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

Synopsis

Usage:

integralClosure(R, Limit => n)
Inputs:
- n, an integer, how many steps to perform

Description

The integral closure algorithm proceeds by finding a suitable ideal $J$, and then computing $Hom_R(J,J)$, and repeating these steps. This optional argument limits the number of such steps to perform.

The result is an integral extension, but is not necessarily integrally closed.

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

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
oeis(...,Limit=>...) -- see oeis -- OEIS lookup
simpleDocFrob(...,Limit=>...) -- see simpleDocFrob -- a sample documentation node