# map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry

## Synopsis

• Function: map
• Usage:
map(M,n,f)
• Inputs:
• 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 map from a graded free module of rank n to the module M whose matrix entry h_(i,j) is obtained from the function f by evaluating f(i,j).

## Description

This is the same as calling map(M,R^n,f), except that the degrees of the basis elements of the source module are chosen in an attempt to ensure that the resulting map is homogeneous of degree zero.
 i1 : R = GF(9,Variable=>a)[x,y,z]; i2 : f = map(R^1, 3, (i,j) -> (a^j * x - y)^(j+1)) o2 = | x-y (a+1)x2+axy+y2 (-a-1)x3-y3 | 1 3 o2 : Matrix R <--- R i3 : source f 3 o3 = R o3 : R-module, free, degrees {1..3} i4 : isHomogeneous f o4 = true