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 .00133272 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00423376 seconds idlizer1: .0150755 seconds idlizer2: .0427205 seconds minpres: .0308209 seconds time .128918 sec #fractions 4] [step 1: radical (use minprimes) .00714753 seconds idlizer1: .145764 seconds idlizer2: .0736748 seconds minpres: .0416832 seconds time .313638 sec #fractions 4] [step 2: radical (use minprimes) .00714016 seconds idlizer1: .0266488 seconds idlizer2: .0856251 seconds minpres: .0389062 seconds time .204009 sec #fractions 5] [step 3: radical (use minprimes) .00758857 seconds idlizer1: .102552 seconds idlizer2: .0992847 seconds minpres: .101047 seconds time .382051 sec #fractions 5] [step 4: radical (use minprimes) .00742464 seconds idlizer1: .0471263 seconds idlizer2: .298651 seconds minpres: .0486454 seconds time .470687 sec #fractions 5] [step 5: radical (use minprimes) .00750189 seconds idlizer1: .0311289 seconds time .0600045 sec #fractions 5] -- used 1.57135 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

• Default value: 0
• Function: integralClosure -- integral closure of an ideal or a domain
• Option key: Verbosity -- an optional argument

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