Description
The list
v must be a doubly nested list of ring elements, which are used to fill the matrix, row by row.
The ring elements appearing in
v should be in
R, or in a base ring of
R.
Each list in v gives a row of the matrix. The length of the list
v should be the number of generators of
M, and the length of each element of
v (which is itself a list of ring elements) should be the number of generators of the source module
N.
i1 : R = ZZ/101[x,y,z]
o1 = R
o1 : PolynomialRing

i2 : p = map(R^2,,{{x^2,0,3},{0,y^2,5}})
o2 =  x2 0 3 
 0 y2 5 
2 3
o2 : Matrix R < R

i3 : isHomogeneous p
o3 = true

Another way is to use the
matrix(List) routine:
i4 : p = matrix {{x^2,0,3},{0,y^2,5}}
o4 =  x2 0 3 
 0 y2 5 
2 3
o4 : Matrix R < R

The absence of the second argument indicates that the source of the map is to be a free module constructed with an attempt made to assign degrees to its basis elements so as to make the map homogeneous of degree zero.
i5 : R = ZZ/101[x,y]
o5 = R
o5 : PolynomialRing

i6 : f = map(R^2,,{{x^2,y^2},{x*y,0}})
o6 =  x2 y2 
 xy 0 
2 2
o6 : Matrix R < R

i7 : degrees source f
o7 = {{2}, {2}}
o7 : List

i8 : isHomogeneous f
o8 = true
