fmpq_poly.c File Reference

Fast implementation of the rational function field. More...

#include "fmpq_poly.h"
#include <stdio.h>
#include <gmp.h>
#include "fmpz.h"
#include "fmpz_poly.h"

Defines
#define	FMPQ_POLY_INV_NEWTON_CUTOFF 32
Functions
unsigned int	fmpq_poly_places (ulong n)
void	fmpq_poly_canonicalize (fmpq_poly_ptr f, fmpz_t temp)
	Puts `f` into canonical form.This method ensures that the denominator is coprime to the content of the numerator polynomial, and that the denominator is positive.
void	fmpq_poly_neg (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_inv (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_get_coeff_mpq (mpq_t rop, const fmpq_poly_ptr op, ulong i)
void	fmpq_poly_set_coeff_fmpz (fmpq_poly_ptr rop, ulong i, const fmpz_t x)
void	fmpq_poly_set_coeff_mpz (fmpq_poly_ptr rop, ulong i, const mpz_t x)
void	fmpq_poly_set_coeff_mpq (fmpq_poly_ptr rop, ulong i, const mpq_t x)
void	fmpq_poly_set_coeff_si (fmpq_poly_ptr rop, ulong i, long x)
int	fmpq_poly_equal (const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
	Returns whether `op1` and `op2` are equal.Returns whether the two elements `op1` and `op2` are equal.
int	fmpq_poly_cmp (const fmpq_poly_ptr left, const fmpq_poly_ptr right)
	Compares the two polynomials `left` and `right`.Compares the two polnomials `left` and `right`, returning `-1`, `0`, or `1` as `left` is less than, equal to, or greater than `right`.
static void	_fmpq_poly_add_in_place (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_add (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
static void	_fmpq_poly_sub_in_place (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_sub (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
void	fmpq_poly_addmul (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
void	fmpq_poly_submul (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
void	fmpq_poly_scalar_mul_si (fmpq_poly_ptr rop, const fmpq_poly_ptr op, long x)
void	fmpq_poly_scalar_mul_mpz (fmpq_poly_ptr rop, const fmpq_poly_ptr op, const mpz_t x)
void	fmpq_poly_scalar_mul_mpq (fmpq_poly_ptr rop, const fmpq_poly_ptr op, const mpq_t x)
static void	_fmpq_poly_scalar_div_si_in_place (fmpq_poly_ptr rop, long x)
void	fmpq_poly_scalar_div_si (fmpq_poly_ptr rop, const fmpq_poly_ptr op, long x)
static void	_fmpq_poly_scalar_div_mpz_in_place (fmpq_poly_ptr rop, const mpz_t x)
void	fmpq_poly_scalar_div_mpz (fmpq_poly_ptr rop, const fmpq_poly_ptr op, const mpz_t x)
void	fmpq_poly_scalar_div_mpq (fmpq_poly_ptr rop, const fmpq_poly_ptr op, const mpq_t x)
static void	_fmpq_poly_mul_in_place (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_mul (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2)
void	fmpq_poly_floordiv (fmpq_poly_ptr q, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_mod (fmpq_poly_ptr r, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_divrem (fmpq_poly_ptr q, fmpq_poly_ptr r, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_inv_series (fmpq_poly_ptr rop, const fmpq_poly_ptr op, long n)
void	fmpq_poly_div_series (fmpq_poly_ptr rop, const fmpq_poly_ptr op1, const fmpq_poly_ptr op2, long n)
void	fmpq_poly_power (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong exp)
void	fmpq_poly_gcd (fmpq_poly_ptr rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_xgcd (fmpq_poly_ptr rop, fmpq_poly_ptr s, fmpq_poly_ptr t, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_lcm (fmpq_poly_ptr rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_derivative (fmpq_poly_ptr rop, fmpq_poly_ptr op)
static void	_fmpz_poly_evaluate_mpq_horner (mpq_t rop, const fmpz_poly_t f, const mpq_t a)
void	fmpq_poly_evaluate_mpz (mpq_t rop, fmpq_poly_ptr f, const mpz_t a)
void	fmpq_poly_evaluate_mpq (mpq_t rop, fmpq_poly_ptr f, const mpq_t a)
void	fmpq_poly_content (mpq_t rop, const fmpq_poly_ptr op)
void	fmpq_poly_primitive_part (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
int	fmpq_poly_is_monic (const fmpq_poly_ptr op)
	Returns whether `op` is monic.Returns whether `op` is monic.
void	fmpq_poly_monic (fmpq_poly_ptr rop, const fmpq_poly_ptr op)
void	fmpq_poly_resultant (mpq_t rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
	Returns the resultant of `a` and `b`.Returns the resultant of `a` and `b`.
void	fmpq_poly_discriminant (mpq_t disc, fmpq_poly_t a)
	Computes the discriminant of `a`.Computes the discriminant of the polynomial .
void	fmpq_poly_compose (fmpq_poly_ptr rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
	Returns the composition of `a` and `b`.Returns the composition of `a` and `b`.
void	fmpq_poly_rescale (fmpq_poly_ptr rop, const fmpq_poly_ptr op, const mpq_t x)
	Rescales the co-ordinate.Denoting this polynomial , computes the polynomial .
int	fmpq_poly_is_squarefree (const fmpq_poly_ptr op)
	Returns whether `op` is squarefree.Returns whether `op` is squarefree.
void	fmpq_poly_getslice (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong i, ulong j)
	Returns a contiguous subpolynomial.Returns the slice with coefficients from (including) to (excluding).
void	fmpq_poly_left_shift (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong n)
	Shifts this polynomial to the left by coefficients.Notionally multiplies `op` by and stores the result in `rop`.
void	fmpq_poly_right_shift (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong n)
	Shifts this polynomial to the right by coefficients.Notationally returns the quotient of floor division of `rop` by `op`.
void	fmpq_poly_truncate (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong n)
	Truncates this polynomials.Truncates `op` modulo whenever is positive. Returns zero otherwise.
void	fmpq_poly_reverse (fmpq_poly_ptr rop, const fmpq_poly_ptr op, ulong n)
	Reverses this polynomial.Reverses the coefficients of `op` - thought of as a polynomial of length `n` - and places the result in `rop`.
void	fmpq_poly_from_list (fmpq_poly_ptr rop, mpq_t *a, ulong n)
	Constructs a polynomial from a list of rationals.
int	fmpq_poly_from_string (fmpq_poly_ptr rop, const char *str)
char *	fmpq_poly_to_string (const fmpq_poly_ptr op)
char *	fmpq_poly_to_string_pretty (const fmpq_poly_ptr op, const char *var)
void	fmpq_poly_print (const fmpq_poly_ptr op)
void	fmpq_poly_print_pretty (const fmpq_poly_ptr op, const char *x)

