Given an n x n Matrix A of elements in F, a field, HessenbergAlgorithm[F](A) returns a Vector V of n+1 values from F encoding the characteristic polynomial of A as V[1] x^n + V[2] x^(n-1) + .... + V[n] x + V[n+1]

The algorithm converts a copy of A into upper Hessenberg form H using O(n^3) operations in F then expands the determinant of x I - H in a further O(n^3) operations in F. The algorithm requires that F be a field and should only be used if F is finite as there is severe expression swell in computing H.

The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:

F[`0`]: a constant for the zero of the ring F

F[`1`]: a constant for the (multiplicative) identity of F

F[`+`]: a procedure for adding elements of F (nary)

F[`-`]: a procedure for negating and subtracting elements of F (unary and binary)

F[`*`]: a procedure for multiplying two elements of F (commutative)

F[`/`]: a procedure for dividing two elements of F

F[`=`]: a boolean procedure for testing if two elements in F are equal