seminormalize(...,Variable=>...) -- set the name for new variables created by the function

Description

This option sets the default variable for new variables created by the above functions. You must pass it a symbol. We first give an example of this in the context of seminormalization.

i1 : A = QQ[a,b]/ideal(a^2-b^5);

i2 : seminormalize(A, Variable=>X)

                 QQ[X ..X ]                            QQ[X ..X ]           
                     0   2                                 0   2            
o2 = {-------------------------------, map (-------------------------------,
        2        2          3                 2        2          3         
      (X  - X , X X  - X , X  - X X )       (X  - X , X X  - X , X  - X X ) 
        2    0   0 2    1   0    1 2          2    0   0 2    1   0    1 2  
     ------------------------------------------------------------------------
                                   QQ[Yy   , a..b]            
                                        1,0                   
     A, {X , X }), map (-------------------------------------,
          1   0                2        2       2    2        
                        (Yy   b  - a, Yy   b - b , Yy    - b) 
                           1,0          1,0          1,0      
     ------------------------------------------------------------------------
                QQ[X ..X ]
                    0   2
     -------------------------------, {b, a, Yy   })}
       2        2          3                   1,0
     (X  - X , X X  - X , X  - X X )
       2    0   0 2    1   0    1 2

o2 : List

Here is an example where we normalize a non-domain.

i3 : B = QQ[u,v]/ideal(u*v);

i4 : betterNormalizationMap(B, Variable=>Y)

                  QQ[Y0, Y1, Y2]
o4 = map (-----------------------------, B, {Y1, Y0})
             2
          (Y2  - Y2, Y1*Y2 - Y1, Y0*Y2)

                     QQ[Y0, Y1, Y2]
o4 : RingMap ----------------------------- <-- B
                2
             (Y2  - Y2, Y1*Y2 - Y1, Y0*Y2)

We conclude with an example of taking the product of two rings.

i5 : C = QQ[x];

i6 : D = QQ[y];

i7 : ringProduct({C,D}, Variable=>z)

                  QQ[z0, z1, z2, z3]
o7 = {------------------------------------------, MutableList{...2...},
                      2
      (z1 + z3 - 1, z3  - z3, z2*z3 - z2, z0*z3)
     ------------------------------------------------------------------------
     {{z0}, {z2}}}

o7 : List

Further information

Default value: Yy
Function: seminormalize -- seminormalize a reduced ring
Option key: Variable -- specify a name for a variable

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
betterNormalizationMap(...,Variable=>...)
ringProduct(...,Variable=>...)
seminormalize(...,Variable=>...) -- set the name for new variables created by the function
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