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

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

i2 : seminormalize(A, Variable=>X)

               QQ[X , X , X ]         
                   0   1   2          
o2 = {-------------------------------,
        2        2          3         
      (X  - X , X X  - X , X  - X X ) 
        2    0   0 2    1   0    1 2  
     ------------------------------------------------------------------------
                  QQ[X , X , X ]                     
                      0   1   2                      
     map(-------------------------------,A,{X , X }),
           2        2          3             1   0   
         (X  - X , X X  - X , X  - X X )             
           2    0   0 2    1   0    1 2              
     ------------------------------------------------------------------------
                                                                             
                               QQ[Yy01000RE1, aRE1, bRE1]                    
     map(--------------------------------------------------------------------
                         2                   2           2            2      
         (Yy01000RE1*bRE1  - aRE1, Yy01000RE1 bRE1 - bRE1 , Yy01000RE1  - bRE
                                                                             
     ------------------------------------------------------------------------
                 QQ[X , X , X ]
                     0   1   2
     --,-------------------------------,{bRE1, aRE1, Yy01000RE1})}
          2        2          3
     1) (X  - X , X X  - X , X  - X X )
          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,{Y0, Y1})
            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 = {------------------------------------------, {- z3 + 1, z3}, {{z0},
                      2
      (z1 + z3 - 1, z3  - z3, z2*z3 - z2, z0*z3)
     ------------------------------------------------------------------------
     {z2}}}

o7 : List