mmx Namespace Reference

Namespaces
	array
	Module for generic functions on vectors. Generic implementations for vectors are gathered in the namespace array. These are generic functions, that can be used to build new linear classes. The type R must provide the following definitions or methods:
	bernstein
	brnops
	let
	Namespace for explicit type conversion.
	linear
	memory
	meta
	numerics
	realroot
	solvers
	sparse
	namespace for representation of polynomials as sequence of monomials
	tensor
	namespace for representation of polynomials as dense tensor product.
	texp
	univariate
	Module for Univariate POLynomials with a Direct Access Representation.
	upoldse_
	vct
	vctops
	xml
	Namespace for parsing and printing in xml format.

Classes
struct	abs_max
struct	AkritasBound
struct	algebraic
struct	Approximate
struct	as_helper
struct	as_helper< double, char * >
struct	as_helper< double, const char * >
struct	as_helper< double, mpf_t >
struct	as_helper< double, RR >
struct	as_helper< double, scalar< EMPQ > >
struct	as_helper< double, scalar< EMPZ > >
struct	as_helper< double, scalar< MPQ > >
struct	as_helper< double, scalar< MPZ > >
struct	as_helper< Interval< double >, QQ >
struct	as_helper< Interval< FT >, IntervalData< RT, Poly > >
struct	as_helper< interval< FT >, IntervalData< RT, Poly > >
struct	as_helper< interval< T >, interval< F > >
struct	as_helper< monom< T, TR >, monom< F, FR > >
struct	as_helper< QQ, RR >
struct	as_helper< QQ, ZZ >
struct	as_helper< RR, double >
struct	as_helper< RR, QQ >
struct	as_helper< scalar< EMPQ >, scalar< EMPZ > >
struct	as_helper< set_of< U >, set_of< T > >
struct	as_helper< ZZ, double >
struct	as_helper< ZZ, QQ >
struct	as_helper< ZZ, unsigned >
struct	AsSize
struct	Bernstein
struct	BezierBound
struct	bigunsigned
struct	binary_approx
struct	binary_convert
struct	binary_convert< K, Approximate >
struct	binary_convert< K, Isolate >
struct	binary_isolate
struct	binary_sleeve_subdivision
struct	binary_subdivision
struct	binomials
struct	bound
struct	Bspline
struct	cast_helper
struct	cast_helper< double, QQ >
struct	cast_helper< double, RR >
struct	cast_helper< double, ZZ >
struct	cast_helper< QQ, ZZ >
struct	Cauchy
	Cauchy bound. More...
class	cell_mv_bernstein
class	cell_uv_bernstein
struct	CFallIsolate
struct	CFdecide
struct	CFfirstApproximate
struct	CFfirstFloor
struct	CFfirstIsolate
struct	CFseparate
struct	ContFrac
struct	ContFrac_t
	Class. More...
struct	continued_fraction_approximate
struct	continued_fraction_approximate< K, B, false_t >
struct	continued_fraction_approximate< K, B, true_t >
struct	continued_fraction_isolate
struct	continued_fraction_isolate< K, B, false_t >
struct	continued_fraction_isolate< K, B, true_t >
struct	continued_fraction_subdivision
struct	data_t
struct	default_variant_of
struct	default_variant_of< Sparse >
struct	DegRevLex
	Degree Reverse Lexicographic monomial ordering. More...
struct	Dual
struct	dynamic_exp
	Dynamic exponent. More...
struct	euclidean
struct	extended
struct	GMP
	Numerical kernel based on gmp. More...
struct	homography
struct	homography_mv
struct	HongBound
struct	IEEE754
	Default numerical kernel. More...
struct	Interval
	Generic class for intervals. More...
struct	interval_newton
class	interval_rep
struct	IntervalData
struct	IntervalNewton
struct	Intervals
struct	is_extended
struct	is_extended< EQQ >
struct	is_extended< EZZ >
struct	Isolate
struct	Lex
	Lexicographic monomial ordering. More...
struct	LexRevDegree
struct	MCFapproximate
struct	MCFisolate
struct	monom
	Monomial class. More...
struct	MonomialOrdering
	Virtual class of monomial ordering. More...
struct	MonomialTensor
struct	mul_helper< polynomial< C, with< Dual, O > >, polynomial< C, with< Sparse, O > > >
struct	mul_helper< polynomial< C, with< Sparse, O > >, polynomial< C, with< Dual, O > > >
struct	mv_binary_approx
struct	mv_binary_isolate
struct	MvBernsteinBinaryApproximate
struct	NISN
	Negative Inverse Sum bound for negative roots. More...
struct	NISP
	Negative Inverse Sum bound for positive roots. More...
struct	operators_of
struct	polynomial
struct	polynomial< C, VARIANT >
struct	polynomial_of
struct	printer
struct	ProjRd
struct	ReferTo
	The structure for obtain the template parameter. More...
struct	ReferTo< shared_object< T > >
	The structure for obtain the template parameter. More...
struct	rep_view
struct	res_t
struct	ring
	Ring of polynomials. More...
struct	ring< C, Bernstein >
struct	ring< C, Dual, O >
	Dual ring of the polynomials. More...
struct	ring< C, MonomialTensor >
	Tensor ring of polynomials in the monomial basis. More...
struct	ring< C, Sparse, O >
	Ring of sparse polynomials. More...
struct	ring< C, Univariate >
	Tensor ring of polynomials in the monomial basis. More...
struct	ring_of
	Generic ring class. More...
struct	ring_of< polynomial< C, V > >
struct	ring_of< polynomial< C, with< Bernstein > > >
struct	ring_of< polynomial< C, with< MonomialTensor > > >
struct	ring_of< polynomial< C, with< V, W > > >
struct	scalar
struct	Seq
	Sequence of terms with reference counter. More...
struct	set_of
class	shared_object
struct	sign_wanted
struct	Sleeve
struct	sleeve_rep
struct	solver
struct	solver< C, ContFrac< Approximate > >
struct	solver< C, ContFrac< Isolate > >
struct	solver< C, MCFapproximate >
struct	solver< C, MCFisolate >
struct	solver< C, ProjRd< MTH > >
	Multivariate Bernstein solver. More...
struct	solver< C, Sleeve< V > >
struct	solver< Ring, Bspline >
struct	solver< Ring, CFallIsolate >
struct	solver< Ring, CFdecide >
struct	solver< Ring, CFfirstApproximate >
struct	solver< Ring, CFfirstFloor >
struct	solver< Ring, CFfirstIsolate >
struct	solver< Ring, CFseparate >
struct	solver_approximate_traits
struct	solver_approximate_traits< C, false_t >
struct	solver_approximate_traits< C, true_t >
struct	solver_bspline
struct	solver_cffirst
struct	solver_isolate_traits
struct	solver_isolate_traits< C, false_t >
struct	solver_isolate_traits< C, true_t >
struct	solver_of
struct	solver_of< C, IntervalNewton< IT, C > >
struct	solver_of< C, MvBernsteinBinaryApproximate >
struct	solver_of< C, UvBernsteinBinaryApproximate >
struct	Sparse
struct	sub_resultant
class	subdivisor
struct	Univariate
struct	upoldse
struct	use
struct	use< operators_of, POLYNOMIAL >
struct	use< operators_of, Polynomial >
struct	use< operators_of, SparsePolynomial >
struct	use< polynomial_of, polynomial< C, with< Bernstein > > >
struct	use< polynomial_of, polynomial< C, with< Dual, O > > >
struct	use< polynomial_of, polynomial< C, with< MonomialTensor > > >
struct	use< polynomial_of, polynomial< C, with< Sparse, O > > >
struct	use< polynomial_of, polynomial< C, with< Univariate > > >
	Tensor ring of polynomials in the monomial basis. More...
struct	uv_binary_approx
struct	uv_binary_isolate
struct	UvBernsteinBinaryApproximate
struct	variables
struct	with

Typedefs
typedef GMP::rational	QQ
typedef GMP::integer	ZZ
typedef GMP::floating	RR
typedef GMP::extended_rational	EQQ
typedef GMP::extended_integer	EZZ
typedef extended< MPZ >	EMPZ
typedef extended< MPQ >	EMPQ
typedef __mpf_struct	MPF
typedef MP_INT	MPZ
typedef MP_RAT	MPQ

