rmap result f ring R ring S

Interactively define a map of rings . A map of rings from R to S is simply a 1 by n matrix with base ring S, where n is the number of variables of R. The variable of R is mapped to the polynomial which is the column of this matrix. The command ev is used to evaluate a ring map on a matrix.

For example,

%  rmap f R S
! a ---> ?  x5
! b ---> ?  x4y+x3z2
! c ---> ?  y5
! d ---> ?  z5+y3x2

%  type f
; x5 x4y+x3z2 y5 x2y3+z5 

%  pmap f R
; map : R ---> S
; a |--> x5
; b |--> x4y+x3z2
; c |--> y5
; d |--> x2y3+z5

Notice that pmap displays the ring map as a map. The result f is a 1 by 4 matrix over the ring S. The main utility of the rmap command is that you are prompted for the value of each variable. Thus, you don't need to remember the order of the variables of R.