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Seminormalization :: renameVariablesOfTarget

renameVariablesOfTarget -- given a ring map, it renames the variables of the target to the specified name

Synopsis

Description

Given a ring map this returns a list of three things. First, the new map with the variables of target renamed as specified. Second, the map (isomorphism) from old target to the new target. Finally, the map (isomorphism) from new target to the old target.

i1 : A = QQ[a,b]/ideal(a^2-b^5);
i2 : B = QQ[u,v, w];
i3 : f = map(A, B, {a^2, a*b, b^2});

o3 : RingMap A <--- B
i4 : L = renameVariablesOfTarget(X, f);
i5 : L#0

         QQ[X , X ]
             0   1      2         2
o5 = map(----------,B,{X , X X , X })
             5    2     0   0 1   1
          - X  + X
             1    0

             QQ[X , X ]
                 0   1
o5 : RingMap ---------- <--- B
                 5    2
              - X  + X
                 1    0
i6 : L#1

         QQ[X , X ]
             0   1
o6 = map(----------,A,{X , X })
             5    2     0   1
          - X  + X
             1    0

             QQ[X , X ]
                 0   1
o6 : RingMap ---------- <--- A
                 5    2
              - X  + X
                 1    0
i7 : L#2

           QQ[X , X ]
               0   1
o7 = map(A,----------,{a, b})
               5    2
            - X  + X
               1    0

                    QQ[X , X ]
                        0   1
o7 : RingMap A <--- ----------
                        5    2
                     - X  + X
                        1    0

Ways to use renameVariablesOfTarget :