Functions
std::string	to_string (int x)
	to_string convert int to std::string In C++11, it should use std::to_string More...
std::string	to_string (double x)
	to_string convert double to std::string In C++11, it should use std::to_string More...
template<typename T , typename F >
T	as (const F &x)
template<typename T , typename F , class U >
T	as (const F &x, const U &u)
template<typename T , typename F , class U , class V >
T	as (const F &x, const U &u, const V &v)
template<class T >
T	pow (const T &a, int i)
template<typename T >
T	factorial (int n)
template<typename T >
T	binomial (int n, int p)
template<class C >
meta::rationalof< C >::T	to_rational (const C &a, const C &b)
template<class NT , class LB >
Seq< typename ContFrac< NT, LB >::root_t >	solve (const typename ContFrac< NT >::Poly &f, ContFrac< NT, LB >)
template<typename K >
void	CF_positive (const typename K::Poly &f, Seq< typename K::FIT > &RL, bool posneg, K)
template<typename K >
void	MCF_positive (const typename K::Poly &f, Seq< typename K::root_t > &RL, bool posneg, K)
template<typename OutputIterator , typename K >
OutputIterator	CF_solve (const typename K::Poly &f, OutputIterator sol, int mult, K)
template<typename K , typename OutputIterator >
OutputIterator	solve_contfrac (const typename K::Poly &h, OutputIterator sol, K)
template<class POL >
void	div_x (POL &p, int k)
template<typename FT >
Interval< FT >	as_interval (const FT &a, const FT &b)
template<typename RT , typename Poly >
IntervalData< RT, Poly >	as_interval_data (const RT &a, const RT &b, const RT &c, const RT &d, const Poly &f)
template<class C >
texp::rationalof< C >::T	to_FT (const C &a, const C &b)
template<typename FT >
Interval< FT >	to_FIT (const FT &a, const FT &b)
template<typename K >
K::FIT	to_FIT (const typename K::RT &a, const typename K::RT &b, const typename K::RT &c, const typename K::RT &d, const typename K::FT &B)
template<typename Poly >
void	reverse (Poly &R, const Poly &P)
template<typename Poly >
void	reverse (Poly &R)
template<typename RT , typename Poly >
void	reverse (IntervalData< RT, Poly > &I1)
template<typename Poly >
void	shift_by_1 (Poly &R, const Poly &P)
template<typename RT , typename Poly >
void	shift_by_1 (IntervalData< RT, Poly > &I1, const IntervalData< RT, Poly > &I2)
template<typename RT , typename Poly >
void	shift_by_1 (IntervalData< RT, Poly > &I1)
template<typename Poly >
void	shift_by_1 (Poly &R)
template<typename RT , typename Poly >
void	scale (IntervalData< RT, Poly > &ID, const RT &a)
template<typename RT , typename Poly , typename RT2 >
void	scale (IntervalData< RT, Poly > &ID, const RT2 &a)
template<typename RT , typename Poly >
void	scale (IntervalData< RT, Poly > &ID, long k)
template<typename RT , typename Poly >
void	inv_scale (IntervalData< RT, Poly > &ID, const RT &a)
template<typename RT , typename Poly >
void	shift (IntervalData< RT, Poly > &ID, const RT &a)
template<typename RT , typename Poly , typename RT2 >
void	shift (IntervalData< RT, Poly > &ID, const RT2 &a)
template<typename RT , typename Poly >
void	reverse_shift_homography (IntervalData< RT, Poly > &I2, const IntervalData< RT, Poly > &ID)
template<typename RT , typename Poly >
void	reverse_shift (IntervalData< RT, Poly > &I2, const IntervalData< RT, Poly > &ID)
template<class E >
dynamic_exp< E >::degree_t	degree (const dynamic_exp< E > &t)
template<class E >
std::ostream &	operator<< (std::ostream &os, const dynamic_exp< E > &t)
template<class E >
int	lvar (const dynamic_exp< E > &A)
template<class E >
void	erase (dynamic_exp< E > &A)
template<class E >
void	add (dynamic_exp< E > &r, const dynamic_exp< E > &A, const dynamic_exp< E > &B)
template<class NT >
bool	operator== (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
bool	operator!= (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
extended< NT >	operator* (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
extended< NT >	operator/ (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
extended< NT >	operator+ (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
extended< NT >	operator- (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
extended< NT >	operator- (const extended< NT > &lhs)
template<class NT >
extended< NT > &	operator<<= (extended< NT > &x, long int s)
template<class NT >
extended< NT > &	operator+= (extended< NT > &x, const extended< NT > &other)
template<class NT >
extended< NT > &	operator-= (extended< NT > &x, const extended< NT > &other)
template<class NT >
extended< NT > &	operator*= (extended< NT > &x, const extended< NT > &other)
template<class NT >
extended< NT > &	operator/= (extended< NT > &x, const extended< NT > &other)
template<class NT >
bool	operator< (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
bool	operator<= (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
bool	operator> (const extended< NT > &lhs, const extended< NT > &rhs)
template<class NT >
bool	operator>= (const extended< NT > &lhs, const extended< NT > &rhs)
int	sign (const QQ &a)
bool	with_plus_sign (const ZZ &c)
bool	with_plus_sign (const QQ &c)
bool	with_plus_sign (const RR &c)
double	to_double (const RR &a)
double	as_double (const RR &a)
double	to_XT (const ZZ &a)
double	to_XT (const QQ &a)
double	to_XT (const RR &a)
void	bit_precision (unsigned long l)
void	bit_precision (RR b, unsigned long l)
double	gcd (const double &, const double &)
QQ	to_FT (const ZZ &a, const ZZ &b=1)
QQ	to_FT (const QQ &a, const QQ &b=1)
long int	bit_size (const ZZ &z)
ZZ	gcd (const ZZ &a, const ZZ &b)
ZZ	lcm (const ZZ &a, const ZZ &b)
int	sign (const RR &a)
QQ	Size (const QQ &r)
ZZ	Size (const ZZ &z)
ZZ	size (const ZZ &z)
QQ	size (const QQ &r)
int	compare (const QQ &a, const QQ &b)
int	compare (const RR &a, const RR &b)
double	to_double (const QQ &a)
double	to_double (const ZZ &z)
ZZ	numerator (const QQ &a)
ZZ	denominator (const QQ &a)
ZZ	pow (const ZZ &a, unsigned n)
ZZ	isqrt (const ZZ &a)
RR	fracpart (const RR &r)
void	Precision (unsigned long l)
void	Precision (RR b, unsigned long l)
template<class OSTREAM , class T , int r>
void	print (OSTREAM &os, const Interval< T, r > &a)
template<class T , int r>
void	hull (Interval< T, r > &v, const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
bool	intersect (Interval< T, r > &result, const Interval< T, r > &a, const Interval< T, r > &b)
template<typename T >
int	sign (const T &x)
template<class C , int r>
bool	with_plus_sign (const Interval< C, r > &I)
template<class T , int r>
T	lower (const Interval< T, r > &x)
template<class T , int r>
T	upper (const Interval< T, r > &x)
template<class T , int r>
T	median (const Interval< T, r > &x)
template<class T , int r>
T	width (const Interval< T, r > &x)
template<class T , int r>
bool	singleton (const Interval< T, r > &x)
template<class T , int r>
bool	contain_zero (const Interval< T, r > &x)
template<class T , int r>
bool	in (const T &x, const Interval< T, r > &y)
template<class T , int r>
std::pair< Interval< T, r >, Interval< T, r > >	bissect (const Interval< T, r > &x)
template<class T , int r>
void	bissect (Interval< T, r > &g, Interval< T, r > &d, const Interval< T, r > &x)
template<class T , int r>
Interval< T, r >	hull (const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
Interval< T, r >	min (const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
Interval< T, r >	max (const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
bool	intersectp (const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
Interval< T, r >	intersection (const Interval< T, r > &a, const Interval< T, r > &b)
template<class T , int r>
T	size (const Interval< T, r > &i)
template<class T , int r>
std::ostream &	operator<< (std::ostream &o, const Interval< T, r > &i)
template<class C , int r>
void	abs (Interval< C, r > &x, const Interval< C, r > &a)
template<class C , int r>
void	neg (Interval< C, r > &a)
template<class C , int r>
void	neg (Interval< C, r > &a, const Interval< C, r > &b)
template<class C , int r>
void	add (Interval< C, r > &a, const C &x)
template<class C , int r>
void	add (Interval< C, r > &a, const Interval< C, r > &b, const C &x)
template<class C , int r>
void	add (Interval< C, r > &a, const C &x, const Interval< C, r > &b)
template<class C , int r>
void	sub (Interval< C, r > &a, const C &x)
template<class C , int r>
void	sub (Interval< C, r > &a, const Interval< C, r > &b, const C &x)
template<class C , int r>
void	sub (Interval< C, r > &a, const C &x, const Interval< C, r > &b)
template<class C , int r>
void	add (Interval< C, r > &a, const Interval< C, r > &x)
template<class C , int r>
void	add (Interval< C, r > &a, const Interval< C, r > &b, const Interval< C, r > &x)
template<class C , int r>
void	sub (Interval< C, r > &a, const Interval< C, r > &x)
template<class C , int r>
void	sub (Interval< C, r > &a, const Interval< C, r > &b, const Interval< C, r > &x)
template<class C , int r>
void	mul (Interval< C, r > &a, const C &x)
template<class C , int r>
void	mul (Interval< C, r > &a, const Interval< C, r > &b, const C &x)
template<class C , int r>
void	mul (Interval< C, r > &a, const C &x, const Interval< C, r > &b)
template<class C , int r>
void	mul (Interval< C, r > &a, const Interval< C, r > &b)
template<class C , int r>
void	mul (Interval< C, r > &x, const Interval< C, r > &a, const Interval< C, r > &b)
template<class C , int r>
void	div (Interval< C, r > &a, const C &x)
template<class C , int r>
void	div (Interval< C, r > &a, const Interval< C, r > &b, const C &x)
template<class C , int r>
void	div (Interval< C, r > &a, const C &x, const Interval< C, r > &b)
template<class C , int r>
void	div (Interval< C, r > &a, const Interval< C, r > &b)
template<class C , int r>
void	div (Interval< C, r > &x, const Interval< C, r > &a, const Interval< C, r > &b)
template<class C , int R>
void	split (Interval< C, R > &l, Interval< C, R > &r)
template<class C , int R>
Interval< C, R >	operator- (const Interval< C, R > &I)
TMPL texp::sup< ARG0, ARG1 >::T	operator+ (const ARG0 &Ia, const ARG1 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator- (const ARG0 &Ia, const ARG1 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator* (const ARG0 &Ia, const ARG1 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator/ (const ARG0 &Ia, const ARG1 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator+ (const ARG1 &Ia, const ARG0 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator- (const ARG1 &Ia, const ARG0 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator* (const ARG1 &Ia, const ARG0 &Ib)
TMPL texp::sup< ARG0, ARG1 >::T	operator/ (const ARG1 &Ia, const ARG0 &Ib)
	declare_binary_operator (TMPL, ARG1, ARG0, _add_, operator+)
	declare_binary_operator (TMPL, ARG1, ARG0, _sub_, operator-)
	declare_binary_operator (TMPL, ARG1, ARG0, _mul_, operator*)
	declare_binary_operator (TMPL, ARG1, ARG0, _div_, operator/)
	declare_binary_operator (TMPL, ARG0, ARG1, _add_, operator+)
	declare_binary_operator (TMPL, ARG0, ARG1, _sub_, operator-)
	declare_binary_operator (TMPL, ARG0, ARG1, _mul_, operator*)
	declare_binary_operator (TMPL, ARG0, ARG1, _div_, operator/)
	FORALL (C) inline mmx
TMPL Monomial	operator* (const Monomial &m1, const Monomial &m2)
TMPL Monomial	operator/ (const Monomial &m1, const Monomial &m2)
TMPL bool	divide (const Monomial &m1, const Monomial &m2, Monomial &r)
TMPL void	mul (Monomial &a, const Monomial &m1, const Monomial &m2)
TMPL void	div (Monomial &a, const Monomial &m1, const Monomial &m2)
TMPL Monomial	div (const Monomial &m1, const Monomial &m2)
TMPL Monomial	div_quo (const Monomial &m1, const Monomial &m2)
template<class C , class E >
E::degree_t	degree (const Monomial &m)
TMPL Monomial	MGcd (const Monomial &m1, const Monomial &m2)
TMPL Monomial	pow (const Monomial &m1, int n)
template<class C , class E >
Monomial	operator+ (const Monomial &m1, const Monomial &m2)
template<class C , class E >
Monomial	operator- (const Monomial &m1, const Monomial &m2)
template<class C , class E >
Monomial	operator* (const Monomial &m1, const C &c2)
template<class C , class E >
Monomial	operator* (const C &c2, const Monomial &m1)
template<class C , class E >
Monomial	operator/ (const Monomial &m1, const C &c2)
bool	is_polynomial (const std::ostringstream &sm)
template<class OSTREAM , class C , class E >
OSTREAM &	print (OSTREAM &os, const Monomial &m, const variables &V)
template<class C , class E >
std::string	to_string_pp (const Monomial &m, const variables &V)
template<class C , class E >
std::string	to_string (const Monomial &m, const variables &V)
template<class OSTREAM , class C , class E >
OSTREAM &	print_as_double (OSTREAM &os, const Monomial &m, const variables &V)
template<class C , class E >
std::ostream &	operator<< (std::ostream &os, const monom< C, E > &m)
	Output operator. More...
TMPL bool	exact_eq (const Monomial &v1, const Monomial &v2)
TMPL bool	exact_neq (const Monomial &v1, const Monomial &v2)
TMPL unsigned	hash (const Monomial &v)
TMPL unsigned	exact_hash (const Monomial &m)
TMPL unsigned	soft_hash (const Monomial &m)
TMPL syntactic	flatten (const MONOMIAL &v)
TMPL MONOMIAL	monomial_from_vector (const vector< int > &t)
TMPL vector< int >	vector_from_monomial (const MONOMIAL &m)
TMPL int	N (const MONOMIAL &v)
TMPL int	size (const MONOMIAL &v)
TMPL Seq< typename ring< C, Bernstein >::Polynomial >	coefficients (const typename ring< C, Bernstein >::Polynomial &pol, int v)
TMPL unsigned	hash (const RING &p)
TMPL unsigned	exact_hash (const RING &p)
TMPL unsigned	soft_hash (const RING &p)
TMPL bool	exact_eq (const RING &p, const RING &q)
TMPL bool	exact_neq (const RING &p, const RING &q)
TMPL bool	operator== (const RING &p, const RING &q)
TMPL bool	operator!= (const RING &p, const RING &q)
TMPL syntactic	flatten (const RING &rg)
TMPL RING	ring_bernstein_string (const scalar_set< C > &rg, const vector< string > &s)
TMPL RING	ring_tensor_of (const ring< C, Bernstein > &r)
TMPL RING	ring_bernstein_of (const ring< C, Sparse, DegRevLex > &r)
TMPL RING	ring_bernstein_generic (const scalar_set< C > &rg, const Bernstein &b, const vector< generic > &s)
TMPL RING	ring_bernstein_extend_generic (const RING &R, const vector< generic > &s)
TMPL syntactic	flatten (const POLYNOMIAL &p)
TMPL POLYNOMIAL	polynomial_bernstein (const RING &r, const C &c)
TMPL POLYNOMIAL	polynomial_bernstein (const RING &r, const C &c, const int &d, const int &v)
TMPL POLYNOMIAL	polynomial_bernstein (const RING &r, const string &s)
TMPL POLYNOMIAL	polynomial_bernstein (const RING &r, const generic &s)
TMPL POLYNOMIAL	polynomial_bernstein_of (const polynomial< C, with< Sparse, DegRevLex > > &f)
TMPL polynomial< C, with< Sparse, DegRevLex > >	polynomial_sparse_of (const POLYNOMIAL &f)
TMPL polynomial< C, with< MonomialTensor > >	polynomial_tensor_of (const POLYNOMIAL &f)
TMPL vector< generic >	polynomial_bernstein_coefficients (const POLYNOMIAL &f, const int &v)
TMPL vector< generic >	polynomial_bernstein_coefficients (const POLYNOMIAL &p)
template<class C , class O >
C	sample (const RING &rg)
TMPL	define_operator_rrr (DUALPOL, POL, DUALPOL, operator*, sparse::mul) TMPL define_operator_rrr(POL
TMPL RING	dual_of (const RING_POL &rg)
TMPL RING	dual_of (const RING_POL &rg, const generic &x)
TMPL syntactic	flatten (const Polynomial &p)
TMPL Polynomial	polynomial_dual (const RING &rg, const C &c)
TMPL Polynomial	polynomial_dual (const RING &rg, const C &c, int d, int v)
TMPL Polynomial	polynomial_dual (const RING &rg, const string &s)
TMPL Polynomial	polynomial_dual (const RING &r, const generic &s)
TMPL vector< generic >	polynomial_dual_coefficients (const Polynomial &f, const int &v)
TMPL vector< generic >	polynomial_dual_coefficients (const Polynomial &p)
TMPL int	nbvar (const Polynomial &mp)
TMPL int	degree (const Polynomial &mp)
TMPL int	degree (const Polynomial &mp, int v)
TMPL unsigned	size (const Polynomial &p)
TMPL std::string	to_string (const Polynomial &mp, const variables &var)
TMPL std::ostream &	operator<< (std::ostream &os, const Polynomial &mp)
template<class OSTREAM , class C , class Rep , class Ord >
OSTREAM &	print (OSTREAM &os, const Polynomial &mp)
template<class OSTREAM , class C , class Rep , class Ord >
OSTREAM &	print (OSTREAM &os, const Polynomial &mp, const variables &Var)
TMPL std::string	as_string (const Polynomial &p)
TMPL std::string	as_string (const Polynomial &p, const variables &var)
TMPL Polynomial	diff (const Polynomial &pol, int v)
	Multivariate Polynomial Differentiation. More...
TMPL Polynomial	diff (const Polynomial &pol)
	Multivariate Polynomial Differentiation. More...
TMPL Seq< C >	coefficients (const Polynomial &pol)
TMPL Seq< Polynomial >	coefficients (const Polynomial &pol, int v)
template<class Result , class C , class Rep , class Ord , class Parameters >
Result	eval (const Polynomial &polynomial, const Parameters &parameters)
	Multivariate Polynomial Evaluation. More...
template<class Result , class C , class Rep , class Ord , class Parameters >
Result	eval (const Polynomial &polynomial, const Parameters &parameters, int n)
template<class Result , class C , class Rep , class Ord , class Parameters >
void	eval (Result &result, const Polynomial &polynomial, const Parameters &parameters)
TMPL Polynomial	homogenize (const Polynomial &p, const Polynomial &v)
TMPL Polynomial	homogenize (const Polynomial &p, int i, const Polynomial &v)
template<class POL1 , class C2 , class R2 , class V2 >
POL1	as (const polynomial< C2, with< R2, V2 > > &p)
template<class MP >
MP	binomial (typename MP::coeff_t coeff, int i, int d, typename MP::coeff_t a)
TMPL void	shift (Polynomial &f, const C &t, const int &v)
TMPL void	shift (Polynomial &r, const Polynomial &p, int d, int v=0)
TMPL void	reciprocal (Polynomial &f, const int &v)
TMPL Polynomial::Scalar	content (const Polynomial &p)
TMPL unsigned	hash (const Polynomial &p)
TMPL unsigned	exact_hash (const Polynomial &p)
TMPL unsigned	soft_hash (const Polynomial &p)
TMPL bool	exact_eq (const Polynomial &p, const Polynomial &q)
TMPL bool	exact_neq (const Polynomial &p, const Polynomial &q)
TMPL Polynomial	diff (const Polynomial &p, const generic &v)
TMPL vector< generic >	polynomial_sturm_sequence (const Polynomial &p, const Polynomial &q, int v)
TMPL Polynomial	polynomial_resultant (const Polynomial &p, const Polynomial &q, int v)
TMPL Polynomial	polynomial_gcd (const Polynomial &p, const Polynomial &q, int v)
TMPL void	add (POLYNOMIAL &r, const POLYNOMIAL &a)
TMPL void	add (POLYNOMIAL &r, const POLYNOMIAL &a, const POLYNOMIAL &b)
TMPL void	add (POLYNOMIAL &r, const POLYNOMIAL &a, const C &b)
TMPL void	add (POLYNOMIAL &r, const C &a, const POLYNOMIAL &b)
TMPL void	sub (POLYNOMIAL &r, const POLYNOMIAL &a)
TMPL void	sub (POLYNOMIAL &r, const POLYNOMIAL &a, const POLYNOMIAL &b)
TMPL void	sub (POLYNOMIAL &r, const C &a, const POLYNOMIAL &b)
TMPL void	sub (POLYNOMIAL &r, const POLYNOMIAL &a, const C &b)
TMPL void	mul (POLYNOMIAL &r, const POLYNOMIAL &a)
TMPL void	mul (POLYNOMIAL &r, const POLYNOMIAL &a, const POLYNOMIAL &b)
TMPL void	mul (POLYNOMIAL &r, const POLYNOMIAL &a, const C &b)
TMPL void	mul (POLYNOMIAL &r, const C &a, const POLYNOMIAL &b)
TMPL void	div (POLYNOMIAL &r, const POLYNOMIAL &a, const POLYNOMIAL &b)
TMPL void	div (POLYNOMIAL &r, const POLYNOMIAL &a, const C &b)
TMPL void	rem (POLYNOMIAL &r, const POLYNOMIAL &a, const POLYNOMIAL &b)
TMPL POLYNOMIAL	operator- (const POLYNOMIAL &p)
TMPL	define_operator_rrr (POLYNOMIAL, POLYNOMIAL, POLYNOMIAL, operator+, OP::add) TMPLX define_operator_r_r(POLYNOMIAL
TMPL bool	operator== (const POLYNOMIAL &mp, const C &c)
TMPL bool	operator== (const POLYNOMIAL &mp, unsigned n)
template<class C , class V , class X >
bool	operator!= (const polynomial< C, V > &p, const X &q)
TMPL RING	ring_sparse_string (const scalar_set< C > &rg, const vector< string > &s)
TMPL RING	ring_sparse_generic (const scalar_set< C > &rg, const vector< generic > &s)
TMPL RING	ring_sparse_extend_generic (const RING &R, const vector< generic > &s)
TMPL Polynomial	polynomial_sparse (const RING &r, const C &c)
TMPL Polynomial	polynomial_sparse (const RING &r, const C &c, const int &d, const int &v)
TMPL Polynomial	polynomial_sparse (const RING &r, const string &s)
TMPL Polynomial	polynomial_sparse (const RING &r, const generic &s)
TMPL vector< generic >	polynomial_sparse_coefficients (const Polynomial &f, const int &v)
TMPL vector< generic >	polynomial_sparse_coefficients (const Polynomial &p)
TMPL vector< generic >	polynomial_sparse_monomials (const Polynomial &p)
TMPL generic	polynomial_sparse_eval_generic (const Polynomial &p, const vector< generic > &v)
TMPL Seq< POLYNOMIAL >	coefficients (const POLYNOMIAL &f, const int &v)
TMPL Seq< C >	coefficients (const POLYNOMIAL &f)
TMPL RING	ring_tensor_string (const scalar_set< C > &rg, const vector< string > &s)
TMPL RING	ring_tensor_of (const ring< C, Sparse, DegRevLex > &r)
TMPL RING	ring_tensor_generic (const scalar_set< C > &rg, const MonomialTensor &b, const vector< generic > &s)
TMPL RING	ring_tensor_extend_generic (const RING &R, const vector< generic > &s)
TMPL POLYNOMIAL	polynomial_tensor (const RING &r, const C &c)
