Description

Functions for polynomial manipulation.

We represent polynomials as a vector of coefficients with the highest power term on the left at vector index 0. The following polynomial manipulation functions are designed to behave like their counterparts in the Numerical Renaissance codebase.

Author: James Strawson

Date: 2016

Functions
int	rc_poly_print (rc_vector_t v)
	Prints a polynomial in human-readable format in one line. More...

int	rc_poly_conv (rc_vector_t a, rc_vector_t b, rc_vector_t *c)
	Convolutes the polynomials a&b and places the result in vector c. More...

int	rc_poly_power (rc_vector_t a, int n, rc_vector_t *b)
	Raises a polynomial a to itself n times where n is greater than or equal to 0. More...

int	rc_poly_add (rc_vector_t a, rc_vector_t b, rc_vector_t *c)
	Add two polynomials a&b with right justification and place the result in c. More...

int	rc_poly_add_inplace (rc_vector_t *a, rc_vector_t b)
	Adds polynomials a&b with right justification. More...

int	rc_poly_subtract (rc_vector_t a, rc_vector_t b, rc_vector_t *c)
	Subtracts two polynomials a-b with right justification and places the result in c. More...

int	rc_poly_subtract_inplace (rc_vector_t *a, rc_vector_t b)
	Subtracts b from a with right justification. More...

int	rc_poly_differentiate (rc_vector_t a, int d, rc_vector_t *b)
	Calculates the dth derivative of the polynomial a and places the result in vector b. More...

int	rc_poly_divide (rc_vector_t n, rc_vector_t d, rc_vector_t div, rc_vector_t rem)
	Divides denominator d into numerator n. The remainder is placed into vector rem and the divisor is placed into vector div. More...

int	rc_poly_butter (int N, double wc, rc_vector_t *b)
	Calculates coefficients for continuous-time Butterworth polynomial of order N and cutoff wc (rad/s) and places them in vector b. More...

Function Documentation

◆ rc_poly_print()

int rc_poly_print ( rc_vector_t v )

Prints a polynomial in human-readable format in one line.

Like rc_print_vector, but assumes the contents represent a polynomial and prints the coefficients with trailing powers of x for easier reading. This relies on your terminal supporting unicode UTF-8. numer of coefficients and there the length of vector v must be less than or equal to 10.

Parameters

[in] v polynomial coefficients to be printed

Returns: 0 on success or -1 on failure

Examples:: rc_test_polynomial.c.

◆ rc_poly_conv()

int rc_poly_conv	(	rc_vector_t	a,
		rc_vector_t	b,
		rc_vector_t *	c
	)

Convolutes the polynomials a&b and places the result in vector c.

This finds the coefficients of the polynomials resulting from multiply a*b. The original contents of c are freed and new memory is allocated if necessary.

Parameters

[in]	a	First set of coefficients
[in]	b	Second set of coefficients
[out]	c	Vector to output resulting coefficients

Returns: Returns 0 on success or -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_power()

int rc_poly_power	(	rc_vector_t	a,
		int	n,
		rc_vector_t *	b
	)

Raises a polynomial a to itself n times where n is greater than or equal to 0.

Places the result in vector b, any existing memory allocated for b is freed and its contents are lost. Returns 0 on success and -1 on failure.

Parameters

[in]	a	Initial coefficients
[in]	n	Power, must be >=0
[out]	b	resulting coefficients

Returns: Returns 0 on success or -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_add()

int rc_poly_add	(	rc_vector_t	a,
		rc_vector_t	b,
		rc_vector_t *	c
	)

Add two polynomials a&b with right justification and place the result in c.

Any existing memory allocated for c is freed and its contents are lost.

Parameters

[in]	a	First input
[in]	b	second input
[out]	c	output

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_add_inplace()

int rc_poly_add_inplace	(	rc_vector_t *	a,
		rc_vector_t	b
	)

Adds polynomials a&b with right justification.

The result is placed in vector a and a's original contents are lost. More memory is allocated for a if necessary.

Parameters

	a	First input and where output is written
[in]	b	second input

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_subtract()

int rc_poly_subtract	(	rc_vector_t	a,
		rc_vector_t	b,
		rc_vector_t *	c
	)

Subtracts two polynomials a-b with right justification and places the result in c.

Any existing memory allocated for c is freed and its contents are lost. Returns 0 on success and -1 on failure.

Parameters

[in]	a	First input
[in]	b	second input
[out]	c	output

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_subtract_inplace()

int rc_poly_subtract_inplace	(	rc_vector_t *	a,
		rc_vector_t	b
	)

Subtracts b from a with right justification.

a stays in place and new memory is allocated only if b is longer than a.

Parameters

	a	First input and where output is written
[in]	b	second input

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_differentiate()

int rc_poly_differentiate	(	rc_vector_t	a,
		int	d,
		rc_vector_t *	b
	)

Calculates the dth derivative of the polynomial a and places the result in vector b.

Parameters

[in]	a	Input polynomial coefficients
[in]	d	which derivative to take (>=0)
[out]	b	result

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_divide()

int rc_poly_divide	(	rc_vector_t	n,
		rc_vector_t	d,
		rc_vector_t *	div,
		rc_vector_t *	rem
	)

Divides denominator d into numerator n. The remainder is placed into vector rem and the divisor is placed into vector div.

Parameters

[in]	n	numerator
[in]	d	denominator
	div	The resulting divisor
	rem	The resulting remainder

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.

◆ rc_poly_butter()

int rc_poly_butter	(	int	N,
		double	wc,
		rc_vector_t *	b
	)

Calculates coefficients for continuous-time Butterworth polynomial of order N and cutoff wc (rad/s) and places them in vector b.

Parameters

[in]	N	Order of the polynomial
[in]	wc	cutoff frequency in rad/s
[out]	b	resulting coefficients

Returns: Returns 0 on success and -1 on failure.

Examples:: rc_test_polynomial.c.