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

## Synopsis

• 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 .000674761 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00496995 seconds idlizer1: .00744644 seconds idlizer2: .0138152 seconds minpres: .00908961 seconds time .0495217 sec #fractions 4] [step 1: radical (use minprimes) .00575838 seconds idlizer1: .00818342 seconds idlizer2: .059498 seconds minpres: .0140242 seconds time .101893 sec #fractions 4] [step 2: radical (use minprimes) .00613218 seconds idlizer1: .0121322 seconds idlizer2: .0260823 seconds minpres: .0117795 seconds time .108658 sec #fractions 5] [step 3: radical (use minprimes) .00692885 seconds idlizer1: .0096282 seconds idlizer2: .0392916 seconds minpres: .0291609 seconds time .14596 sec #fractions 5] [step 4: radical (use minprimes) .00742626 seconds idlizer1: .0169081 seconds idlizer2: .107323 seconds minpres: .0139118 seconds time .166317 sec #fractions 5] [step 5: radical (use minprimes) .00762241 seconds idlizer1: .0125543 seconds time .0278994 sec #fractions 5] -- used 0.604331 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

• Default value: 0
• Function: integralClosure -- integral closure of an ideal or a domain
• Option name: Verbosity -- optional argument describing how verbose the output should be

## Caveat

The exact information displayed may change.