# 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

## 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