mapOntoImage -- Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).

Synopsis

• Usage:

  h = mapOntoImage(f)

  h = mapOntoImage(a,b,l)

  h = mapOntoImage(R,S,l)

• Inputs:
  • a, an ideal, defining equations for X
  • b, an ideal, defining equations for Y
  • l, a basic list, projective rational map given by polynomial represenatives of the same degree
  • f, a ring map, the ring map corresponding to $f : X \to Y$
  • R, a ring, coordinate ring for X
  • S, a ring, coordinate ring for Y
• Optional inputs:
  • QuickRank => ..., default value true, An option for computing how rank is computed
• Outputs:
  • h, a ring map, the map of rings corresponding to $f : X \to f(X)$.

Description

i1 : R = QQ[x,y];

i2 : S = QQ[a,b,c];

i3 : f = map(R, S, {x^2, x*y, y^2});

o3 : RingMap R <--- S

i4 : mapOntoImage(f)

                 S       2        2
o4 = map (R, --------, {x , x*y, y })
              2
             b  - a*c

                        S
o4 : RingMap R <--- --------
                     2
                    b  - a*c

i5 : mapOntoImage(R,S,{x^2,x*y,y^2})

                 S       2        2
o5 = map (R, --------, {x , x*y, y })
              2
             b  - a*c

                        S
o5 : RingMap R <--- --------
                     2
                    b  - a*c