TMPL POLYNOMIAL	polynomial_tensor (const RING &r, const C &c, const int &d, const int &v)
TMPL POLYNOMIAL	polynomial_tensor (const RING &r, const string &s)
TMPL POLYNOMIAL	polynomial_tensor (const RING &r, const generic &s)
TMPL POLYNOMIAL	polynomial_tensor_of (const polynomial< C, with< Sparse, DegRevLex > > &f)
TMPL vector< generic >	polynomial_tensor_coefficients (const POLYNOMIAL &f, const int &v)
TMPL vector< generic >	polynomial_tensor_coefficients (const POLYNOMIAL &p)
TMPL void	print (OSTREAM &os, int x)
TMPL void	print (OSTREAM &os, long int x)
TMPL void	print (OSTREAM &os, unsigned x)
TMPL void	print (OSTREAM &os, double x)
TMPL C	sample (const SELF &R)
	Function which returns an element of the ring (here 0). More...
TMPL POLYNOMIAL	polynomial_bernstein_tensor (const RING &r, const C &c)
TMPL POLYNOMIAL	polynomial_bernstein_tensor (const RING &r, const C &c, const int &d, const int &v)
TMPL POLYNOMIAL	polynomial_bernstein_tensor (const RING &r, const string &s)
TMPL POLYNOMIAL	polynomial_bernstein_tensor (const RING &r, const generic &s)
TMPL POLYNOMIAL	polynomial_bernstein_tensor_of (const polynomial< C, with< Sparse, DegRevLex > > &f)
TMPL vector< generic >	polynomial_bernstein_tensor_coefficients (const POLYNOMIAL &f, const int &v)
TMPL vector< generic >	polynomial_bernstein_tensor_coefficients (const POLYNOMIAL &p)
TMPL polynomial< C, with< Sparse, DegRevLex > >	ring_sparse_of (const POLYNOMIAL &f)
template<class T >
scalar< T > &	operator+ (const scalar< T > &b, unsigned long ul)
template<class T >
scalar< T > &	operator- (const scalar< T > &b, unsigned long ul)
template<class T >
scalar< T > &	operator* (const scalar< T > &b, unsigned long ul)
template<class T >
scalar< T > &	operator/ (const scalar< T > &b, unsigned long ul)
template<class T >
scalar< T > &	operator% (const scalar< T > &b, unsigned long ul)
template<class T >
scalar< T > &	operator+ (unsigned long ul, const scalar< T > &b)
template<class T >
scalar< T > &	operator* (unsigned long ul, const scalar< T > &b)
template<class T >
scalar< T > &	operator+ (const scalar< T > &b, long sl)
template<class T >
scalar< T > &	operator- (const scalar< T > &b, long sl)
template<class T >
scalar< T > &	operator* (const scalar< T > &b, long sl)
template<class T >
scalar< T > &	operator/ (const scalar< T > &b, long sl)
template<class T >
scalar< T > &	operator% (const scalar< T > &b, long sl)
template<class T >
scalar< T > &	operator+ (long sl, const scalar< T > &b)
template<class T >
scalar< T > &	operator* (int sl, const scalar< T > &b)
template<class T >
scalar< T > &	operator* (long sl, const scalar< T > &b)
template<class T >
scalar< T > &	operator* (double d, const scalar< T > &b)
template<class T >
scalar< T > &	Div2Exp (const scalar< T > &b, unsigned long exponent_of_2)
template<class T >
scalar< T > &	GCD (const scalar< T > &b1, const scalar< T > &b2)
template<class T >
scalar< T > &	gcd (const scalar< T > &b1, const scalar< T > &b2)
template<class T >
scalar< T > &	Mod2Exp (const scalar< T > &b, unsigned long exponent_of_2)
template<class T >
scalar< T > &	Mul2Exp (const scalar< T > &b, unsigned long exponent_of_2)
template<class T >
scalar< T > &	PowMod (const scalar< T > &b, const scalar< T > &exp, const scalar< T > &m)
template<class T >
scalar< T > &	PowMod (const scalar< T > &b, unsigned long exp, const scalar< T > &m)
template<class T >
scalar< T >	abs (const scalar< T > &b)
template<class T >
scalar< T > &	neg (const scalar< T > &b)
template<class T >
scalar< T >	pow (const scalar< T > &base, unsigned long exp)
template<class T >
scalar< T > &	quo (const scalar< T > &dividend, unsigned long divisor)
template<class T >
scalar< T > &	rem (const scalar< T > &dividend, const scalar< T > &divisor)
template<class T >
unsigned long	rem (const scalar< T > &b, unsigned long divisor)
template<class T >
scalar< T >	sqrt (const scalar< T > &b)
template<class T >
scalar< T > &	BigIntFactorial (unsigned long n)
template<class T >
scalar< T > &	operator+ (const scalar< T > &b, unsigned sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator- (const scalar< T > &b, unsigned sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator* (const scalar< T > &b, unsigned sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator/ (const scalar< T > &b, unsigned sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator% (const scalar< T > &b, unsigned sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator+ (const scalar< T > &b, int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator- (const scalar< T > &b, int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator* (const scalar< T > &b, int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator/ (const scalar< T > &b, int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator% (const scalar< T > &b, int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator+ (const scalar< T > &b, long int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator- (const scalar< T > &b, long int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator* (const scalar< T > &b, long int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator/ (const scalar< T > &b, long int sl) NRVAL(r(b))
template<class T >
scalar< T > &	operator% (const scalar< T > &b, long int sl) NRVAL(r(b))
template<class T >
scalar< T >	quo (const scalar< T > &dividend, const scalar< T > &divisor) NRVAL(r(dividend))
template<class T >
scalar< T >	quo (const scalar< T > &dividend, unsigned long divisor) NRVAL(r(dividend))
template<class T >
scalar< T > &	BigIntPow (unsigned long base, unsigned long exp) NRVAL(r)
template<class T >
scalar< T >	Size (const scalar< T > &r)
double	rfloor (double x)
double	rceil (double x)
long int	bit_size (double x)
template<unsigned N>
bigunsigned< N >	operator<< (const bigunsigned< N > &b, unsigned n)
template<unsigned N>
bigunsigned< N >	operator| (const bigunsigned< N > &b, unsigned n)
template<unsigned N>
bigunsigned< N >	operator+ (const bigunsigned< N > &b, unsigned n)
template<unsigned N>
unsigned	operator& (const bigunsigned< N > &b, unsigned n)
template<unsigned N>
void	add (bigunsigned< N > &r, typename bigunsigned< N >::hdwi_t n)
void	add (bigunsigned< 1 > &r, const bigunsigned< 1 > &a)
template<unsigned N>
void	add (bigunsigned< N > &r, const bigunsigned< N > &a)
template<unsigned N>
void	reverse (bigunsigned< N > &r, const bigunsigned< N > &lu)
void	rprint (std::ostream &o, unsigned n)
template<unsigned N>
void	rprint (std::ostream &o, bigunsigned< N > &bu)
template<unsigned N>
void	print (std::ostream &o, const bigunsigned< N > &bi)
template<unsigned N>
std::ostream &	operator<< (std::ostream &o, const bigunsigned< N > &bi)
std::ostream &	operator<< (std::ostream &os, const scalar< EMPZ > &b)
scalar< EMPZ >	operator+ (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator- (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator- (const scalar< EMPZ > &a1)
scalar< EMPZ >	operator* (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator* (const scalar< EMPZ > &a1, const scalar< MPZ > &a2)
scalar< EMPZ >	operator* (const scalar< MPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator* (const scalar< EMPZ > &a2, int a1)
scalar< EMPZ >	operator* (int a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator/ (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	operator/ (const scalar< EMPZ > &a1, const scalar< MPZ > &a2)
template<class OSTREAM >
void	print (OSTREAM &os, const scalar< EMPZ > &b)
scalar< EMPZ >	operator<< (const scalar< EMPZ > &x, long int s)
scalar< EMPZ > &	operator<<= (scalar< EMPZ > &x, long int s)
int	compare (const scalar< EMPZ > &b1, const scalar< EMPZ > &b2)
int	compare (const scalar< EMPZ > &b, unsigned long ul)
int	compare (const scalar< EMPZ > &b, long sl)
int	compare (const scalar< EMPZ > &b, int si)
scalar< EMPZ >	min (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
scalar< EMPZ >	max (const scalar< EMPZ > &a1, const scalar< EMPZ > &a2)
long int	bit_size (const scalar< EMPZ > &z)
std::ostream &	operator<< (std::ostream &os, const scalar< EMPQ > &b)
scalar< EMPQ >	operator+ (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator- (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator- (const scalar< EMPQ > &a1)
scalar< EMPQ >	operator* (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator* (const scalar< EMPQ > &a1, const scalar< EMPZ > &a2)
scalar< EMPQ >	operator* (const scalar< EMPZ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator* (const scalar< EMPQ > &a1, const scalar< MPQ > &a2)
scalar< EMPQ >	operator* (const scalar< MPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator* (const scalar< EMPQ > &a2, int a1)
scalar< EMPQ >	operator* (int a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator/ (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	operator/ (const scalar< EMPQ > &a1, const scalar< MPQ > &a2)
scalar< EMPQ >	operator/ (const scalar< EMPQ > &a1, const scalar< EMPZ > &a2)
int	compare (const scalar< EMPQ > &b1, const scalar< EMPQ > &b2)
int	compare (const scalar< EMPQ > &b, unsigned long ul)
int	compare (const scalar< EMPQ > &b, long sl)
int	compare (const scalar< EMPQ > &b, int si)
scalar< EMPQ >	min (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< EMPQ >	max (const scalar< EMPQ > &a1, const scalar< EMPQ > &a2)
scalar< MPF >	operator+ (const scalar< MPF > &a1, const scalar< MPF > &a2)
scalar< MPF >	operator- (const scalar< MPF > &a1, const scalar< MPF > &a2)
scalar< MPF >	operator- (const scalar< MPF > &a1)
scalar< MPF >	operator* (const scalar< MPF > &a1, const scalar< MPF > &a2)
scalar< MPF >	operator/ (const scalar< MPF > &a1, const scalar< MPF > &a2)
void	convert (scalar< MPF > &n, char *s)
std::ostream &	operator<< (std::ostream &os, const scalar< MPF > &b)
std::istream &	operator>> (std::istream &is, scalar< MPF > &b)
void	Precision (scalar< MPF > &b, unsigned long l)
size_t	log (const scalar< MPF > &b)
int	sign (const scalar< MPF > &b)
int	compare (const scalar< MPF > &b1, const scalar< MPF > &b2)
int	compare (const scalar< MPF > &b, unsigned long ul)
int	compare (const scalar< MPF > &b, long sl)
void	assign (double &r, const scalar< MPF > &z)
void	assign (scalar< MPF > &r, double d)
scalar< MPZ >	operator+ (const scalar< MPZ > &a1, const scalar< MPZ > &a2)
scalar< MPZ >	operator- (const scalar< MPZ > &a1, const scalar< MPZ > &a2)
scalar< MPZ >	operator- (const scalar< MPZ > &a1)
scalar< MPZ >	operator* (const scalar< MPZ > &a1, const scalar< MPZ > &a2)
scalar< MPZ >	operator/ (const scalar< MPZ > &a1, const scalar< MPZ > &a2)
void	convert (scalar< MPZ > &n, char *s)
std::ostream &	operator<< (std::ostream &os, const scalar< MPZ > &b)
char *	as_charp (const scalar< MPZ > &b)
std::string	to_string (const scalar< MPZ > &b)
template<class OSTREAM >
void	print (OSTREAM &os, const scalar< MPZ > &b)
std::istream &	operator>> (std::istream &is, scalar< MPZ > &b)
scalar< MPZ >	rfloor (const scalar< MPZ > &q)
scalar< MPZ >	rceil (const scalar< MPZ > &q)
void	SqrtRem (scalar< MPZ > &sqrt, scalar< MPZ > &rem, const scalar< MPZ > &b)
void	QuoRem (scalar< MPZ > &q, scalar< MPZ > &r, const scalar< MPZ > &divdend, const scalar< MPZ > &divisor)
unsigned long	QuoRem (scalar< MPZ > &q, scalar< MPZ > &r, const scalar< MPZ > &divdend, unsigned long divisor)
void	DivMod (scalar< MPZ > &q, scalar< MPZ > &r, const scalar< MPZ > &divdend, const scalar< MPZ > &divisor)
void	DivMod (scalar< MPZ > &q, scalar< MPZ > &r, const scalar< MPZ > &divdend, unsigned long divisor)
void	ExtGCD (scalar< MPZ > &gcd, scalar< MPZ > &a, scalar< MPZ > &b, const scalar< MPZ > &x, const scalar< MPZ > &y)
void	HalfExtGCD (scalar< MPZ > &gcd, scalar< MPZ > &a, const scalar< MPZ > &x, const scalar< MPZ > &y)
unsigned long	BigIntToUL (const scalar< MPZ > &b)
signed long	BigIntToSL (const scalar< MPZ > &b)
size_t	log (const scalar< MPZ > &b)
size_t	log (const scalar< MPZ > &b, int base)
int	sign (const scalar< MPZ > &b)
int	compare (const scalar< MPZ > &b1, const scalar< MPZ > &b2)
int	compare (const scalar< MPZ > &b, unsigned long ul)
int	compare (const scalar< MPZ > &b, long sl)
bool	IsPositive (const scalar< MPZ > &b)
bool	IsNegative (const scalar< MPZ > &b)
bool	IsZero (const scalar< MPZ > &b)
bool	IsOne (const scalar< MPZ > &b)
bool	IsMinusOne (const scalar< MPZ > &b)
bool	IsOdd (const scalar< MPZ > &b)
bool	IsEven (const scalar< MPZ > &b)
bool	IsPerfectSquare (const scalar< MPZ > &b)
bool	IsProbablyPrime (const scalar< MPZ > &b, int reps)
scalar< MPZ >	operator<< (const scalar< MPZ > &x, long int s)
scalar< MPZ > &	operator<<= (scalar< MPZ > &x, long int s)
scalar< MPZ >	Size (const scalar< MPZ > &z)
long int	bit_size (const scalar< MPZ > &z)
scalar< MPZ >	gcd (const scalar< MPZ > &a, const scalar< MPZ > &b)
scalar< MPZ >	lcm (const scalar< MPZ > &a, const scalar< MPZ > &b)
scalar< MPZ >	pow (const scalar< MPZ > &a, unsigned n)
scalar< MPZ >	isqrt (const scalar< MPZ > &a)
double	to_double (const scalar< MPZ > &z)
double	as_double (const scalar< MPZ > &z)
double	as_double (const double &d)
std::ostream &	operator<< (std::ostream &os, const scalar< MPQ > &b)
scalar< MPQ >	operator+ (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator- (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator- (const scalar< MPQ > &a1)
scalar< MPQ >	operator* (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator* (const scalar< MPQ > &a1, const scalar< MPZ > &a2)
scalar< MPQ >	operator* (const scalar< MPZ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator* (const scalar< MPQ > &a2, int a1)
scalar< MPQ >	operator* (int a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator/ (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	operator/ (const scalar< MPQ > &a1, const scalar< MPZ > &a2)
char *	as_charp (const scalar< MPQ > &b)
std::string	to_string (const scalar< MPQ > &b)
template<class OSTREAM >
void	print (OSTREAM &os, const scalar< MPQ > &b)
std::istream &	operator>> (std::istream &is, scalar< MPQ > &b)
scalar< MPZ >	numerator (const scalar< MPQ > &q)
scalar< MPZ >	denominator (const scalar< MPQ > &q)
scalar< MPZ >	rfloor (const scalar< MPQ > &q)
scalar< MPZ >	rceil (const scalar< MPQ > &q)
int	compare (const scalar< MPQ > &b1, const scalar< MPQ > &b2)
int	compare (const scalar< MPQ > &b, unsigned long ul)
int	compare (const scalar< MPQ > &b, long sl)
scalar< MPQ >	min (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
scalar< MPQ >	max (const scalar< MPQ > &a1, const scalar< MPQ > &a2)
void	convert (scalar< MPQ > &dd, char *s)
scalar< MPQ >	Size (const scalar< MPQ > &r)
double	to_double (const scalar< MPQ > &a)
double	as_double (const scalar< MPQ > &a)
template<class C >
std::ostream &	operator<< (std::ostream &os, const std::vector< C > &V)
template<class C , class R >
const C &	read (const Seq< C, R > &m, unsigned i)
template<class C , class R >
bool	eq (const Seq< C, R > &v1, const Seq< C, R > &v2)
template<class C , class R >
bool	neq (const Seq< C, R > &v1, const Seq< C, R > &v2)
template<class C , class R >
unsigned	hash (const Seq< C, R > &v)
template<class C , class R >
unsigned	soft_hash (const Seq< C, R > &m)
template<class C , class R >
Seq< C, R >::const_iterator	iterate (const Seq< C, R > &m)
template<class C , class R >
Seq< C, R > &	operator<< (Seq< C, R > &r, const C &x)
template<class C , class R >
bool	operator== (const Seq< C, R > &a, const Seq< C, R > &b)
template<class C , class R >
bool	operator!= (const Seq< C, R > &a, const Seq< C, R > &b)
template<class C , class R >
std::ostream &	operator<< (std::ostream &os, const Seq< C, R > &s)
	Output operator. More...
template<class C , class R >
std::istream &	operator>> (std::istream &is, Seq< C, R > &V)
template<class C , class R >
Seq< C, R >	operator+ (Seq< C, R > a, const Seq< C, R > &b)
template<class C , class R >
Seq< C, R >	adds (Seq< C, R > a, const Seq< C, R > &b)
template<class C , class R >
Seq< C, R >	mul (C b, Seq< C, R > a)
template<class C , class R >
Seq< C, R >	operator/ (Seq< C, R > a, const C b)
template<class X >
bool	operator== (const set_of< X > &r1, const set_of< X > &r2)
template<class X >
bool	operator!= (const set_of< X > &r1, const set_of< X > &r2)
template<class C >
set_of< C >	make_set (const C &c)
template<class C >
int	hash (const set_of< C > &R)
template<class C >
int	soft_hash (const set_of< C > &R)
template<class C >
bool	eq (const set_of< C > &R1, const set_of< C > &R2)
template<class X >
syntactic	flatten (const set_of< X > &s)
	DECLARE_SET ("ZZ", integer)
	DECLARE_SET ("QQ", rational)
template<class R >
R &	rep (R &r)
template<class R >
const R &	rep (const R &r)
template<class R >
R &	rep (shared_object< R > &r)
template<class R >
const R &	rep (const shared_object< R > &r)
template<typename Iterator >
unsigned	sign_variation (Iterator b, Iterator e)
template<typename Iterator >
unsigned	sign_variation (Iterator b, Iterator e, unsigned maxv)
template<typename Vector >
unsigned	sign_variation_n (const Vector &t, unsigned l, unsigned maxv)
template<typename Iterator >
bool	has_sign_variation (Iterator b, Iterator e)
template<typename Iterator >
bool	has_no_strict_sign_variation (Iterator b, Iterator e)
template<typename Vector >
bool	has_sign_variation (const Vector &t)
template<typename Vector >
int	sign_of (const Vector &t)
template<typename T >
int	sign_variation (const T &v)
template<typename T >
int	sign_variation (const T &v, unsigned maxv)
template<typename C , unsigned N>
unsigned	sign_variation (const C(&t)[N])
template<typename C , unsigned N>
unsigned	sign_variation (const C(&t)[N], unsigned maxv)
template<typename C >
unsigned	sign_variation (const C *t, unsigned size)
template<typename C >
unsigned	sign_variation (const C *t, unsigned size, unsigned maxv)
template<typename T >
int	Var (const T &v)
template<typename T >
int	Per (const T &v)
	Per is computing the number of equal consecutive signs -1 to 1. More...
template<typename T >
int	Eps (const T &v)
template<typename T >
int	Count (const T &v)
template<typename C , typename Iterator >
C	min_value (Iterator b, Iterator e)
template<typename C , typename Iterator >
C	max_value (Iterator b, Iterator e)
template<class POL , class SLV >
solver< typename POL::Scalar, SLV >::Solutions	solve (const POL &p, const SLV &s)
template<class POL , class SLV >
solver< typename POL::Scalar, SLV >::Solutions	solve (const POL &p, SLV &s)
template<class POL , class SLV , class Domain >
solver< typename POL::Scalar, SLV >::Solutions	solve (const POL &p, const SLV &s, const Domain &D)
template<class POL , class SLV , class Domain1 , class Domain2 >
solver< typename POL::Scalar, SLV >::Solutions	solve (const POL &p, const SLV &s, const Domain1 &D1, const Domain2 &D2)
template<class C , class MPC , class Domains , int MTH>
Seq< std::vector< C > >	solve (const MPC &l, const ProjRd< MTH > &, const Domains &D, bool verbose=false)
	Solve function. More...
template<class POL , class SLV >
void	run_solver (int argc, char **argv)
TMPL vector< generic >	solver_univariate_contfrac_prec (const POLYNOMIAL &p, const int &prec)
TMPL vector< generic >	solver_univariate_contfrac (const POLYNOMIAL &p)
TMPL vector< generic >	solver_univariate_contfrac (const POLYNOMIAL &p, const interval< rational > &D)
TMPL vector< generic >	solver_univariate_contfrac_approx_prec (const POLYNOMIAL &p, const int &prec)
TMPL vector< generic >	solver_univariate_contfrac_approx (const POLYNOMIAL &p)
TMPL vector< generic >	solver_univariate_sleeve (const POLYNOMIAL &p)
TMPL interval< floating<> >	solver_univariate_newton (const POLYNOMIAL &p, const interval< floating<> > &I)
TMPL Real	knotSum (Real *t, int k, int d)
template<class POL , class M >
solver< typename POL::Scalar, ContFrac< M > >::Solutions	solve (const POL &p, const ContFrac< M > &slv)
template<class POL , class M , class B >
solver< typename POL::Scalar, ContFrac< M > >::Solutions	solve (const POL &p, const ContFrac< M > &slv, const B &b1, const B &b2)
template<class POL , class IT >
IntervalNewton< IT, typename POL::coeff_t >::solutions_t	solve (const POL &f, IntervalNewton< IT, typename POL::coeff_t > &s)
template<class POL , class M , class B >
solver< B, Sleeve< M > >::Solutions	solve (const POL &p, const Sleeve< M > &slv, const B &u, const B &v)
template<class POL , class M >
solver< typename POL::Scalar, Sleeve< M > >::Solutions	solve (const POL &p, const Sleeve< M > &slv)
template<class C , class V >
polynomial< C, V >	sr_gcd (const polynomial< C, V > &p, const polynomial< C, V > &q)
template<class X >
bool	with_plus_sign (const X &x)
template<class C >
bool	with_plus_sign (const tensor::monomials< C > &x)
template<typename T >
T	abs (const T &x)
template<class T >
T	pow2 (int i)
template<typename FT , typename POLY >
FT	bound_root (const POLY &p, const Cauchy< FT > &m)
template<typename FT , typename POLY >
FT	max_bound (const POLY &p, const Cauchy< FT > &m)
template<typename FT , typename POLY >
FT	min_bound (const POLY &p, Cauchy< FT >)
template<class ISTREAM , typename C , typename R >
bool	read (ISTREAM &is, polynomial< C, R > &p, variables &V)
	Read a polynomial, enclosed in polynomial tags. More...

