Find zeros of a real or complex polynomial.

`polyroot(z)`

z

the vector of polynomial coefficients in increasing order.

A complex vector of length \(n - 1\), where \(n\) is the position
of the largest non-zero element of `z`

.

A polynomial of degree \(n - 1\),
$$
p(x) = z_1 + z_2 x + \cdots + z_n x^{n-1}$$
is given by its coefficient vector `z[1:n]`

.
`polyroot`

returns the \(n-1\) complex zeros of \(p(x)\)
using the Jenkins-Traub algorithm.

If the coefficient vector `z`

has zeroes for the highest powers,
these are discarded.

There is no maximum degree, but numerical stability may be an issue for all but low-degree polynomials.

Jenkins, M. A. and Traub, J. F. (1972).
Algorithm 419: zeros of a complex polynomial.
*Communications of the ACM*, **15**(2), 97--99.
10.1145/361254.361262.

`uniroot`

for numerical root finding of arbitrary
functions;
`complex`

and the `zero`

example in the demos
directory.

# NOT RUN { polyroot(c(1, 2, 1)) round(polyroot(choose(8, 0:8)), 11) # guess what! for (n1 in 1:4) print(polyroot(1:n1), digits = 4) polyroot(c(1, 2, 1, 0, 0)) # same as the first # }