integralClosure(...,Limit=>...) -- do a partial integral closure

Synopsis

• Usage:

  integralClosure(R, Limit => n)

• Inputs:
  • n, an integer, how many steps to perform

Description

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4-z^3);

i2 : R' = integralClosure(R, Variable => symbol t, Limit => 2)

o2 = R'

o2 : QuotientRing

i3 : trim ideal R'

                     2 2    4           2 2        4    5 2    5 2   2       4 2     4 3    4   3      3 4 2     3 2 4    3 6  
o3 = ideal (t   x - y z  - z  - z, t   y z  + t   z  - x y  - x z , t   z - x y z - x z  - x , t    - x y z  - 2x y z  - x z  -
             1,1                    1,1        1,1                   1,1                        1,1
     ----------------------------------------------------------------------------------------------------------------------------
       3 2      3 3    3
     2x y z - 2x z  - x )

o3 : Ideal of QQ[t   , x..z]
                  1,1

i4 : icFractions R

       2 2    4
      y z  + z  + z
o4 = {-------------, x, y, z}
            x

o4 : List

Further information

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

Functions with optional argument named Limit :

• "basis(...,Limit=>...)" -- see basis -- basis or generating set of all or part of a ring, ideal or module
• hermite(...,Limit=>...) (missing documentation)
• icFracP(...,Limit=>...) -- Limits the number of computed intermediate modules.
• "independentSets(...,Limit=>...)" -- see independentSets -- some size-maximal independent subsets of variables modulo an ideal
• integralClosure(...,Limit=>...) -- do a partial integral closure
• kernelLLL(...,Limit=>...) (missing documentation)
• LLL(...,Limit=>...) (missing documentation)
• "minors(...,Limit=>...)" -- see minors(ZZ,Matrix) -- ideal generated by minors
• "simpleDocFrob(...,Limit=>...)" -- see simpleDocFrob -- a sample documentation node