Variables
const C &	b
const C &	c
const Interval &	I
char *	synaps_inputptr
TMPL	DUALPOL
TMPL	POL
TMPL	X
TMPL	POLYNOMIAL

Typedef Documentation

typedef extended<MPQ> mmx::EMPQ

typedef extended<MPZ> mmx::EMPZ

typedef GMP::extended_rational mmx::EQQ

typedef GMP::extended_integer mmx::EZZ

typedef __mpf_struct mmx::MPF

typedef MP_RAT mmx::MPQ

typedef MP_INT mmx::MPZ

typedef GMP::rational mmx::QQ

typedef GMP::floating mmx::RR

Examples:

solver_uv_inewton_test.cpp.

typedef GMP::integer mmx::ZZ

Examples:

solver_uv_inewton_test.cpp.

Function Documentation

template<typename T >

T mmx::abs ( const T &  x )

inline

template<class C , int r>

void mmx::abs	(	Interval< C, r > &	x,
		const Interval< C, r > &	a
	)

template<class T >

scalar< T > mmx::abs ( const scalar< T > &  b )

inline

TMPL void mmx::add ( POLYNOMIAL &  r, const POLYNOMIAL &  a  )

inline

TMPL void mmx::add ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::add ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const C &  b  )

inline

TMPL void mmx::add ( POLYNOMIAL &  r, const C &  a, const POLYNOMIAL &  b  )

inline

template<unsigned N>

void mmx::add ( bigunsigned< N > &  r, typename bigunsigned< N >::hdwi_t  n  )

inline

void mmx::add ( bigunsigned< 1 > &  r, const bigunsigned< 1 > &  a  )

inline

template<unsigned N>

void mmx::add ( bigunsigned< N > &  r, const bigunsigned< N > &  a  )

inline

template<class C , int r>

void mmx::add ( Interval< C, r > &  a, const C &  x  )

inline

template<class C , int r>

void mmx::add ( Interval< C, r > &  a, const Interval< C, r > &  b, const C &  x  )

inline

template<class C , int r>

void mmx::add ( Interval< C, r > &  a, const C &  x, const Interval< C, r > &  b  )

inline

template<class C , int r>

void mmx::add ( Interval< C, r > &  a, const Interval< C, r > &  x  )

inline

template<class C , int r>

void mmx::add ( Interval< C, r > &  a, const Interval< C, r > &  b, const Interval< C, r > &  x  )

inline

template<class E >

void mmx::add	(	dynamic_exp< E > &	r,
		const dynamic_exp< E > &	A,
		const dynamic_exp< E > &	B
	)

template<class C , class R >

Seq<C,R> mmx::adds	(	Seq< C, R >	a,
		const Seq< C, R > &	b
	)

template<typename T , typename F >

T mmx::as ( const F &  x )

inline

template<typename T , typename F , class U >

T mmx::as ( const F &  x, const U &  u  )

inline

template<typename T , typename F , class U , class V >

T mmx::as ( const F &  x, const U &  u, const V &  v  )

inline

template<class POL1 , class C2 , class R2 , class V2 >

POL1 mmx::as ( const polynomial< C2, with< R2, V2 > > &  p )

inline

char* mmx::as_charp ( const scalar< MPZ > &  b )

inline

char* mmx::as_charp ( const scalar< MPQ > &  b )

inline

double mmx::as_double ( const RR &  a )

inline

double mmx::as_double ( const scalar< MPQ > &  a )

inline

double mmx::as_double ( const scalar< MPZ > &  z )

inline

double mmx::as_double ( const double &  d )

inline

template<typename FT >

Interval< FT > mmx::as_interval ( const FT &  a, const FT &  b  )

inline

template<typename RT , typename Poly >

IntervalData<RT,Poly> mmx::as_interval_data	(	const RT &	a,
		const RT &	b,
		const RT &	c,
		const RT &	d,
		const Poly &	f
	)

TMPL std::string mmx::as_string

(

const Polynomial &

p

)

TMPL std::string mmx::as_string	(	const Polynomial &	p,
		const variables &	var
	)

void mmx::assign ( double &  r, const scalar< MPF > &  z  )

inline

void mmx::assign ( scalar< MPF > &  r, double  d  )

inline

template<class T >

scalar< T > & mmx::BigIntFactorial ( unsigned long  n )

inline

template<class T >

scalar<T>& mmx::BigIntPow ( unsigned long  base, unsigned long  exp  )

inline

signed long mmx::BigIntToSL ( const scalar< MPZ > &  b )

inline

unsigned long mmx::BigIntToUL ( const scalar< MPZ > &  b )

inline

template<typename T >

T mmx::binomial	(	int	n,
		int	p
	)

Binomial coefficients

template<class MP >

MP mmx::binomial	(	typename MP::coeff_t	coeff,
		int	i,
		int	d,
		typename MP::coeff_t	a
	)

Expansion of coeff*(x_i+a)^d, where i is the index of the variable x, a is the shift, d is the degree.

template<class T , int r>

std::pair< Interval<T,r>, Interval<T,r> > mmx::bissect ( const Interval< T, r > &  x )

inline

template<class T , int r>

void mmx::bissect ( Interval< T, r > &  g, Interval< T, r > &  d, const Interval< T, r > &  x  )

inline

void mmx::bit_precision ( unsigned long  l )

inline

Set the default precision for the MPZ numbers. This is not the precision of the results of operations on these numbers, because of error propagations.

