# POLY

## Purpose:

Calculates coefficients of the characteristic polynomial.

## Syntax:

POLY(x)

 x - A series or matrix. A matrix where the eigenvalues are the roots of the returned polynomial coefficients or a series of the roots of the returned polynomial coefficients.

## Returns:

A series, the polynomial coefficients in descending order.

## Example:

W1: {{1, 2, 3},

{3, 4, 5},

{5, 6, 0}}

W2: poly(W1)

W3: polyroot(W2, 1)

W4: eig(W1)

W2 contains the series {1, -5, -47, -14}, the coefficients in descending order of the characteristic polynomial of the matrix in W1. The roots of this polynomial are the eigenvalues of the input matrix.

W3 == {9.894, -4.585, -0.309}

W4 == {9.894, -0.309, -4.585}

## Example:

If the input is a series, the input represents the roots of the polynomial coefficients returned by POLY. For example, consider the polynomial: poly({-2, -1}) == {1, 3, 2}

polyroot({1, 3, 2}, 1) == {-2, -1}

## Remarks:

As indicated above, if the input is a matrix, POLY returns the coefficients of the characteristic polynomial in descending order.

If the input is a series, the input represents the roots of a polynomial and POLY returns the coefficients of this polynomial in descending order.

EIG

POLYFIT

POLYDER

POLYINT

POLYROOT

POLYSTAB

POLYVAL

ROOTS