transfer-matrix method calculations in linbox

[tshun]

Dear Linbox Support team,

I have a question on a calculation concerning
"the transfer-matrix method" as you can see
in section 4.7 of P.Stanley's famous book
"Enumerative Combinatorics vol I".

In the transfer-matrix method, we need to compute
the following two quantities (1) and (2).
(1) det ( I - zA )
(2) det( I - zA; i, j )
for a nxn matrix A and a pair (i,j) with 1\leq i,j\leq n.
Here, (B; i, j) denotes the matrix obtained by removing
the i-th row and j-th column of B.

Since det ( I - zA ) can be obtained immediately from
the characteristic polynomial det ( zI - A ),
the computation of (1) is easily performed using linbox.
I want to know what is a good way to calculate the
quantity (2) using linbox?

Best regards,
Shunsuke