Examples:

solver_mv_fatarcs_test.cpp.

void mmx::bit_precision ( RR  b, unsigned long  l  )

inline

Set the precision for RR. This precision is not the precision of the result of operations on this number.

long int mmx::bit_size ( const ZZ &  z )

inline

long int mmx::bit_size ( const scalar< EMPZ > &  z )

inline

long int mmx::bit_size ( double  x )

inline

long int mmx::bit_size ( const scalar< MPZ > &  z )

inline

template<typename FT , typename POLY >

FT mmx::bound_root	(	const POLY &	p,
		const Cauchy< FT > &	m
	)

template<typename K >

void mmx::CF_positive	(	const typename K::Poly &	f,
		Seq< typename K::FIT > &	RL,
		bool	posneg,
		K
	)

template<typename OutputIterator , typename K >

OutputIterator mmx::CF_solve	(	const typename K::Poly &	f,
		OutputIterator	sol,
		int	mult,
		K
	)

TMPL Seq<typename ring<C,Bernstein>::Polynomial> mmx::coefficients ( const typename ring< C, Bernstein >::Polynomial &  pol, int  v  )

inline

Examples:

polynomial_mv_test.cpp.

TMPL Seq< POLYNOMIAL > mmx::coefficients ( const POLYNOMIAL &  f, const int &  v  )

inline

TMPL Seq< C > mmx::coefficients ( const POLYNOMIAL &  f )

inline

TMPL Seq<C> mmx::coefficients ( const Polynomial &  pol )

inline

TMPL Seq<Polynomial> mmx::coefficients ( const Polynomial &  pol, int  v  )

inline

int mmx::compare ( const QQ &  a, const QQ &  b  )

inline

int mmx::compare ( const RR &  a, const RR &  b  )

inline

int mmx::compare ( const scalar< EMPZ > &  b1, const scalar< EMPZ > &  b2  )

inline

int mmx::compare ( const scalar< EMPZ > &  b, unsigned long  ul  )

inline

int mmx::compare ( const scalar< EMPZ > &  b, long  sl  )

inline

int mmx::compare ( const scalar< EMPQ > &  b1, const scalar< EMPQ > &  b2  )

inline

int mmx::compare ( const scalar< EMPZ > &  b, int  si  )

inline

int mmx::compare ( const scalar< EMPQ > &  b, unsigned long  ul  )

inline

int mmx::compare ( const scalar< EMPQ > &  b, long  sl  )

inline

int mmx::compare ( const scalar< EMPQ > &  b, int  si  )

inline

int mmx::compare ( const scalar< MPF > &  b1, const scalar< MPF > &  b2  )

inline

int mmx::compare ( const scalar< MPF > &  b, unsigned long  ul  )

inline

int mmx::compare ( const scalar< MPQ > &  b1, const scalar< MPQ > &  b2  )

inline

int mmx::compare ( const scalar< MPF > &  b, long  sl  )

inline

int mmx::compare ( const scalar< MPQ > &  b, unsigned long  ul  )

inline

int mmx::compare ( const scalar< MPQ > &  b, long  sl  )

inline

int mmx::compare ( const scalar< MPZ > &  b1, const scalar< MPZ > &  b2  )

inline

int mmx::compare ( const scalar< MPZ > &  b, unsigned long  ul  )

inline

int mmx::compare ( const scalar< MPZ > &  b, long  sl  )

inline

template<class T , int r>

bool mmx::contain_zero ( const Interval< T, r > &  x )

inline

TMPL Polynomial::Scalar mmx::content

(

const Polynomial &

p

)

void mmx::convert ( scalar< MPZ > &  n, char *  s  )

inline

void mmx::convert ( scalar< MPF > &  n, char *  s  )

inline

void mmx::convert ( scalar< MPQ > &  dd, char *  s  )

inline

template<typename T >

int mmx::Count

(

const T &

v

)

mmx::declare_binary_operator	(	TMPL	,
		ARG1	,
		ARG0	,
		_add_	,
		operator+
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG1	,
		ARG0	,
		_sub_	,
		operator-
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG1	,
		ARG0	,
		_mul_	,
		operator*
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG1	,
		ARG0	,
		_div_	,
		operator/
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG0	,
		ARG1	,
		_add_	,
		operator+
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG0	,
		ARG1	,
		_sub_	,
		operator-
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG0	,
		ARG1	,
		_mul_	,
		operator*
	)

mmx::declare_binary_operator	(	TMPL	,
		ARG0	,
		ARG1	,
		_div_	,
		operator/
	)

mmx::DECLARE_SET	(	"ZZ"	,
		integer
	)

mmx::DECLARE_SET	(	"QQ"	,
		rational
	)

TMPL mmx::define_operator_rrr	(	DUALPOL	,
		POL	,
		DUALPOL	,
		operator*	,
		sparse::mul
	)

TMPL mmx::define_operator_rrr	(	POLYNOMIAL	,
		POLYNOMIAL	,
		POLYNOMIAL	,
		operator+	,
		OP::add
	)

TMPL int mmx::degree ( const Polynomial &  mp )

inline

TMPL int mmx::degree ( const Polynomial &  mp, int  v  )

inline

template<class E >

dynamic_exp<E>::degree_t mmx::degree ( const dynamic_exp< E > &  t )

inline

Examples:

polynomial_mv_sparse_test.cpp.

template<class C , class E >

E::degree_t mmx::degree ( const Monomial &  m )

inline

ZZ mmx::denominator ( const QQ &  a )

inline

scalar<MPZ> mmx::denominator ( const scalar< MPQ > &  q )

inline

TMPL Polynomial mmx::diff	(	const Polynomial &	p,
		const generic &	v
	)

TMPL Polynomial mmx::diff ( const Polynomial &  pol, int  v  )

inline

Multivariate Polynomial Differentiation.

Compute the partial derivative of polynomial w.r.t v the vth variable of polynomial.

Examples:

subresultant_test.cpp.

TMPL Polynomial mmx::diff ( const Polynomial &  pol )

inline

Multivariate Polynomial Differentiation.

Compute the partial derivative of polynomial w.r.t v the vth variable of polynomial.

TMPL void mmx::div ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::div ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const C &  b  )

inline

TMPL void mmx::div ( Monomial &  a, const Monomial &  m1, const Monomial &  m2  )

inline

TMPL Monomial mmx::div ( const Monomial &  m1, const Monomial &  m2  )

inline

template<class C , int r>

void mmx::div ( Interval< C, r > &  a, const C &  x  )

inline

template<class C , int r>

void mmx::div ( Interval< C, r > &  a, const Interval< C, r > &  b, const C &  x  )

inline

template<class C , int r>

void mmx::div ( Interval< C, r > &  a, const C &  x, const Interval< C, r > &  b  )

inline

template<class C , int r>

void mmx::div ( Interval< C, r > &  a, const Interval< C, r > &  b  )

inline

template<class C , int r>

void mmx::div ( Interval< C, r > &  x, const Interval< C, r > &  a, const Interval< C, r > &  b  )

inline

template<class T >

scalar< T > & mmx::Div2Exp ( const scalar< T > &  b, unsigned long  exponent_of_2  )

inline

TMPL Monomial mmx::div_quo ( const Monomial &  m1, const Monomial &  m2  )

inline

template<class POL >

void mmx::div_x	(	POL &	p,
		int	k
	)

TMPL bool mmx::divide ( const Monomial &  m1, const Monomial &  m2, Monomial &  r  )

inline

void mmx::DivMod ( scalar< MPZ > &  q, scalar< MPZ > &  r, const scalar< MPZ > &  divdend, const scalar< MPZ > &  divisor  )

inline

void mmx::DivMod ( scalar< MPZ > &  q, scalar< MPZ > &  r, const scalar< MPZ > &  divdend, unsigned long  divisor  )

inline

TMPL RING mmx::dual_of

(

const RING_POL &

rg

)

TMPL RING mmx::dual_of	(	const RING_POL &	rg,
		const generic &	x
	)

template<typename T >

int mmx::Eps

(

const T &

v

)

template<class C >

bool mmx::eq ( const set_of< C > &  R1, const set_of< C > &  R2  )

inline

template<class C , class R >

bool mmx::eq	(	const Seq< C, R > &	v1,
		const Seq< C, R > &	v2
	)

template<class E >

void mmx::erase

(

dynamic_exp< E > &

A

)

template<class Result , class C , class Rep , class Ord , class Parameters >

Result mmx::eval ( const Polynomial &  polynomial, const Parameters &  parameters  )

inline

Multivariate Polynomial Evaluation.

The type Prm must a container type, parameters corresponds to the 0..nvr() coordinates. The computation is done in the Sup Type of the Contained Type of Prm and Coeff. The type Result is the type of the result, it is assumed that an operator = on the computation type exists.

template<class Result , class C , class Rep , class Ord , class Parameters >

Result mmx::eval ( const Polynomial &  polynomial, const Parameters &  parameters, int  n  )

inline

template<class Result , class C , class Rep , class Ord , class Parameters >

void mmx::eval ( Result &  result, const Polynomial &  polynomial, const Parameters &  parameters  )

inline

TMPL bool mmx::exact_eq	(	const Polynomial &	p,
		const Polynomial &	q
	)

TMPL bool mmx::exact_eq	(	const RING &	p,
		const RING &	q
	)

TMPL bool mmx::exact_eq	(	const Monomial &	v1,
		const Monomial &	v2
	)

TMPL unsigned mmx::exact_hash

(

const Polynomial &

p

)

TMPL unsigned mmx::exact_hash

(

const RING &

p

)

TMPL unsigned mmx::exact_hash

(

const Monomial &

m

)

TMPL bool mmx::exact_neq	(	const Polynomial &	p,
		const Polynomial &	q
	)

TMPL bool mmx::exact_neq	(	const RING &	p,
		const RING &	q
	)

TMPL bool mmx::exact_neq	(	const Monomial &	v1,
		const Monomial &	v2
	)

void mmx::ExtGCD ( scalar< MPZ > &  gcd, scalar< MPZ > &  a, scalar< MPZ > &  b, const scalar< MPZ > &  x, const scalar< MPZ > &  y  )

inline

template<typename T >

T mmx::factorial

(

int

n

)

Factorial

TMPL syntactic mmx::flatten

(

const RING &

rg

)

template<class X >

syntactic mmx::flatten ( const set_of< X > &  s )

inline

TMPL syntactic mmx::flatten

(

const MONOMIAL &

v

)

TMPL syntactic mmx::flatten

(

const Polynomial &

p

)

TMPL syntactic mmx::flatten

(

const POLYNOMIAL &

p

)

mmx::FORALL

(

C

)

RR mmx::fracpart ( const RR &  r )

inline

ZZ mmx::gcd ( const ZZ &  a, const ZZ &  b  )

inline

double mmx::gcd ( const double &  , const double &    )

inline

template<class T >

scalar< T > & mmx::GCD ( const scalar< T > &  b1, const scalar< T > &  b2  )

inline

template<class T >

scalar< T > & mmx::gcd ( const scalar< T > &  b1, const scalar< T > &  b2  )

inline

scalar<MPZ> mmx::gcd ( const scalar< MPZ > &  a, const scalar< MPZ > &  b  )

inline

void mmx::HalfExtGCD ( scalar< MPZ > &  gcd, scalar< MPZ > &  a, const scalar< MPZ > &  x, const scalar< MPZ > &  y  )

inline

template<typename Iterator >

bool mmx::has_no_strict_sign_variation	(	Iterator	b,
		Iterator	e
	)

template<typename Iterator >

bool mmx::has_sign_variation	(	Iterator	b,
		Iterator	e
	)

template<typename Vector >

bool mmx::has_sign_variation

(

const Vector &

t

)

TMPL unsigned mmx::hash

(

const Polynomial &

p

)

TMPL unsigned mmx::hash

(

const RING &

p

)

TMPL unsigned mmx::hash

(

const Monomial &

v

)

template<class C >

int mmx::hash ( const set_of< C > &  R )

inline

template<class C , class R >

unsigned mmx::hash

(

const Seq< C, R > &

v

)

TMPL Polynomial mmx::homogenize ( const Polynomial &  p, const Polynomial &  v  )

inline

TMPL Polynomial mmx::homogenize ( const Polynomial &  p, int  i, const Polynomial &  v  )

inline

template<class T , int r>

Interval<T,r> mmx::hull ( const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

template<class T , int r>

void mmx::hull ( Interval< T, r > &  v, const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

template<class T , int r>

bool mmx::in ( const T &  x, const Interval< T, r > &  y  )

inline

Examples:

solver_uv_inewton_test.cpp.

template<class T , int r>

bool mmx::intersect ( Interval< T, r > &  result, const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

template<class T , int r>

Interval<T,r> mmx::intersection ( const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

template<class T , int r>

bool mmx::intersectp ( const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

template<typename RT , typename Poly >

void mmx::inv_scale ( IntervalData< RT, Poly > &  ID, const RT &  a  )

inline

bool mmx::is_polynomial ( const std::ostringstream &  sm )

inline

bool mmx::IsEven ( const scalar< MPZ > &  b )

inline

bool mmx::IsMinusOne ( const scalar< MPZ > &  b )

inline

bool mmx::IsNegative ( const scalar< MPZ > &  b )

inline

bool mmx::IsOdd ( const scalar< MPZ > &  b )

inline

bool mmx::IsOne ( const scalar< MPZ > &  b )

inline

bool mmx::IsPerfectSquare ( const scalar< MPZ > &  b )

inline

bool mmx::IsPositive ( const scalar< MPZ > &  b )

inline

bool mmx::IsProbablyPrime ( const scalar< MPZ > &  b, int  reps  )

inline

ZZ mmx::isqrt ( const ZZ &  a )

inline

scalar<MPZ> mmx::isqrt ( const scalar< MPZ > &  a )

inline

bool mmx::IsZero ( const scalar< MPZ > &  b )

inline

template<class C , class R >

Seq<C,R>::const_iterator mmx::iterate

(

const Seq< C, R > &

m

)

TMPL Real mmx::knotSum	(	Real *	t,
		int	k,
		int	d
	)

