# polynomial_functions module reference¶

Polynomial functions.

More…

## Functions/Subroutines¶

 evaluation_polynomial() Pointwise evaluation of a polynomial at x. first_derivative_polynomial() Calculates the first derivative of a polynomial evaluated at a point x. integration_polynomial() Exact integration of polynomial of degree npoly.

## Detailed Description¶

This module contains routines that handle polynomials.

## Function/Subroutine Documentation¶

function polynomial_functions/evaluation_polynomial(coeff, ncoef, x) [real]

Pointwise evaluation of a polynomial at x.

The polynomial is defined by the coefficients contained in the array of the same name, as follows: C(1) + C(2)x + C(3)x^2 + C(4)x^3 + … where C refers to the array ‘coeff’. The number of coefficients is given by ncoef and x is the coordinate where the polynomial is to be evaluated.

Parameters
• coeff :: [in] The coefficients of the polynomial

• ncoef :: [in] The number of polynomial coefficients

• x :: [in] The position at which to evaluate the polynomial

Called from
function polynomial_functions/first_derivative_polynomial(coeff, ncoef, x) [real]

Calculates the first derivative of a polynomial evaluated at a point x.

The polynomial is defined by the coefficients contained in the array of the same name, as follows: C(1) + C(2)x + C(3)x^2 + C(4)x^3 + … where C refers to the array ‘coeff’. The number of coefficients is given by ncoef and x is the coordinate where the polynomial’s derivative is to be evaluated.

Parameters
• coeff :: [in] The coefficients of the polynomial

• ncoef :: [in] The number of polynomial coefficients

• x :: [in] The position at which to evaluate the derivative

function polynomial_functions/integration_polynomial(xi0, xi1, Coeff, npoly) [real]

Exact integration of polynomial of degree npoly.

The array of coefficients (Coeff) must be of size npoly+1.

Parameters
• xi0 :: [in] The lower bound of the integral

• xi1 :: [in] The lower bound of the integral

• coeff :: [in] The coefficients of the polynomial

• npoly :: [in] The degree of the polynomial