Detailed Description

Fast implementation of the rational function field.

Author:: Sebastian Pancratz

Date:: Mar 2010 -- July 2010

Version:: 0.1.8

Define Documentation

#define FMPQ_POLY_INV_NEWTON_CUTOFF 32

Threshold value for power series inversion using Newton's method.

Function Documentation

static void _fmpq_poly_scalar_div_si_in_place	(	fmpq_poly_ptr	rop,
		long	x
	)			`[static]`

/ingroup ScalarMul

Divides rop by the integer x.

Assumes that x is non-zero. Otherwise, an exception is raised in the form of an abort statement.

void fmpq_poly_discriminant	(	mpq_t	disc,
		fmpq_poly_t	a
	)

Computes the discriminant of a.Computes the discriminant of the polynomial $a$ .

The discriminant $R_n$ is defined as

$R_n = a_n^{2 n-2} \prod_{1 \le i < j \le n} (r_i - r_j)^2,$

where $n$ is the degree of this polynomial, $a_n$ is the leading coefficient and $r_1, \ldots, r_n$ are the roots over $\bar{\mathbf{Q}}$ are.

The discriminant of constant polynomials is defined to be $0$ .

This implementation uses the identity

$R_n(f) := (-1)^(n (n-1)/2) R(f,f') / a_n,$

where $n$ is the degree of this polynomial, $a_n$ is the leading coefficient and $f'$ is the derivative of $f$ .

See also:: fmpq_poly_resultant()

void fmpq_poly_monic	(	fmpq_poly_ptr	rop,
		const fmpq_poly_ptr	op
	)

Sets rop to the unique monic scalar multiple of op.

As the only special case, if op is the zero polynomial, rop is set to zero, too.

unsigned int fmpq_poly_places ( ulong n )

Returns the number of digits in the decimal representation of n.

void fmpq_poly_print ( const fmpq_poly_ptr op )

void fmpq_poly_print_pretty	(	const fmpq_poly_ptr	op,
		const char *	x
	)

fmpq_poly.c File Reference

Defines

Functions

Detailed Description

Define Documentation

Function Documentation