ZZ mmx::lcm ( const ZZ &  a, const ZZ &  b  )

inline

scalar<MPZ> mmx::lcm ( const scalar< MPZ > &  a, const scalar< MPZ > &  b  )

inline

size_t mmx::log ( const scalar< MPF > &  b )

inline

size_t mmx::log ( const scalar< MPZ > &  b )

inline

size_t mmx::log ( const scalar< MPZ > &  b, int  base  )

inline

template<class T , int r>

T mmx::lower ( const Interval< T, r > &  x )

inline

template<class E >

int mmx::lvar

(

const dynamic_exp< E > &

A

)

template<class C >

set_of<C> mmx::make_set ( const C &  c )

inline

template<class T , int r>

Interval<T,r> mmx::max ( const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

scalar<EMPZ> mmx::max ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::max ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

scalar<MPQ> mmx::max ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

template<typename FT , typename POLY >

FT mmx::max_bound	(	const POLY &	p,
		const Cauchy< FT > &	m
	)

template<typename C , typename Iterator >

C mmx::max_value	(	Iterator	b,
		Iterator	e
	)

template<typename K >

void mmx::MCF_positive	(	const typename K::Poly &	f,
		Seq< typename K::root_t > &	RL,
		bool	posneg,
		K
	)

template<class T , int r>

T mmx::median ( const Interval< T, r > &  x )

inline

TMPL Monomial mmx::MGcd	(	const Monomial &	m1,
		const Monomial &	m2
	)

template<class T , int r>

Interval<T,r> mmx::min ( const Interval< T, r > &  a, const Interval< T, r > &  b  )

inline

scalar<EMPZ> mmx::min ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::min ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

scalar<MPQ> mmx::min ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

template<typename FT , typename POLY >

FT mmx::min_bound	(	const POLY &	p,
		Cauchy< FT >
	)

template<typename C , typename Iterator >

C mmx::min_value	(	Iterator	b,
		Iterator	e
	)

template<class T >

scalar< T > & mmx::Mod2Exp ( const scalar< T > &  b, unsigned long  exponent_of_2  )

inline

TMPL MONOMIAL mmx::monomial_from_vector

(

const vector< int > &

t

)

TMPL void mmx::mul ( POLYNOMIAL &  r, const POLYNOMIAL &  a  )

inline

TMPL void mmx::mul ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::mul ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const C &  b  )

inline

TMPL void mmx::mul ( POLYNOMIAL &  r, const C &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::mul ( Monomial &  a, const Monomial &  m1, const Monomial &  m2  )

inline

template<class C , int r>

void mmx::mul ( Interval< C, r > &  a, const C &  x  )

inline

Examples:

polynomial_mv_sparse_test.cpp.

template<class C , int r>

void mmx::mul ( Interval< C, r > &  a, const Interval< C, r > &  b, const C &  x  )

inline

template<class C , int r>

void mmx::mul ( Interval< C, r > &  a, const C &  x, const Interval< C, r > &  b  )

inline

template<class C , int r>

void mmx::mul ( Interval< C, r > &  a, const Interval< C, r > &  b  )

inline

template<class C , class R >

Seq<C,R> mmx::mul	(	C	b,
		Seq< C, R >	a
	)

template<class C , int r>

void mmx::mul ( Interval< C, r > &  x, const Interval< C, r > &  a, const Interval< C, r > &  b  )

inline

template<class T >

scalar< T > & mmx::Mul2Exp ( const scalar< T > &  b, unsigned long  exponent_of_2  )

inline

TMPL int mmx::N ( const MONOMIAL &  v )

inline

TMPL int mmx::nbvar ( const Polynomial &  mp )

inline

Examples:

polynomial_with_all_test.cpp.

template<class C , int r>

void mmx::neg ( Interval< C, r > &  a )

inline

template<class C , int r>

void mmx::neg ( Interval< C, r > &  a, const Interval< C, r > &  b  )

inline

template<class T >

scalar<T>& mmx::neg

(

const scalar< T > &

b

)

template<class C , class R >

bool mmx::neq	(	const Seq< C, R > &	v1,
		const Seq< C, R > &	v2
	)

ZZ mmx::numerator ( const QQ &  a )

inline

scalar<MPZ> mmx::numerator ( const scalar< MPQ > &  q )

inline

TMPL bool mmx::operator!=	(	const RING &	p,
		const RING &	q
	)

template<class X >

bool mmx::operator!=	(	const set_of< X > &	r1,
		const set_of< X > &	r2
	)

template<class NT >

bool mmx::operator!= ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

template<class C , class V , class X >

bool mmx::operator!=	(	const polynomial< C, V > &	p,
		const X &	q
	)

template<class C , class R >

bool mmx::operator!=	(	const Seq< C, R > &	a,
		const Seq< C, R > &	b
	)

template<class T >

scalar< T > & mmx::operator% ( const scalar< T > &  b, unsigned long  ul  )

inline

template<class T >

scalar<T>& mmx::operator%	(	const scalar< T > &	b,
		long	sl
	)

template<class T >

scalar<T>& mmx::operator% ( const scalar< T > &  b, unsigned  sl  )

inline

template<class T >

scalar<T>& mmx::operator% ( const scalar< T > &  b, int  sl  )

inline

template<class T >

scalar<T>& mmx::operator% ( const scalar< T > &  b, long int  sl  )

inline

template<unsigned N>

unsigned mmx::operator&	(	const bigunsigned< N > &	b,
		unsigned	n
	)

template<class NT >

extended<NT> mmx::operator* ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

TMPL Monomial mmx::operator* ( const Monomial &  m1, const Monomial &  m2  )

inline

template<class T >

scalar< T > & mmx::operator* ( const scalar< T > &  b, unsigned long  ul  )

inline

template<class T >

scalar< T > & mmx::operator* ( unsigned long  ul, const scalar< T > &  b  )

inline

template<class T >

scalar<T>& mmx::operator*	(	const scalar< T > &	b,
		long	sl
	)

scalar<EMPZ> mmx::operator* ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

template<class T >

scalar<T>& mmx::operator*	(	int	sl,
		const scalar< T > &	b
	)

template<class T >

scalar< T > & mmx::operator* ( long  sl, const scalar< T > &  b  )

inline

template<class T >

scalar<T>& mmx::operator*	(	double	d,
		const scalar< T > &	b
	)

scalar<EMPZ> mmx::operator* ( const scalar< EMPZ > &  a1, const scalar< MPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< EMPQ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPZ> mmx::operator* ( const scalar< MPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< EMPZ > &  a1, const scalar< EMPQ > &  a2  )

inline

scalar<EMPZ> mmx::operator* ( const scalar< EMPZ > &  a2, int  a1  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< EMPQ > &  a1, const scalar< MPQ > &  a2  )

inline

scalar<EMPZ> mmx::operator* ( int  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< MPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

scalar<EMPQ> mmx::operator* ( const scalar< EMPQ > &  a2, int  a1  )

inline

scalar<EMPQ> mmx::operator* ( int  a1, const scalar< EMPQ > &  a2  )

inline

template<class T >

scalar<T>& mmx::operator* ( const scalar< T > &  b, unsigned  sl  )

inline

template<class T >

scalar<T>& mmx::operator* ( const scalar< T > &  b, int  sl  )

inline

template<class T >

scalar<T>& mmx::operator* ( const scalar< T > &  b, long int  sl  )

inline

scalar<MPZ> mmx::operator* ( const scalar< MPZ > &  a1, const scalar< MPZ > &  a2  )

inline

scalar<MPF> mmx::operator* ( const scalar< MPF > &  a1, const scalar< MPF > &  a2  )

inline

scalar<MPQ> mmx::operator* ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

scalar<MPQ> mmx::operator* ( const scalar< MPQ > &  a1, const scalar< MPZ > &  a2  )

inline

template<class C , class E >

Monomial mmx::operator* ( const Monomial &  m1, const C &  c2  )

inline

scalar<MPQ> mmx::operator* ( const scalar< MPZ > &  a1, const scalar< MPQ > &  a2  )

inline

template<class C , class E >

Monomial mmx::operator* ( const C &  c2, const Monomial &  m1  )

inline

scalar<MPQ> mmx::operator* ( const scalar< MPQ > &  a2, int  a1  )

inline

scalar<MPQ> mmx::operator* ( int  a1, const scalar< MPQ > &  a2  )

inline

TMPL texp::sup< ARG0, ARG1 >::T mmx::operator*	(	const ARG0 &	Ia,
		const ARG1 &	Ib
	)

TMPL texp::sup<ARG0,ARG1>::T mmx::operator*	(	const ARG1 &	Ia,
		const ARG0 &	Ib
	)

template<class NT >

extended<NT>& mmx::operator*= ( extended< NT > &  x, const extended< NT > &  other  )

inline

template<class NT >

extended<NT> mmx::operator+ ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

template<unsigned N>

bigunsigned<N> mmx::operator+ ( const bigunsigned< N > &  b, unsigned  n  )

inline

scalar<EMPZ> mmx::operator+ ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator+ ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

template<class T >

scalar< T > & mmx::operator+ ( const scalar< T > &  b, unsigned long  ul  )

inline

template<class T >

scalar< T > & mmx::operator+ ( unsigned long  ul, const scalar< T > &  b  )

inline

template<class T >

scalar<T>& mmx::operator+	(	const scalar< T > &	b,
		long	sl
	)

template<class T >

scalar< T > & mmx::operator+ ( long  sl, const scalar< T > &  b  )

inline

template<class C , class R >

Seq<C,R> mmx::operator+	(	Seq< C, R >	a,
		const Seq< C, R > &	b
	)

template<class T >

scalar<T>& mmx::operator+ ( const scalar< T > &  b, unsigned  sl  )

inline

template<class T >

scalar<T>& mmx::operator+ ( const scalar< T > &  b, int  sl  )

inline

template<class T >

scalar<T>& mmx::operator+ ( const scalar< T > &  b, long int  sl  )

inline

scalar<MPZ> mmx::operator+ ( const scalar< MPZ > &  a1, const scalar< MPZ > &  a2  )

inline

template<class C , class E >

Monomial mmx::operator+ ( const Monomial &  m1, const Monomial &  m2  )

inline

scalar<MPF> mmx::operator+ ( const scalar< MPF > &  a1, const scalar< MPF > &  a2  )

inline

scalar<MPQ> mmx::operator+ ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

TMPL texp::sup< ARG0, ARG1 >::T mmx::operator+	(	const ARG0 &	Ia,
		const ARG1 &	Ib
	)

TMPL texp::sup<ARG0,ARG1>::T mmx::operator+	(	const ARG1 &	Ia,
		const ARG0 &	Ib
	)

template<class NT >

extended<NT>& mmx::operator+= ( extended< NT > &  x, const extended< NT > &  other  )

inline

template<class NT >

extended<NT> mmx::operator- ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

TMPL POLYNOMIAL mmx::operator- ( const POLYNOMIAL &  p )

inline

template<class NT >

extended<NT> mmx::operator- ( const extended< NT > &  lhs )

inline

scalar<EMPZ> mmx::operator- ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator- ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

template<class T >

scalar< T > & mmx::operator- ( const scalar< T > &  b, unsigned long  ul  )

inline

scalar<EMPZ> mmx::operator- ( const scalar< EMPZ > &  a1 )

inline

scalar<EMPQ> mmx::operator- ( const scalar< EMPQ > &  a1 )

inline

template<class T >

scalar<T>& mmx::operator-	(	const scalar< T > &	b,
		long	sl
	)

template<class T >

scalar<T>& mmx::operator- ( const scalar< T > &  b, unsigned  sl  )

inline

template<class T >

scalar<T>& mmx::operator- ( const scalar< T > &  b, int  sl  )

inline

template<class T >

scalar<T>& mmx::operator- ( const scalar< T > &  b, long int  sl  )

inline

scalar<MPZ> mmx::operator- ( const scalar< MPZ > &  a1, const scalar< MPZ > &  a2  )

inline

template<class C , class E >

Monomial mmx::operator- ( const Monomial &  m1, const Monomial &  m2  )

inline

scalar<MPF> mmx::operator- ( const scalar< MPF > &  a1, const scalar< MPF > &  a2  )

inline

scalar<MPZ> mmx::operator- ( const scalar< MPZ > &  a1 )

inline

scalar<MPQ> mmx::operator- ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

scalar<MPF> mmx::operator- ( const scalar< MPF > &  a1 )

inline

scalar<MPQ> mmx::operator- ( const scalar< MPQ > &  a1 )

inline

template<class C , int R>

Interval<C,R> mmx::operator-

(

const Interval< C, R > &

I

)

TMPL texp::sup< ARG0, ARG1 >::T mmx::operator-	(	const ARG0 &	Ia,
		const ARG1 &	Ib
	)

TMPL texp::sup<ARG0,ARG1>::T mmx::operator-	(	const ARG1 &	Ia,
		const ARG0 &	Ib
	)

template<class NT >

extended<NT>& mmx::operator-= ( extended< NT > &  x, const extended< NT > &  other  )

inline

template<class NT >

extended<NT> mmx::operator/ ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

TMPL Monomial mmx::operator/ ( const Monomial &  m1, const Monomial &  m2  )

inline

template<class T >

scalar< T > & mmx::operator/ ( const scalar< T > &  b, unsigned long  ul  )

inline

template<class T >

scalar<T>& mmx::operator/	(	const scalar< T > &	b,
		long	sl
	)

scalar<EMPZ> mmx::operator/ ( const scalar< EMPZ > &  a1, const scalar< EMPZ > &  a2  )

inline

scalar<EMPZ> mmx::operator/ ( const scalar< EMPZ > &  a1, const scalar< MPZ > &  a2  )

inline

scalar<EMPQ> mmx::operator/ ( const scalar< EMPQ > &  a1, const scalar< EMPQ > &  a2  )

inline

scalar<EMPQ> mmx::operator/ ( const scalar< EMPQ > &  a1, const scalar< MPQ > &  a2  )

inline

scalar<EMPQ> mmx::operator/ ( const scalar< EMPQ > &  a1, const scalar< EMPZ > &  a2  )

inline

template<class C , class R >

Seq<C,R> mmx::operator/	(	Seq< C, R >	a,
		const C	b
	)

template<class T >

scalar<T>& mmx::operator/ ( const scalar< T > &  b, unsigned  sl  )

inline

template<class T >

scalar<T>& mmx::operator/ ( const scalar< T > &  b, int  sl  )

inline

template<class T >

scalar<T>& mmx::operator/ ( const scalar< T > &  b, long int  sl  )

inline

scalar<MPZ> mmx::operator/ ( const scalar< MPZ > &  a1, const scalar< MPZ > &  a2  )

inline

scalar<MPF> mmx::operator/ ( const scalar< MPF > &  a1, const scalar< MPF > &  a2  )

inline

template<class C , class E >

Monomial mmx::operator/ ( const Monomial &  m1, const C &  c2  )

inline

scalar<MPQ> mmx::operator/ ( const scalar< MPQ > &  a1, const scalar< MPQ > &  a2  )

inline

scalar<MPQ> mmx::operator/ ( const scalar< MPQ > &  a1, const scalar< MPZ > &  a2  )

inline

TMPL texp::sup< ARG0, ARG1 >::T mmx::operator/	(	const ARG0 &	Ia,
		const ARG1 &	Ib
	)

