Find the Roots of a Polynomial
DESCRIPTION:
Finds all roots of a polynomial with real or complex coefficients.
USAGE: 
polyroot(z)
REQUIRED ARGUMENTS:
z:
numeric or complex vector containing the polynomial coefficients. The ith component of z is the coefficient of x^(i-1). The highest order coefficient should not be 0+i0, and length(z) should not be greater that 49.
VALUE:
the roots of the polynomial as a complex vector.
DETAILS:
The object is to find all solutions x of

z[i]*x^(i-1) + ... + z[2]*x + z[1] = 0.

The algorithm to do so is described in Jenkins and Traub (1972) with modifications from Withers (1974).

REFERENCES:
Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day, Oakland, Calif.

Jenkins, M. A. and Traub, J. F. (1972). Zeros of a complex polynomial. Communications of the ACM 15, 97-99.

Withers, D. H. (1974). Remark on algorithm 419. Communications of the ACM 17, 157.

SEE ALSO:
uniroot
EXAMPLES: 
a <- c(1.2, .5, .3, 1) # some AR coefficients


# Compute and plot the roots of the characteristic equation to
# check for stationarity of the process (see Box and Jenkins, p. 55).


root <- polyroot(c(1, -a))
plot(root)
symbols(0, 0, circles=1, add=T, inches=F, col=5)
# All roots outside the unit circle, implies a stationary process.