Section Resultant.
Variables (R : ringType) (p q : {poly R}).
Let dS := ((size q).-1 + (size p).-1)%N.
Local Notation band r := (lin1_mx (poly_rV \o r \o* rVpoly)).
Definition Sylvester_mx : 'M[R]_dS := col_mx (band p) (band q).

Lemma Sylvester_mxE (i j : 'I_dS) :
let S_ r k := r`_(j - k) *+ (k <= j) in
Sylvester_mx i j = match split i with inl k => S_ p k | inr k => S_ q k end.