TMPL texp::sup<ARG0,ARG1>::T mmx::operator/	(	const ARG1 &	Ia,
		const ARG0 &	Ib
	)

template<class NT >

extended<NT>& mmx::operator/= ( extended< NT > &  x, const extended< NT > &  other  )

inline

template<class NT >

bool mmx::operator< ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

std::ostream & mmx::operator<< ( std::ostream &  os, const scalar< EMPZ > &  b  )

inline

std::ostream & mmx::operator<< ( std::ostream &  os, const scalar< MPQ > &  b  )

inline

std::ostream & mmx::operator<< ( std::ostream &  os, const scalar< EMPQ > &  b  )

inline

template<class C >

std::ostream& mmx::operator<<	(	std::ostream &	os,
		const std::vector< C > &	V
	)

TMPL std::ostream& mmx::operator<<	(	std::ostream &	os,
		const Polynomial &	mp
	)

template<unsigned N>

bigunsigned<N> mmx::operator<<	(	const bigunsigned< N > &	b,
		unsigned	n
	)

template<class T , int r>

std::ostream& mmx::operator<<	(	std::ostream &	o,
		const Interval< T, r > &	i
	)

template<class E >

std::ostream& mmx::operator<<	(	std::ostream &	os,
		const dynamic_exp< E > &	t
	)

template<class C , class R >

Seq<C,R>& mmx::operator<< ( Seq< C, R > &  r, const C &  x  )

inline

template<class C , class R >

std::ostream& mmx::operator<<	(	std::ostream &	os,
		const Seq< C, R > &	s
	)

Output operator.

template<unsigned N>

std::ostream& mmx::operator<<	(	std::ostream &	o,
		const bigunsigned< N > &	bi
	)

scalar<EMPZ> mmx::operator<< ( const scalar< EMPZ > &  x, long int  s  )

inline

std::ostream& mmx::operator<< ( std::ostream &  os, const scalar< MPZ > &  b  )

inline

std::ostream& mmx::operator<< ( std::ostream &  os, const scalar< MPF > &  b  )

inline

template<class C , class E >

std::ostream& mmx::operator<< ( std::ostream &  os, const monom< C, E > &  m  )

inline

Output operator.

scalar<MPZ> mmx::operator<< ( const scalar< MPZ > &  x, long int  s  )

inline

template<class NT >

extended<NT>& mmx::operator<<= ( extended< NT > &  x, long int  s  )

inline

scalar<EMPZ>& mmx::operator<<= ( scalar< EMPZ > &  x, long int  s  )

inline

scalar<MPZ>& mmx::operator<<= ( scalar< MPZ > &  x, long int  s  )

inline

template<class NT >

bool mmx::operator<= ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

template<class X >

bool mmx::operator==	(	const set_of< X > &	r1,
		const set_of< X > &	r2
	)

TMPL bool mmx::operator==	(	const RING &	p,
		const RING &	q
	)

template<class NT >

bool mmx::operator== ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

TMPL bool mmx::operator==	(	const POLYNOMIAL &	mp,
		const C &	c
	)

TMPL bool mmx::operator==	(	const POLYNOMIAL &	mp,
		unsigned	n
	)

template<class C , class R >

bool mmx::operator==	(	const Seq< C, R > &	a,
		const Seq< C, R > &	b
	)

template<class NT >

bool mmx::operator> ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

template<class NT >

bool mmx::operator>= ( const extended< NT > &  lhs, const extended< NT > &  rhs  )

inline

template<class C , class R >

std::istream& mmx::operator>> ( std::istream &  is, Seq< C, R > &  V  )

inline

Input operator for standard matrices. The input format is of the form s c0 c1 ... where s is the number of elements.

std::istream& mmx::operator>> ( std::istream &  is, scalar< MPF > &  b  )

inline

std::istream& mmx::operator>> ( std::istream &  is, scalar< MPZ > &  b  )

inline

std::istream& mmx::operator>> ( std::istream &  is, scalar< MPQ > &  b  )

inline

template<unsigned N>

bigunsigned<N> mmx::operator|	(	const bigunsigned< N > &	b,
		unsigned	n
	)

template<typename T >

int mmx::Per

(

const T &

v

)

Per is computing the number of equal consecutive signs -1 to 1.

TMPL POLYNOMIAL mmx::polynomial_bernstein	(	const RING &	r,
		const C &	c
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein	(	const RING &	r,
		const C &	c,
		const int &	d,
		const int &	v
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein	(	const RING &	r,
		const string &	s
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein	(	const RING &	r,
		const generic &	s
	)

TMPL vector<generic> mmx::polynomial_bernstein_coefficients	(	const POLYNOMIAL &	f,
		const int &	v
	)

TMPL vector<generic> mmx::polynomial_bernstein_coefficients

(

const POLYNOMIAL &

p

)

TMPL POLYNOMIAL mmx::polynomial_bernstein_of

(

const polynomial< C, with< Sparse, DegRevLex > > &

f

)

TMPL POLYNOMIAL mmx::polynomial_bernstein_tensor	(	const RING &	r,
		const C &	c
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein_tensor	(	const RING &	r,
		const C &	c,
		const int &	d,
		const int &	v
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein_tensor	(	const RING &	r,
		const string &	s
	)

TMPL POLYNOMIAL mmx::polynomial_bernstein_tensor	(	const RING &	r,
		const generic &	s
	)

TMPL vector<generic> mmx::polynomial_bernstein_tensor_coefficients	(	const POLYNOMIAL &	f,
		const int &	v
	)

TMPL vector<generic> mmx::polynomial_bernstein_tensor_coefficients

(

const POLYNOMIAL &

p

)

TMPL POLYNOMIAL mmx::polynomial_bernstein_tensor_of

(

const polynomial< C, with< Sparse, DegRevLex > > &

f

)

TMPL Polynomial mmx::polynomial_dual	(	const RING &	rg,
		const C &	c
	)

TMPL Polynomial mmx::polynomial_dual	(	const RING &	rg,
		const C &	c,
		int	d,
		int	v
	)

TMPL Polynomial mmx::polynomial_dual	(	const RING &	rg,
		const string &	s
	)

TMPL Polynomial mmx::polynomial_dual	(	const RING &	r,
		const generic &	s
	)

TMPL vector<generic> mmx::polynomial_dual_coefficients	(	const Polynomial &	f,
		const int &	v
	)

TMPL vector<generic> mmx::polynomial_dual_coefficients

(

const Polynomial &

p

)

TMPL Polynomial mmx::polynomial_gcd	(	const Polynomial &	p,
		const Polynomial &	q,
		int	v
	)

TMPL Polynomial mmx::polynomial_resultant	(	const Polynomial &	p,
		const Polynomial &	q,
		int	v
	)

TMPL Polynomial mmx::polynomial_sparse	(	const RING &	r,
		const C &	c
	)

TMPL Polynomial mmx::polynomial_sparse	(	const RING &	r,
		const C &	c,
		const int &	d,
		const int &	v
	)

TMPL Polynomial mmx::polynomial_sparse	(	const RING &	r,
		const string &	s
	)

TMPL Polynomial mmx::polynomial_sparse	(	const RING &	r,
		const generic &	s
	)

TMPL vector< generic > mmx::polynomial_sparse_coefficients	(	const Polynomial &	f,
		const int &	v
	)

TMPL vector< generic > mmx::polynomial_sparse_coefficients

(

const Polynomial &

p

)

TMPL generic mmx::polynomial_sparse_eval_generic	(	const Polynomial &	p,
		const vector< generic > &	v
	)

TMPL vector< generic > mmx::polynomial_sparse_monomials

(

const Polynomial &

p

)

TMPL polynomial< C, with< Sparse, DegRevLex > > mmx::polynomial_sparse_of

(

const POLYNOMIAL &

f

)

TMPL vector<generic> mmx::polynomial_sturm_sequence	(	const Polynomial &	p,
		const Polynomial &	q,
		int	v
	)

TMPL POLYNOMIAL mmx::polynomial_tensor	(	const RING &	r,
		const C &	c
	)

TMPL POLYNOMIAL mmx::polynomial_tensor	(	const RING &	r,
		const C &	c,
		const int &	d,
		const int &	v
	)

TMPL POLYNOMIAL mmx::polynomial_tensor	(	const RING &	r,
		const string &	s
	)

TMPL POLYNOMIAL mmx::polynomial_tensor	(	const RING &	r,
		const generic &	s
	)

TMPL vector< generic > mmx::polynomial_tensor_coefficients	(	const POLYNOMIAL &	f,
		const int &	v
	)

TMPL vector< generic > mmx::polynomial_tensor_coefficients

(

const POLYNOMIAL &

p

)

TMPL POLYNOMIAL mmx::polynomial_tensor_of

(

const polynomial< C, with< Sparse, DegRevLex > > &

f

)

TMPL polynomial< C, with< MonomialTensor > > mmx::polynomial_tensor_of

(

const POLYNOMIAL &

f

)

template<class T >

T mmx::pow	(	const T &	a,
		int	i
	)

ZZ mmx::pow ( const ZZ &  a, unsigned  n  )

inline

template<class T >

scalar< T > mmx::pow ( const scalar< T > &  base, unsigned long  exp  )

inline

TMPL Monomial mmx::pow ( const Monomial &  m1, int  n  )

inline

scalar<MPZ> mmx::pow ( const scalar< MPZ > &  a, unsigned  n  )

inline

template<class T >

T mmx::pow2

(

int

i

)

template<class T >

scalar< T > & mmx::PowMod ( const scalar< T > &  b, const scalar< T > &  exp, const scalar< T > &  m  )

inline

template<class T >

scalar< T > & mmx::PowMod ( const scalar< T > &  b, unsigned long  exp, const scalar< T > &  m  )

inline

void mmx::Precision ( unsigned long  l )

inline

Set the default precision for the MPZ numbers. This is not the precision of the results of operations on these numbers, because of error propagations.

void mmx::Precision ( RR  b, unsigned long  l  )

inline

Set the precision for RR. This precision is not the precision of the result of operations on this number.

void mmx::Precision ( scalar< MPF > &  b, unsigned long  l  )

inline

Set the precision for MPZ. This precision is not the precision of the result of operations on this number.

TMPL void mmx::print ( OSTREAM &  os, int  x  )

inline

TMPL void mmx::print ( OSTREAM &  os, long int  x  )

inline

TMPL void mmx::print ( OSTREAM &  os, unsigned  x  )

inline

TMPL void mmx::print ( OSTREAM &  os, double  x  )

inline

template<class OSTREAM , class C , class Rep , class Ord >

OSTREAM& mmx::print ( OSTREAM &  os, const Polynomial &  mp  )

inline

template<class OSTREAM , class C , class Rep , class Ord >

OSTREAM& mmx::print ( OSTREAM &  os, const Polynomial &  mp, const variables &  Var  )

inline

template<class OSTREAM , class T , int r>

void mmx::print ( OSTREAM &  os, const Interval< T, r > &  a  )

inline

Examples:

polynomial_mv_sparse_test.cpp.

template<unsigned N>

void mmx::print	(	std::ostream &	o,
		const bigunsigned< N > &	bi
	)

template<class OSTREAM >

void mmx::print ( OSTREAM &  os, const scalar< EMPZ > &  b  )

inline

template<class OSTREAM , class C , class E >

OSTREAM& mmx::print ( OSTREAM &  os, const Monomial &  m, const variables &  V  )

inline

template<class OSTREAM >

void mmx::print ( OSTREAM &  os, const scalar< MPZ > &  b  )

inline

template<class OSTREAM >

void mmx::print ( OSTREAM &  os, const scalar< MPQ > &  b  )

inline

template<class OSTREAM , class C , class E >

OSTREAM& mmx::print_as_double ( OSTREAM &  os, const Monomial &  m, const variables &  V  )

inline

template<class T >

scalar<T>& mmx::quo ( const scalar< T > &  dividend, unsigned long  divisor  )

inline

template<class T >

scalar<T> mmx::quo ( const scalar< T > &  dividend, const scalar< T > &  divisor  )

inline

template<class T >

scalar<T> mmx::quo ( const scalar< T > &  dividend, unsigned long  divisor  )

inline

void mmx::QuoRem ( scalar< MPZ > &  q, scalar< MPZ > &  r, const scalar< MPZ > &  divdend, const scalar< MPZ > &  divisor  )

inline

unsigned long mmx::QuoRem ( scalar< MPZ > &  q, scalar< MPZ > &  r, const scalar< MPZ > &  divdend, unsigned long  divisor  )

inline

scalar<MPZ> mmx::rceil ( const scalar< MPQ > &  q )

inline

scalar<MPZ> mmx::rceil ( const scalar< MPZ > &  q )

inline

double mmx::rceil ( double  x )

inline

template<class ISTREAM , typename C , typename R >

bool mmx::read	(	ISTREAM &	is,
		polynomial< C, R > &	p,
		variables &	V
	)

Read a polynomial, enclosed in polynomial tags.

template<class C , class R >

const C& mmx::read ( const Seq< C, R > &  m, unsigned  i  )

inline

TMPL void mmx::reciprocal ( Polynomial &  f, const int &  v  )

inline

Inplace reciprocal w.r.t. variable v

TMPL void mmx::rem ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const POLYNOMIAL &  b  )

inline

template<class T >

scalar< T > & mmx::rem ( const scalar< T > &  dividend, const scalar< T > &  divisor  )

inline

template<class T >

unsigned long mmx::rem ( const scalar< T > &  b, unsigned long  divisor  )

inline

template<class R >

R& mmx::rep ( R &  r )

inline

Allows us to access to the data when we don't use shared object.

template<class R >

const R& mmx::rep ( const R &  r )

inline

Allows us to access to the data when we don't use shared object.

template<class R >

R& mmx::rep ( shared_object< R > &  r )

inline

Allows us to access to the data when we use shared object.

template<class R >

const R& mmx::rep ( const shared_object< R > &  r )

inline

Allows us to access to the data when we use shared object.

template<typename Poly >

void mmx::reverse ( Poly &  R, const Poly &  P  )

inline

template<typename Poly >

void mmx::reverse ( Poly &  R )

inline

template<typename RT , typename Poly >

void mmx::reverse ( IntervalData< RT, Poly > &  I1 )

inline

template<unsigned N>

void mmx::reverse	(	bigunsigned< N > &	r,
		const bigunsigned< N > &	lu
	)

template<typename RT , typename Poly >

void mmx::reverse_shift ( IntervalData< RT, Poly > &  I2, const IntervalData< RT, Poly > &  ID  )

inline

template<typename RT , typename Poly >

void mmx::reverse_shift_homography ( IntervalData< RT, Poly > &  I2, const IntervalData< RT, Poly > &  ID  )

inline

scalar<MPZ> mmx::rfloor ( const scalar< MPQ > &  q )

inline

scalar<MPZ> mmx::rfloor ( const scalar< MPZ > &  q )

inline

double mmx::rfloor ( double  x )

inline

TMPL RING mmx::ring_bernstein_extend_generic	(	const RING &	R,
		const vector< generic > &	s
	)

TMPL RING mmx::ring_bernstein_generic	(	const scalar_set< C > &	rg,
		const Bernstein &	b,
		const vector< generic > &	s
	)

