cgwtools (version 4.1)

ratRoot: Function to find the rational roots of any polynomial (when they exist).

Description

.

Usage

ratRoot(Anum, Adenom = rep(1,times=length(Anum)) )

Value

A vector of bigq fractions representing all real rational roots found. If empty, all roots are irrational (or perhaps complex).

Arguments

Anum

A vector of the polynomial coefficients' numerators, starting with the highest power. Values can be numeric or bigz.

Adenom

A vector of the polynomial coefficients' denominators, starting with the highest power. Values can be numeric or bigz. Default is all ones, indicating that all input coefficients are integers.

Author

Carl Witthoft,

Details

The code makes use of the 'Rational Root Theorem,' which states that all real, rational roots p/q meet two criteria. Given a polynomial of the form An *x^n + A_(n-1) * x^(n-1) + ... + A0 = 0, all coefficients adjusted to be integers, 'p' must be a factor of the zero-power polynomial coefficient A0, and 'q' must be a factor of the maximum-power polynomial coefficient An. If any of the input Adenom are not '1', the function will make this adjustment.

References

https://en.wikipedia.org/wiki/Rational_root_theorem

Examples

ratRoot(c(6, -15, 261), c(1,1,49))
ratRoot(c(1,0,0,0,-1))
ratRoot(c(1,-2,1))