# 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 HomR(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, y, 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 name: Limit -- name for an optional argument