TMPL RING mmx::ring_bernstein_of

(

const ring< C, Sparse, DegRevLex > &

r

)

TMPL RING mmx::ring_bernstein_string	(	const scalar_set< C > &	rg,
		const vector< string > &	s
	)

TMPL RING mmx::ring_sparse_extend_generic	(	const RING &	R,
		const vector< generic > &	s
	)

TMPL RING mmx::ring_sparse_generic	(	const scalar_set< C > &	rg,
		const vector< generic > &	s
	)

TMPL polynomial<C, with<Sparse, DegRevLex> > mmx::ring_sparse_of

(

const POLYNOMIAL &

f

)

TMPL RING mmx::ring_sparse_string	(	const scalar_set< C > &	rg,
		const vector< string > &	s
	)

TMPL RING mmx::ring_tensor_extend_generic	(	const RING &	R,
		const vector< generic > &	s
	)

TMPL RING mmx::ring_tensor_generic	(	const scalar_set< C > &	rg,
		const MonomialTensor &	b,
		const vector< generic > &	s
	)

TMPL RING mmx::ring_tensor_of

(

const ring< C, Sparse, DegRevLex > &

r

)

TMPL RING mmx::ring_tensor_of

(

const ring< C, Bernstein > &

r

)

TMPL RING mmx::ring_tensor_string	(	const scalar_set< C > &	rg,
		const vector< string > &	s
	)

void mmx::rprint ( std::ostream &  o, unsigned  n  )

inline

template<unsigned N>

void mmx::rprint	(	std::ostream &	o,
		bigunsigned< N > &	bu
	)

template<class POL , class SLV >

void mmx::run_solver	(	int	argc,
		char **	argv
	)

TMPL C mmx::sample

(

const SELF &

R

)

Function which returns an element of the ring (here 0).

template<class C , class O >

C mmx::sample

(

const RING &

rg

)

template<typename RT , typename Poly >

void mmx::scale ( IntervalData< RT, Poly > &  ID, const RT &  a  )

inline

template<typename RT , typename Poly , typename RT2 >

void mmx::scale ( IntervalData< RT, Poly > &  ID, const RT2 &  a  )

inline

template<typename RT , typename Poly >

void mmx::scale ( IntervalData< RT, Poly > &  ID, long  k  )

inline

TMPL void mmx::shift ( Polynomial &  f, const C &  t, const int &  v  )

inline

Inplace shift by t in variable v

TMPL void mmx::shift ( Polynomial &  r, const Polynomial &  p, int  d, int  v = 0  )

inline

Inplace shift p by degree d in variable v

template<typename RT , typename Poly >

void mmx::shift ( IntervalData< RT, Poly > &  ID, const RT &  a  )

inline

template<typename RT , typename Poly , typename RT2 >

void mmx::shift ( IntervalData< RT, Poly > &  ID, const RT2 &  a  )

inline

template<typename Poly >

void mmx::shift_by_1 ( Poly &  R, const Poly &  P  )

inline

template<typename RT , typename Poly >

void mmx::shift_by_1 ( IntervalData< RT, Poly > &  I1, const IntervalData< RT, Poly > &  I2  )

inline

template<typename RT , typename Poly >

void mmx::shift_by_1 ( IntervalData< RT, Poly > &  I1 )

inline

template<typename Poly >

void mmx::shift_by_1 ( Poly &  R )

inline

template<typename T >

int mmx::sign ( const T &  x )

inline

int mmx::sign ( const QQ &  a )

inline

int mmx::sign ( const RR &  a )

inline

int mmx::sign ( const scalar< MPF > &  b )

inline

int mmx::sign ( const scalar< MPZ > &  b )

inline

template<typename Vector >

int mmx::sign_of

(

const Vector &

t

)

template<typename Iterator >

unsigned mmx::sign_variation	(	Iterator	b,
		Iterator	e
	)

Function that computes the number of sign changes between b and e.

template<typename Iterator >

unsigned mmx::sign_variation	(	Iterator	b,
		Iterator	e,
		unsigned	maxv
	)

template<typename T >

int mmx::sign_variation ( const T &  v )

inline

Function that computes the number of sign changes in a linear array, using iterators, and counters for the number of sign changes. The parameters v is a linear array of coefficients. The output var is the number of sign changes of v.

template<typename T >

int mmx::sign_variation ( const T &  v, unsigned  maxv  )

inline

template<typename C , unsigned N>

unsigned mmx::sign_variation ( const C(&)  t[N] )

inline

template<typename C , unsigned N>

unsigned mmx::sign_variation ( const C(&)  t[N], unsigned  maxv  )

inline

template<typename C >

unsigned mmx::sign_variation ( const C *  t, unsigned  size  )

inline

template<typename C >

unsigned mmx::sign_variation ( const C *  t, unsigned  size, unsigned  maxv  )

inline

template<typename Vector >

unsigned mmx::sign_variation_n	(	const Vector &	t,
		unsigned	l,
		unsigned	maxv
	)

template<class T , int r>

bool mmx::singleton ( const Interval< T, r > &  x )

inline

TMPL unsigned mmx::size ( const Polynomial &  p )

inline

TMPL int mmx::size ( const MONOMIAL &  v )

inline

QQ mmx::Size ( const QQ &  r )

inline

ZZ mmx::Size ( const ZZ &  z )

inline

ZZ mmx::size ( const ZZ &  z )

inline

Examples:

polynomial_with_all_test.cpp.

QQ mmx::size ( const QQ &  r )

inline

template<class T , int r>

T mmx::size

(

const Interval< T, r > &

i

)

template<class T >

scalar<T> mmx::Size

(

const scalar< T > &

r

)

scalar<MPQ> mmx::Size ( const scalar< MPQ > &  r )

inline

scalar<MPZ> mmx::Size ( const scalar< MPZ > &  z )

inline

TMPL unsigned mmx::soft_hash

(

const Polynomial &

p

)

TMPL unsigned mmx::soft_hash

(

const RING &

p

)

template<class C >

int mmx::soft_hash ( const set_of< C > &  R )

inline

TMPL unsigned mmx::soft_hash

(

const Monomial &

m

)

template<class C , class R >

unsigned mmx::soft_hash

(

const Seq< C, R > &

m

)

template<class POL , class SLV >

solver<typename POL::Scalar,SLV>::Solutions mmx::solve	(	const POL &	p,
		const SLV &	s
	)

template<class POL , class SLV >

solver<typename POL::Scalar,SLV>::Solutions mmx::solve	(	const POL &	p,
		SLV &	s
	)

template<class POL , class SLV , class Domain >

solver<typename POL::Scalar,SLV>::Solutions mmx::solve	(	const POL &	p,
		const SLV &	s,
		const Domain &	D
	)

template<class POL , class SLV , class Domain1 , class Domain2 >

solver<typename POL::Scalar,SLV>::Solutions mmx::solve	(	const POL &	p,
		const SLV &	s,
		const Domain1 &	D1,
		const Domain2 &	D2
	)

template<class NT , class LB >

Seq< typename ContFrac<NT,LB>::root_t > mmx::solve ( const typename ContFrac< NT >::Poly &  f, ContFrac< NT, LB >    )

inline

Examples:

solver_mv_bernstein_binary_test.cpp, solver_uv_all_test.cpp, solver_uv_bernstein_binary_test.cpp, solver_uv_contfrac_extended_test.cpp, solver_uv_inewton_test.cpp, and solver_uv_test.cpp.

template<class POL , class IT >

IntervalNewton<IT,typename POL::coeff_t>::solutions_t mmx::solve	(	const POL &	f,
		IntervalNewton< IT, typename POL::coeff_t > &	s
	)

template<class C , class MPC , class Domains , int MTH>

Seq<std::vector<C> > mmx::solve	(	const MPC &	l,
		const ProjRd< MTH > &	,
		const Domains &	D,
		bool	verbose = false
	)

Solve function.

Interface function for the solvers of the family ProjRd.

Parameters

l	is a sequence of polynomials (with begin() and end() member functions) expressed in the Monomial basis.
D	is the domain for the resolution.
verbose	set to true output complete information on the resolution.

template<class POL , class M >

solver<typename POL::Scalar, ContFrac<M> >::Solutions mmx::solve	(	const POL &	p,
		const ContFrac< M > &	slv
	)

template<class POL , class M , class B >

solver<typename POL::Scalar, ContFrac<M> >::Solutions mmx::solve	(	const POL &	p,
		const ContFrac< M > &	slv,
		const B &	b1,
		const B &	b2
	)

template<class POL , class M , class B >

solver<B, Sleeve<M> >::Solutions mmx::solve	(	const POL &	p,
		const Sleeve< M > &	slv,
		const B &	u,
		const B &	v
	)

template<class POL , class M >

solver<typename POL::Scalar, Sleeve<M> >::Solutions mmx::solve	(	const POL &	p,
		const Sleeve< M > &	slv
	)

template<typename K , typename OutputIterator >

OutputIterator mmx::solve_contfrac ( const typename K::Poly &  h, OutputIterator  sol, K    )

inline

TMPL vector<generic> mmx::solver_univariate_contfrac

(

const POLYNOMIAL &

p

)

TMPL vector<generic> mmx::solver_univariate_contfrac	(	const POLYNOMIAL &	p,
		const interval< rational > &	D
	)

TMPL vector<generic> mmx::solver_univariate_contfrac_approx

(

const POLYNOMIAL &

p

)

TMPL vector<generic> mmx::solver_univariate_contfrac_approx_prec	(	const POLYNOMIAL &	p,
		const int &	prec
	)

TMPL vector<generic> mmx::solver_univariate_contfrac_prec	(	const POLYNOMIAL &	p,
		const int &	prec
	)

TMPL interval<floating<> > mmx::solver_univariate_newton	(	const POLYNOMIAL &	p,
		const interval< floating<> > &	I
	)

TMPL vector<generic> mmx::solver_univariate_sleeve

(

const POLYNOMIAL &

p

)

template<class C , int R>

void mmx::split	(	Interval< C, R > &	l,
		Interval< C, R > &	r
	)

template<class T >

scalar< T > mmx::sqrt ( const scalar< T > &  b )

inline

void mmx::SqrtRem ( scalar< MPZ > &  sqrt, scalar< MPZ > &  rem, const scalar< MPZ > &  b  )

inline

template<class C , class V >

polynomial<C,V> mmx::sr_gcd ( const polynomial< C, V > &  p, const polynomial< C, V > &  q  )

inline

Examples:

subresultant_test.cpp.

TMPL void mmx::sub ( POLYNOMIAL &  r, const POLYNOMIAL &  a  )

inline

TMPL void mmx::sub ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::sub ( POLYNOMIAL &  r, const C &  a, const POLYNOMIAL &  b  )

inline

TMPL void mmx::sub ( POLYNOMIAL &  r, const POLYNOMIAL &  a, const C &  b  )

inline

template<class C , int r>

void mmx::sub ( Interval< C, r > &  a, const C &  x  )

inline

template<class C , int r>

void mmx::sub ( Interval< C, r > &  a, const Interval< C, r > &  b, const C &  x  )

inline

template<class C , int r>

void mmx::sub ( Interval< C, r > &  a, const C &  x, const Interval< C, r > &  b  )

inline

template<class C , int r>

void mmx::sub ( Interval< C, r > &  a, const Interval< C, r > &  x  )

inline

template<class C , int r>

void mmx::sub ( Interval< C, r > &  a, const Interval< C, r > &  b, const Interval< C, r > &  x  )

inline

double mmx::to_double ( const RR &  a )

inline

double mmx::to_double ( const QQ &  a )

inline

double mmx::to_double ( const ZZ &  z )

inline

double mmx::to_double ( const scalar< MPQ > &  a )

inline

double mmx::to_double ( const scalar< MPZ > &  z )

inline

template<typename FT >

Interval< FT > mmx::to_FIT ( const FT &  a, const FT &  b  )

inline

template<typename K >

K::FIT mmx::to_FIT	(	const typename K::RT &	a,
		const typename K::RT &	b,
		const typename K::RT &	c,
		const typename K::RT &	d,
		const typename K::FT &	B
	)

template<class C >

texp::rationalof<C>::T mmx::to_FT	(	const C &	a,
		const C &	b
	)

QQ mmx::to_FT ( const ZZ &  a, const ZZ &  b = 1  )

inline

QQ mmx::to_FT ( const QQ &  a, const QQ &  b = 1  )

inline

template<class C >

meta::rationalof<C>::T mmx::to_rational	(	const C &	a,
		const C &	b
	)

std::string mmx::to_string ( int  x )

inline

to_string convert int to std::string In C++11, it should use std::to_string

std::string mmx::to_string ( double  x )

inline

to_string convert double to std::string In C++11, it should use std::to_string

TMPL std::string mmx::to_string	(	const Polynomial &	mp,
		const variables &	var
	)

std::string mmx::to_string ( const scalar< MPZ > &  b )

inline

std::string mmx::to_string ( const scalar< MPQ > &  b )

inline

template<class C , class E >

std::string mmx::to_string ( const Monomial &  m, const variables &  V  )

inline

template<class C , class E >

std::string mmx::to_string_pp	(	const Monomial &	m,
		const variables &	V
	)

double mmx::to_XT ( const ZZ &  a )

inline

double mmx::to_XT ( const QQ &  a )

inline

double mmx::to_XT ( const RR &  a )

inline

template<class T , int r>

T mmx::upper ( const Interval< T, r > &  x )

inline

template<typename T >

int mmx::Var

(

const T &

v

)

Var is computing the number of sign variations from -1 to 1 or 1 to -1.

TMPL vector<int> mmx::vector_from_monomial

(

const MONOMIAL &

m

)

template<class T , int r>

T mmx::width ( const Interval< T, r > &  x )

inline

template<class X >

bool mmx::with_plus_sign ( const X &  x )

inline

template<class C >

bool mmx::with_plus_sign ( const tensor::monomials< C > &  x )

inline

template<class C , int r>

bool mmx::with_plus_sign ( const Interval< C, r > &  I )

inline

bool mmx::with_plus_sign ( const ZZ &  c )

inline

bool mmx::with_plus_sign ( const QQ &  c )

inline

bool mmx::with_plus_sign ( const RR &  c )

inline

Variable Documentation

const C& mmx::b

Initial value:

{
    return Interval(a,b)

Examples:

solver_mv_bernstein_proj_test.cpp.

const C & mmx::c

Initial value:

{
    return I+ Interval(c,c)

Examples:

polynomial_mv_sparse_test.cpp, solver_uv_all_test.cpp, solver_uv_bernstein_binary_test.cpp, and solver_uv_inewton_test.cpp.

TMPL mmx::DUALPOL

const Interval & mmx::I

Initial value:

{
    return Interval(c,c)+I

Examples:

interval_test.cpp, and solver_uv_bernstein_binary_test.cpp.

TMPL mmx::POL

Examples:

polynomial_uv_dense_test.cpp, polynomial_with_all_test.cpp, solver_mv_monomial_test.cpp, and solver_uv_inewton_test.cpp.

TMPL mmx::POLYNOMIAL

char * mmx::synaps_inputptr

TMPL mmx::X