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

Synopsis

• Function: map

• Usage:

  map(R,m)

• Inputs:
  • R, a ring
  • m, a matrix, a one row matrix
• 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, A ring map f : R --> (ring m), where the entries of m are the images of the variables of R.

Description

i1 : R = QQ[a..d];

i2 : S = QQ[s,t];

i3 : F = map(R,matrix{{s^4,s^3*t,s*t^3,t^4}})

               4   3      3   4
o3 = map(S,R,{s , s t, s*t , t })

o3 : RingMap S <--- R

i4 : kernel F

                        3      2     2    2    3    2
o4 = ideal (b*c - a*d, c  - b*d , a*c  - b d, b  - a c)

o4 : Ideal of R

See also

• substitution and maps between rings
• map(Ring,Ring,Matrix) -- make a ring map