map(Ring,Ring,List) -- make a ring map

Synopsis

Function: map
Usage:

map(R,S,m)
Inputs:
- R, a ring, the target ring
- S, a ring, the source ring
- m, a list, of n elements of R, where n is the number of variables in the polynomial ring S, or a list of pairs x => r, where x is a generator of S and r is an element of R, specifying that x is to be sent to r.
Optional inputs:
- Degree => ..., default value null, specify the degree of a map
- DegreeLift => ..., default value null, make a ring map
- DegreeMap => ..., default value null, make a ring map
Outputs:
- a ring map, the ring homomorphism from S to R which sends the i-th variable of S to the i-th entry in m, or in the second case, performs the indicated substitutions.

i1 : R = ZZ[x,y];

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

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

                  2        2
o3 = map (R, S, {x , x*y, y })

o3 : RingMap R <-- S

i4 : f(a+b+c^2)

      4    2
o4 = y  + x  + x*y

o4 : R

i5 : g = map(R,S,{a=>x^2,b=>x*y,c=>y^2})

                  2        2
o5 = map (R, S, {x , x*y, y })

o5 : RingMap R <-- S

i6 : g(a+b+c^2)

      4    2
o6 = y  + x  + x*y

o6 : R