ideal
minimalPrimes(...,Verbosity=>...) -- see minimalPrimes -- minimal primes of an ideal
ringFromFractions(...,Verbosity=>...) -- see ringFromFractions -- find presentation for f.g. ring

Further information

Default value: 0
Function: integralClosure -- integral closure of an ideal or a domain
Option key: Verbosity (missing documentation)

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/IntegralClosure.m2:1447:0.