polyroot {base} | R Documentation

## Find Zeros of a Real or Complex Polynomial

### Description

Find zeros of a real or complex polynomial.

### Usage

    polyroot(z)

### Arguments

`z` | the vector of polynomial coefficients in increasing order.

### Details

A polynomial of degree n - 1,

p(x) = z1 + z2 * x + … + 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.

### Value

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

### Source

C translation by Ross Ihaka of Fortran code in the reference, with modifications by the R Core Team.

### References

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

### See Also

`uniroot` for numerical root finding of arbitrary functions; `complex` and the `zero` example in the demos directory.

### Examples

    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

[Package base version 3.6.0 Index]