polyfr.h File Reference

Definition of real polynomials with machine floating point coefficients. More...

Go to the source code of this file.

Data Structures
struct	polyfr_struct
	Polynomial with machine floating point real coefficients. More...

Typedefs
typedef polyfr_struct	polyfr_t[1]
	Practical wrapper for polyfr_struct. More...
typedef polyfr_struct *	polyfr
	Convenience pointer to polyfr_struct.

Functions
polyfr	polyfr_new (deg_t degree)
	Returns a new real polynomial of given degree, with machine floating point coefficients. More...
bool	polyfr_free (polyfr P)
	Frees all the memory used by the polynomial P, assuming the struct has been allocated with malloc(), for example with polyfr_new(). More...
bool	polyfr_set (polyfr P, coeff_t coeff, deg_t ind)
	Sets the coefficient corresponding to the power ind to coeff. More...
coeff_t	polyfr_get (polyfr P, deg_t ind)
	Returns the coefficient corresponding to the power ind. More...
bool	polyfr_eval_c (compf res, polyfr P, compf z)
	Evaluates P(z) using Horner's method. More...
coeff_t	polyfr_eval (polyfr P, coeff_t x)
	Evaluates P(x) using Horner's method. More...
polyf	polyfr_comp (polyfr P)
	Return a complex version of the real polynomial P. More...
polyfr	polyfr_derivative (polyfr P)
	Computes the derivative of P. More...
polyfr	polyfr_sum (polyfr P, polyfr Q)
	Computes P+Q. More...
polyfr	polyfr_diff (polyfr P, polyfr Q)
	Computes P-Q. More...
polyfr	polyfr_prod (polyfr P, polyfr Q)
	Computes P*Q. More...
polyfr	polyfr_sqr (polyfr P)
	Computes the square of P. More...
polyfr	polyf_hyp (int n)
	Computes the n-th hyperbolic polynomial, the n-th image of 0 under the iteration of z->z^2+c. It is a polynomial of degree 2^{n-1} in c. More...
polyfr	polyf_cheb (int n)
	Computes the Chebyshev polynomial of degree n. More...
polyfr	polyf_leg (int n)
	Computes the Legendre polynomial of degree n. More...
polyfr	polyf_her (int n)
	Computes the Hermite polynomial of degree n. More...
polyfr	polyf_lag (int n)
	Computes the Laguerre polynomial of degree n. More...

Detailed Description

Definition of real polynomials with machine floating point coefficients.

Definition in file polyfr.h.

Typedef Documentation

polyfr_t

typedef polyfr_struct polyfr_t[1]

Practical wrapper for polyfr_struct.

To avoid the constant use * and & the type polyfr_t is a pointer.

Definition at line 40 of file polyfr.h.

Function Documentation

polyf_cheb()

polyfr polyf_cheb

(

int

n

)

Computes the Chebyshev polynomial of degree n.

Parameters

n	the degree of the polynomial

Returns

the Chebyshev polynomial, NULL if some error occurred.

polyf_her()

polyfr polyf_her

(

int

n

)

Computes the Hermite polynomial of degree n.

Parameters

n	the degree of the polynomial

Returns

the Hermite polynomial, NULL if some error occurred.

polyf_hyp()

polyfr polyf_hyp

(

int

n

)

Computes the n-th hyperbolic polynomial, the n-th image of 0 under the iteration of z->z^2+c. It is a polynomial of degree 2^{n-1} in c.

Parameters

n	the order of the polynomial

Returns

the hyperbolic polynomial, NULL if some error occurred.

polyf_lag()

polyfr polyf_lag

(

int

n

)

Computes the Laguerre polynomial of degree n.

Parameters

n	the degree of the polynomial

Returns

the Laguerre polynomial, NULL if some error occurred.

polyf_leg()

polyfr polyf_leg

(

int

n

)

Computes the Legendre polynomial of degree n.

Parameters

n	the degree of the polynomial

Returns

the Legendre polynomial, NULL if some error occurred.

polyfr_comp()

polyf polyfr_comp

(

polyfr

P

)

Return a complex version of the real polynomial P.

Parameters

P	a polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyfr_derivative()

polyfr polyfr_derivative

(

polyfr

P

)

Computes the derivative of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyfr_diff()

polyfr polyfr_diff	(	polyfr	P,
		polyfr	Q
	)

Computes P-Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyfr_eval()

coeff_t polyfr_eval	(	polyfr	P,
		coeff_t	x
	)

Evaluates P(x) using Horner's method.

Parameters

P	the polynomial
x	the argument

Returns

the result, NaN if some error occurred.

polyfr_eval_c()

bool polyfr_eval_c	(	compf	res,
		polyfr	P,
		compf	z
	)

Evaluates P(z) using Horner's method.

Parameters

res	the result
P	the polynomial
z	the argument

Returns

true if successfull, false otherwise.

polyfr_free()

bool polyfr_free

(

polyfr

P

)

Frees all the memory used by the polynomial P, assuming the struct has been allocated with malloc(), for example with polyfr_new().

Parameters

P	the polynomial

Returns

true if successfull, false otherwise.

polyfr_get()

coeff_t polyfr_get	(	polyfr	P,
		deg_t	ind
	)

Returns the coefficient corresponding to the power ind.

Parameters

P	the polynomial
ind	the index

Returns

the coefficient corresponding to the power ind.

polyfr_new()

polyfr polyfr_new

(

deg_t

degree

)

Returns a new real polynomial of given degree, with machine floating point coefficients.

Parameters

degree

the degree of the polynomial

Returns

the new polynomial, NULL if the degree is larger than MAX_DEG.

polyfr_prod()

polyfr polyfr_prod	(	polyfr	P,
		polyfr	Q
	)

Computes P*Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyfr_set()

bool polyfr_set	(	polyfr	P,
		coeff_t	coeff,
		deg_t	ind
	)

Sets the coefficient corresponding to the power ind to coeff.

Parameters

P	the polynomial
coeff	the coefficient
ind	the index

Returns

true if successfull, false otherwise.

polyfr_sqr()

polyfr polyfr_sqr

(

polyfr

P

)

Computes the square of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyfr_sum()

polyfr polyfr_sum	(	polyfr	P,
		polyfr	Q
	)

Computes P+Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.