Polynomials

Polynomial data type. More...

Collaboration diagram for Polynomials:

Files
file	poly.h

Data Structures
struct	bn_multipoly
struct	bn_poly

Macros
#define	BN_MAX_POLY_DEGREE   6
#define	BN_CK_POLY(_p)   BU_CKMAG(_p, BN_POLY_MAGIC, "struct bn_poly")
#define	BN_POLY_NULL   ((struct bn_poly *)NULL)
#define	BN_POLY_INIT_ZERO   { BN_POLY_MAGIC, 0, {0.0} }

Typedefs
typedef struct bn_multipoly	bn_multipoly_t
typedef struct bn_poly	bn_poly_t

Functions
struct bn_poly *	bn_poly_mul (struct bn_poly *product, const struct bn_poly *m1, const struct bn_poly *m2)
	multiply two polynomials
struct bn_poly *	bn_poly_scale (struct bn_poly *eqn, double factor)
	scale a polynomial
struct bn_poly *	bn_poly_add (struct bn_poly *sum, const struct bn_poly *poly1, const struct bn_poly *poly2)
	add two polynomials
struct bn_poly *	bn_poly_sub (struct bn_poly *diff, const struct bn_poly *poly1, const struct bn_poly *poly2)
	subtract two polynomials
void	bn_poly_synthetic_division (struct bn_poly *quo, struct bn_poly *rem, const struct bn_poly *dvdend, const struct bn_poly *dvsor)
	Divides any polynomial into any other polynomial using synthetic division. Both polynomials must have real coefficients.
int	bn_poly_quadratic_roots (struct bn_complex roots[], const struct bn_poly *quadrat)
	Uses the quadratic formula to find the roots (in ‘complex’ form) of any quadratic equation with real coefficients.
int	bn_poly_cubic_roots (struct bn_complex roots[], const struct bn_poly *eqn)
	Uses the cubic formula to find the roots (in ‘complex’ form) of any cubic equation with real coefficients.
int	bn_poly_quartic_roots (struct bn_complex roots[], const struct bn_poly *eqn)
	Uses the quartic formula to find the roots (in ‘complex’ form) of any quartic equation with real coefficients.
int	bn_poly_findroot (bn_poly_t *eqn, bn_complex_t *nxZ, const char *str)
void	bn_poly_eval_w_2derivatives (bn_complex_t *cZ, bn_poly_t *eqn, bn_complex_t *b, bn_complex_t *c, bn_complex_t *d)
int	bn_poly_checkroots (bn_poly_t *eqn, bn_complex_t *roots, int nroots)
void	bn_poly_deflate (bn_poly_t *oldP, bn_complex_t *root)
int	bn_poly_roots (bn_poly_t *eqn, bn_complex_t roots[], const char *name)
void	bn_pr_poly (const char *title, const struct bn_poly *eqn)
void	bn_pr_roots (const char *title, const struct bn_complex roots[], int n)

Detailed Description

Polynomial data type.

Library for dealing with polynomials.

Macro Definition Documentation

BN_MAX_POLY_DEGREE

#define BN_MAX_POLY_DEGREE   6

Maximum Poly Order

Definition at line 44 of file poly.h.

BN_CK_POLY

#define BN_CK_POLY

(

_p

)

BU_CKMAG(_p, BN_POLY_MAGIC, "struct bn_poly")

Definition at line 56 of file poly.h.

BN_POLY_NULL

#define BN_POLY_NULL   ((struct bn_poly *)NULL)

Definition at line 57 of file poly.h.

BN_POLY_INIT_ZERO

#define BN_POLY_INIT_ZERO   { BN_POLY_MAGIC, 0, {0.0} }

Definition at line 58 of file poly.h.

Typedef Documentation

bn_multipoly_t

typedef struct bn_multipoly bn_multipoly_t

bn_poly_t

typedef struct bn_poly bn_poly_t

Polynomial data type bn_poly->cf[n] corresponds to X^n

Function Documentation

bn_poly_mul()

struct bn_poly * bn_poly_mul ( struct bn_poly *  product, const struct bn_poly *  m1, const struct bn_poly *  m2  )

extern

multiply two polynomials

bn_poly_mul

bn_poly_scale()

struct bn_poly * bn_poly_scale ( struct bn_poly *  eqn, double  factor  )

extern

scale a polynomial

bn_poly_scale

bn_poly_add()

struct bn_poly * bn_poly_add ( struct bn_poly *  sum, const struct bn_poly *  poly1, const struct bn_poly *  poly2  )

extern

add two polynomials

bn_poly_add

bn_poly_sub()

struct bn_poly * bn_poly_sub ( struct bn_poly *  diff, const struct bn_poly *  poly1, const struct bn_poly *  poly2  )

extern

subtract two polynomials

bn_poly_sub

bn_poly_synthetic_division()

void bn_poly_synthetic_division ( struct bn_poly *  quo, struct bn_poly *  rem, const struct bn_poly *  dvdend, const struct bn_poly *  dvsor  )

extern

Divides any polynomial into any other polynomial using synthetic division. Both polynomials must have real coefficients.

bn_poly_quadratic_roots()

int bn_poly_quadratic_roots ( struct bn_complex  roots[], const struct bn_poly *  quadrat  )

extern

Uses the quadratic formula to find the roots (in ‘complex’ form) of any quadratic equation with real coefficients.

   @return 1 for success
   @return 0 for fail.

bn_poly_cubic_roots()

int bn_poly_cubic_roots ( struct bn_complex  roots[], const struct bn_poly *  eqn  )

extern

Uses the cubic formula to find the roots (in ‘complex’ form) of any cubic equation with real coefficients.

to solve a polynomial of the form:

X**3 + c1*X**2 + c2*X + c3 = 0,

first reduce it to the form:

Y**3 + a*Y + b = 0,

where Y = X + c1/3, and a = c2 - c1**2/3, b = (2*c1**3 - 9*c1*c2 + 27*c3)/27.

Then we define the value delta, D = b**2/4 + a**3/27.

If D > 0, there will be one real root and two conjugate complex roots. If D = 0, there will be three real roots at least two of which are equal. If D < 0, there will be three unequal real roots.

Returns 1 for success, 0 for fail.

bn_poly_quartic_roots()

int bn_poly_quartic_roots ( struct bn_complex  roots[], const struct bn_poly *  eqn  )

extern

Uses the quartic formula to find the roots (in ‘complex’ form) of any quartic equation with real coefficients.

   @return 1 for success
   @return 0 for fail.

bn_poly_findroot()

int bn_poly_findroot ( bn_poly_t *  eqn, bn_complex_t *  nxZ, const char *  str  )

extern

bn_poly_eval_w_2derivatives()

void bn_poly_eval_w_2derivatives ( bn_complex_t *  cZ, bn_poly_t *  eqn, bn_complex_t *  b, bn_complex_t *  c, bn_complex_t *  d  )

extern

bn_poly_checkroots()

int bn_poly_checkroots ( bn_poly_t *  eqn, bn_complex_t *  roots, int  nroots  )

extern

bn_poly_deflate()

void bn_poly_deflate ( bn_poly_t *  oldP, bn_complex_t *  root  )

extern

bn_poly_roots()

int bn_poly_roots ( bn_poly_t *  eqn, bn_complex_t  roots[], const char *  name  )

extern

bn_pr_poly()

void bn_pr_poly ( const char *  title, const struct bn_poly *  eqn  )

extern

Print out the polynomial.

bn_pr_roots()

void bn_pr_roots ( const char *  title, const struct bn_complex  roots[], int  n  )

extern

Print out the roots of a given polynomial (complex numbers)