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

Description

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

o2 : List

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)

i5 : C = QQ[x];

i6 : D = QQ[y];

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

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

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 Pluecker 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