RingMap RingElement -- apply a ring map

• Operator: SPACE

• Usage:

  f X

• Inputs:
  • f, a ring map, a ring map from R to S.
  • X, a ring element, an ideal, a matrix, a vector, or a module
• Outputs:
  • a ring element, the image of X under the ring map f. The result has the same type as X, except that its ring will be S.

i1 : R = QQ[x,y];

i2 : S = QQ[t];

i3 : f = map(S,R,{t^2,t^3})

                  2   3
o3 = map (S, R, {t , t })

o3 : RingMap S <-- R

i4 : f (x+y^2)

      6    2
o4 = t  + t

o4 : S

i5 : f image vars R

o5 = image | t2 t3 |

                             1
o5 : S-module, submodule of S

i6 : f ideal (x^2,y^2)

             4   6
o6 = ideal (t , t )

o6 : Ideal of S