Given an n x n Matrix A of values from a commutative ring R, BerkowitzAlgorithm[R](A) returns a Vector V of dimension n+1 of values in R with the coefficients of the characteristic polynomial of A.

The characteristic polynomial is the polynomial V[1]*x^n + V[2]*x^(n-1) + ... + V[n]*x + V[n+1].

The Berkowitz algorithm does O(n^4) multiplications and additions in R.

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

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

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

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

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

R[`*`] : a procedure for multiplying elements of R (binary and commutative)

R[`=`] : a boolean procedure for testing if two elements of R are equal