# integralClosure(...,Keep=>...) -- list ring generators which should not be simplified away

## Synopsis

• Usage:
integralClosure(R, Keep=>L)
• Inputs:
• L, a list, a list of variables in the ring R, or null (the default).
• Consequences:
• The given list of variables (or all of the outer generators, if L is null) will be generators of the integral closure

## Description

Consider the cuspidal cubic, and three different possibilities for Keep.

 i1 : R = QQ[x,y]/ideal(x^3-y^2); i2 : R' = integralClosure(R, Variable => symbol t) o2 = R' o2 : QuotientRing i3 : trim ideal R' 2 2 o3 = ideal (t y - x , t x - y, t - x) 0,0 0,0 0,0 o3 : Ideal of QQ[t , x..y] 0,0
 i4 : R = QQ[x,y]/ideal(x^3-y^2); i5 : R' = integralClosure(R, Variable => symbol t, Keep => {x}) o5 = R' o5 : QuotientRing i6 : trim ideal R' 2 o6 = ideal(t - x) 0,0 o6 : Ideal of QQ[t , x] 0,0
 i7 : R = QQ[x,y]/ideal(x^3-y^2); i8 : integralClosure(R, Variable => symbol t, Keep => {}) o8 = QQ[t ] 0,0 o8 : PolynomialRing

## Further information

• Default value: null
• Function: integralClosure -- integral closure of an ideal or a domain
• Option key: Keep -- an optional argument for various functions