# map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix

## Synopsis

• Function: map
• Usage:
map(M,N,p)
• Inputs:
• M,
• N,
• p,
• 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 matrix with the same entries as p, but whose target is M and source is N

## Description

M and N should be modules over the same ring, and have the same number of generators as target p and source p, respectively.
 i1 : R = QQ[x,y,z]; i2 : p = matrix {{x,y,z}} o2 = | x y z | 1 3 o2 : Matrix R <--- R i3 : q = map(R^1,R^3,p) o3 = | x y z | 1 3 o3 : Matrix R <--- R i4 : degrees source p o4 = {{1}, {1}, {1}} o4 : List i5 : degrees source q o5 = {{0}, {0}, {0}} o5 : List

## Caveat

If M or N is not free, then we don't check that the the result is a well defined homomorphism.