poly.h File Reference

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

Go to the source code of this file.

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

Typedefs
typedef poly_struct	poly_t[1]
	Practical wrapper for poly_struct. More...
typedef poly_struct *	poly
	Convenience pointer to poly_struct.

Functions
poly	poly_new (deg_t degree, prec_t prec)
	Returns a new complex polynomial of given degree, with coefficients of precision prec. More...
poly	poly_from_roots (comp_ptr roots, deg_t degree, prec_t prec)
	Returns a new complex polynomial given the list of its roots, with coefficients of precision prec. More...
bool	poly_free (poly P)
	Frees all the memory used by the polynomial P, assuming the struct has been allocated with malloc(), for example with poly_new(). More...
bool	poly_set (poly P, comp coeff, deg_t ind)
	Sets the coefficient of the polynomial P corresponding to the power ind to coeff. More...
bool	poly_eval (comp res, poly P, comp z)
	Evaluates P(z) using Horner's method. More...
bool	poly_eval_r (comp res, poly P, mpfr_t x)
	Evaluates P(x) using Horner's method. More...
poly	poly_derivative (poly P)
	Computes the derivative of P. More...
poly	poly_sum (poly P, poly Q)
	Computes P+Q. More...
poly	poly_diff (poly P, poly Q)
	Computes P-Q. More...
poly	poly_prod (poly P, poly Q)
	Computes P*Q. More...
poly	poly_sqr (poly P)
	Computes the square of P. More...

Detailed Description

Definition of complex polynomials with arbitary precision coefficients.

Definition in file poly.h.

Typedef Documentation

poly_t

typedef poly_struct poly_t[1]

Practical wrapper for poly_struct.

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

Definition at line 43 of file poly.h.

Function Documentation

poly_derivative()

poly poly_derivative

(

poly

P

)

Computes the derivative of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

poly_diff()

poly poly_diff	(	poly	P,
		poly	Q
	)

Computes P-Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

poly_eval()

bool poly_eval	(	comp	res,
		poly	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.

poly_eval_r()

bool poly_eval_r	(	comp	res,
		poly	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.

poly_free()

bool poly_free

(

poly

P

)

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

Parameters

P	the polynomial

Returns

true if successfull, false otherwise.

poly_from_roots()

poly poly_from_roots	(	comp_ptr	roots,
		deg_t	degree,
		prec_t	prec
	)

Returns a new complex polynomial given the list of its roots, with coefficients of precision prec.

Warning

prec must be at least precf

Parameters

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

Returns

the new polynomial, NULL if some error occurred.

poly_new()

poly poly_new	(	deg_t	degree,
		prec_t	prec
	)

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

Warning

prec must be at least precf

Parameters

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

Returns

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

poly_prod()

poly poly_prod	(	poly	P,
		poly	Q
	)

Computes P*Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.

poly_set()

bool poly_set	(	poly	P,
		comp	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.

poly_sqr()

poly poly_sqr

(

poly

P

)

Computes the square of P.

Parameters

P	the polynomial

Returns

the resulted polynomial, NULL if some error occurred.

poly_sum()

poly poly_sum	(	poly	P,
		poly	Q
	)

Computes P+Q.

Parameters

P	a polynomial
Q	another polynomial

Returns

the resulted polynomial, NULL if some error occurred.