polyr.h File Reference

Definition of real polynomials with arbitary precision coefficients. More...

Go to the source code of this file.

Data Structures
struct	polyr_struct
	Polynomial with multi-precision floating point complex coefficients. More...

Typedefs
typedef polyr_struct	polyr_t[1]
	Practical wrapper for polyr_struct. More...
typedef polyr_struct *	polyr
	Convenience pointer to polyr_struct.

Functions
polyr	polyr_new (deg_t degree, prec_t prec)
	Returns a new real polynomial of given degree, with coefficients of precision prec. More...
bool	polyr_free (polyr P)
	Frees all the memory used by the polynomial P, assuming the struct has been allocated with malloc(), for example with polyr_new(). More...
bool	polyr_set (polyr P, mpfr_t coeff, deg_t ind)
	Sets the coefficient of the polynomial P corresponding to the power ind to coeff. More...
bool	polyr_seti (polyr P, long coeff, deg_t ind)
	Sets the coefficient of the polynomial P corresponding to the power ind to coeff. More...
bool	polyr_eval_c (comp res, polyr P, comp z)
	Evaluates P(z) using Horner's method. More...
bool	polyr_eval (mpfr_t res, polyr P, mpfr_t x)
	Evaluates P(x) using Horner's method. More...
polyr	polyr_derivative (polyr P)
	Computes the derivative of P. More...
polyr	polyr_sum (polyr P, polyr Q)
	Computes P+Q. More...
polyr	polyr_diff (polyr P, polyr Q)
	Computes P-Q. More...
polyr	polyr_prod (polyr P, polyr Q)
	Computes P*Q. More...
polyr	polyr_sqr (polyr P)
	Computes the square of P. More...
polyr	poly_hyp (int n, prec_t prec)
	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...
polyr	poly_cheb (int n, prec_t prec)
	Computes the Chebyshev polynomial of degree n. More...
polyr	poly_leg (int n, prec_t prec)
	Computes the Legendre polynomial of degree n. More...
polyr	poly_her (int n, prec_t prec)
	Computes the Hermite polynomial of degree n. More...
polyr	poly_lag (int n, prec_t prec)
	Computes the Laguerre polynomial of degree n. More...

Detailed Description

Definition of real polynomials with arbitary precision coefficients.

Definition in file polyr.h.

Typedef Documentation

polyr_t

typedef polyr_struct polyr_t[1]

Practical wrapper for polyr_struct.

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

Definition at line 43 of file polyr.h.

Function Documentation

poly_cheb()

polyr poly_cheb	(	int	n,
		prec_t	prec
	)

Computes the Chebyshev polynomial of degree n.

Parameters

n	the degree of the polynomial
prec	the precision of the coefficients

Returns

the Chebyshev polynomial, NULL if some error occurred.

poly_her()

polyr poly_her	(	int	n,
		prec_t	prec
	)

Computes the Hermite polynomial of degree n.

Parameters

n	the degree of the polynomial
prec	the precision of the coefficients

Returns

the Hermite polynomial, NULL if some error occurred.

poly_hyp()

polyr poly_hyp	(	int	n,
		prec_t	prec
	)

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
prec	the precision of the coefficients

Returns

the hyperbolic polynomial, NULL if some error occurred.

poly_lag()

polyr poly_lag	(	int	n,
		prec_t	prec
	)

Computes the Laguerre polynomial of degree n.

Parameters

n	the degree of the polynomial
prec	the precision of the coefficients

Returns

the Laguerre polynomial, NULL if some error occurred.

poly_leg()

polyr poly_leg	(	int	n,
		prec_t	prec
	)

Computes the Legendre polynomial of degree n.

Parameters

n	the degree of the polynomial
prec	the precision of the coefficients

Returns

the Legendre polynomial, NULL if some error occurred.

polyr_derivative()

polyr polyr_derivative

(

polyr

P

)

Computes the derivative of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyr_diff()

polyr polyr_diff	(	polyr	P,
		polyr	Q
	)

Computes P-Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyr_eval()

bool polyr_eval	(	mpfr_t	res,
		polyr	P,
		mpfr_t	x
	)

Evaluates P(x) using Horner's method.

Parameters

res	the result
P	the polynomial
x	the real argument

Returns

true if successfull, false otherwise.

polyr_eval_c()

bool polyr_eval_c	(	comp	res,
		polyr	P,
		comp	z
	)

Evaluates P(z) using Horner's method.

Parameters

res	the result
P	the polynomial
z	the argument

Returns

true if successfull, false otherwise.

polyr_free()

bool polyr_free

(

polyr

P

)

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

Parameters

P	the polynomial

Returns

true if successfull, false otherwise.

polyr_new()

polyr polyr_new	(	deg_t	degree,
		prec_t	prec
	)

Returns a new real polynomial of given degree, with coefficients of precision prec.

Warning

prec must be at least precf and the degree at most MAX_DEG.

Parameters

degree	the degree of the polynomial
prec	the precision of the coefficients, in bits

Returns

the new buffer, NULL if some error occurred.

polyr_prod()

polyr polyr_prod	(	polyr	P,
		polyr	Q
	)

Computes P*Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyr_set()

bool polyr_set	(	polyr	P,
		mpfr_t	coeff,
		deg_t	ind
	)

Sets the coefficient of the polynomial P corresponding to the power ind to coeff.

Parameters

P	the polynomial
coeff	the coefficient
ind	the index

Returns

true if successfull, false otherwise.

polyr_seti()

bool polyr_seti	(	polyr	P,
		long	coeff,
		deg_t	ind
	)

Sets the coefficient of the polynomial P corresponding to the power ind to coeff.

Parameters

P	the polynomial
coeff	the coefficient
ind	the index

Returns

true if successfull, false otherwise.

polyr_sqr()

polyr polyr_sqr

(

polyr

P

)

Computes the square of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

polyr_sum()

polyr polyr_sum	(	polyr	P,
		polyr	Q
	)

Computes P+Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.