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

Synopsis

Usage:
map(M,N,p)
Function: map
Inputs:
- M, a module
- N, a module
- p, a matrix
Outputs:
- a matrix, A matrix with the same entries as p, but whose target is M and source is N
Optional inputs:
- Degree => ..., -- set the degree of a map
- DegreeLift => ..., -- make a ring map
- DegreeMap => ..., -- make a ring map

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

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