coefAndMonomials = degHomPolMap(r, l, v, d)
Let R be a polynomial ring in two groups of variables $R=S[X_1,...,X_r]$ and $S=k[a_1,...,a_s]$. Here, $X_1,...,X_r$ are called v and $a_1,...,a_s$ are called 'coefficients'. Let m be a line matrix $f_1,...,f_n$, where fi is an element of R which is homogeneous as a polynomial in the variables 'var', of degree $di$ for all i in 'var'. The matrix 'm' defines a graded map of Rmodules (of degree 0 in 'var') from $R(d_1)+...+R(d_n)$ to R. In particular, looking on each strand d, we have a map of free Smodules of finite rank $f_d: R_{dd_1}+...+R_{dd_n} > R_d$ where $R_d$ is the homogeneous part of degree d in 'var' of R.
This function returns a sequence with two elements: first the list of monomials of degree d in 'var'; Second, the matrix f_d with entries in S in the base of monomials.
For computing the base of monomials, it needs as a second argument the list $d_1,...,d_n$ of the degrees of the fi's in v. There is an auxiliary function computing this automatically from the list of elements fi's and the list of variables v called l.















The object degHomPolMap is a method function.