integralClosure(...,Variable=>...) -- set the base letter for the indexed variables introduced while computing the integral closure

Usage:

integralClosure(R, Variable=>x)
Inputs:
- x, a symbol,
Consequences:
- The new variables will be subscripted using x.

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)

o2 = R'

o2 : QuotientRing

i3 : trim ideal R'

                     2   3      2     3
o3 = ideal (t   z - x , t    - y z - z  - 1)
             3,0         3,0

o3 : Ideal of QQ[t   , x..z]
                  3,0

The algorithm works in stages, each time adding new fractions to the ring. A variable t_(3,0) represents the first (zero-th) variables added at stage 3.

Caveat

The base name should be a symbol The variables added may be changed to t_1, t_2, ... in the future.

Functions with optional argument named Variable:

GF(...,Variable=>...) -- see GF -- make a finite field
Grassmannian(...,Variable=>...) -- see Grassmannian -- compute the ideal of the Grassmannian of linear subspaces of a vector space
idealizer(...,Variable=>...) -- Sets the name of the indexed variables introduced in computing the endomorphism ring Hom(J,J).
integralClosure(...,Variable=>...) -- set the base letter for the indexed variables introduced while computing the integral closure
makeS2(...,Variable=>...) -- Sets the name of the indexed variables introduced in computing the S2-ification.
normalCone(Ideal,RingElement,Variable=>...) (missing documentation)
normalCone(Ideal,Variable=>...) (missing documentation)
ringFromFractions(...,Variable=>...) -- see ringFromFractions -- find presentation for f.g. ring
Schubert(...,Variable=>...) -- see Schubert -- compute the Plücker ideal of a Schubert variety

Further information

Default value: w
Function: integralClosure -- integral closure of an ideal or a domain
Option key: Variable -- an optional argument

The source of this document is in IntegralClosure.m2:1404:0.