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

Synopsis

• 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

Further information

• Default value: w
• Function: integralClosure -- integral closure of an ideal or a domain
• Option key: Variable -- specify a name for a variable

Caveat

Functions with optional argument named Variable :

• conwayPolynomial(...,Variable=>...) (missing documentation)
• "GF(...,Variable=>...)" -- see GF -- make a finite field
• "Grassmannian(...,Variable=>...)" -- see Grassmannian(ZZ,ZZ) -- 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
• "intersectInP(...,Variable=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• "multiplicity(...,Variable=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• makeS2(...,Variable=>...) -- Sets the name of the indexed variables introduced in computing the S2-ification.
• "ringFromFractions(...,Variable=>...)" -- see ringFromFractions -- find presentation for f.g. ring
• "Schubert(...,Variable=>...)" -- see Schubert(ZZ,ZZ,VisibleList) -- find the Plücker ideal of a Schubert variety
• "distinguished(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "isReduction(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "jacobianDual(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "normalCone(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "reesAlgebra(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "reesIdeal(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "specialFiber(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• "specialFiberIdeal(...,Variable=>...)" -- see symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring
• symmetricKernel(...,Variable=>...) -- Choose name for variables in the created ring