B = tril(A,k) extracts lower triangular part of A.
tril(A) is the lower triangular part of A.
tril(A,k) is the elements on and below the k-th diagonal of A. k = 0 is the main diagonal, k > 0 is above the main diagonal and k < 0 is below the main diagonal.

A is a matrix of NCpolys
k is an integer

matrix of NCpolys

possible usage:
tril(A), tril(A,k)

>> A=[x x^2 x*y-y*x; y x*y 2*x-y; x+y y-x x^2+y^2]
A =  x    x^2   x*y-y*x
     y    x*y     2*x-y
   x+y   -x+y   x^2+y^2
>> tril(A)
ans =  x      0         0
       y    x*y         0
     x+y   -x+y   x^2+y^2

>> tril(A,-1)
ans =  0      0   0
       y      0   0
     x+y   -x+y   0