This provides a check on the last displayed formula of page 214.  Recent versions of MATHEMATICA perform the computations too slowly.  For this reason, we have retained the following evaluations that were made with Version 3.0 in March of 2003

$Version

The following computation runs more efficiently on Version 3.0 of Mathematica  than it does on Version 4.1.

NumberOfCases = 45

f[i_, j_] := 
      Sum[Binomial[n - i, j - nu]*Binomial[i, nu]*a^(n - i - j + nu)*
          b^(j - nu)*c^(i - nu)*d^(nu), {nu, 0, j}]

The preceding gives a typical component of the matrix (Subscript[M, A]).

M[n_] := Table[f[i, j], {i, 0, n}, {j, 0, n}]

The preceding defines the matrix (Subscript[M, A]).

Date[]

Do[expr1 = Expand[Det[M[n]]]; 
      expr2 = Expand[(a*d - b*c)^((n*(n + 1))/2)]; 
      expr3 = Expand[expr1 - expr2]; 
      Print["Det[ M[", n, "] ] - (a*d - b*c)^(n(n+1)/2) = ", expr3]; 
      Print[Date[]]; Print["       "], {n, 1, NumberOfCases}]