Arageli Namespace Reference

Classes
struct	algebraic_config_default
class	algebraic
	Algebraic number class. More...
struct	factory< algebraic< TP, TS, Poly, Seg, Cfg > >
class	big_float
class	big_int
	Big integer number. More...
struct	fromnull_t
struct	fromspace_t
struct	fromineq_t
struct	fromeq_t
struct	fromgen_t
struct	frombasis_t
struct	fromdual_t
class	cannot_represent_cone
	This exception is generated when the implementation cannon represent cone in required way. More...
class	cone_default_config
class	cone
	The polyhedral cone representation as a set of facets or a set of generators. More...
struct	factory< cone< TT, M, CFG > >
	Specialization of factory structure for cone template class. More...
class	CCounter
class	exception
	Base for all exception classes. More...
class	assert_failed
	Exception class that can be trhowed when failed the some assertion. More...
class	out_of_range
	Exception situation: an index out of range while indexing the some structure. More...
class	invalid_argument
	Exceprion situation: invalid argument in call of the some operation. More...
class	division_by_zero
	Exception situation: division by zero. More...
class	matrix_is_singular
	Exception situation: the some matrix is singular. More...
class	incorrect_string
	Exception situation: the some object have failed initialization from a string. More...
struct	factory
	Common implementation of factory for the specific type. More...
struct	unary_function_traits_base
	Holds additional information about unary function. More...
struct	binary_function_traits_base
struct	ternary_function_traits_base
struct	unary_function_traits
struct	binary_function_traits
struct	ternary_function_traits
class	interval
	Represents an interval (open, close or semi-open; it depends on performed operations). More...
class	apply_iterator
class	Iterpair
struct	nonsquare_t
	Type for helper object fromsize. More...
struct	colwise_t
	Type for helper object for columnwise filling of the matrix. More...
struct	diag_t
	Type for helper object diag. More...
struct	eye_t
	Type for helper object eye. More...
struct	frommat_t
class	matrix
	Template class matrix. More...
struct	factory< matrix< T, REFCNT > >
	Specialization of the template 'factory' for the Arageli::matrix template. More...
struct	type_traits< matrix< T, REFCNT > >
struct	cnc_value_type
struct	cnc_value_type< const T >
struct	cnc_reference
struct	cnc_reference< const T >
struct	cnc_pointer
struct	cnc_pointer< const T >
struct	cnc_iterator
struct	cnc_iterator< const T >
struct	binary_function_gate_slot
	Gate slot for mixed computations. More...
struct	fromempty_t
struct	fromivert_t
struct	fromvert_t
class	polyhedron_default_config
class	polyhedron
	The polyhedron representation as the base cone. More...
class	pstricks_color_map
class	polynom
struct	rand_config
struct	rnd
class	rational_base
	Base for all rationals. More...
class	rational
	Implementation of a Rational Number. More...
struct	select_numer
	Unary functor: selects a numerator of an argument of type rational. More...
struct	select_denom
	Unary functor: selects a denominator of an argument of type rational. More...
struct	factory< rational< T1 > >
struct	type_traits< rational< T > >
	Specialization of type_traits for rational. More...
class	refcntr
class	refcntr_proxy< T, true, TC, A >
class	refcntr_proxy< T, false, TC, A >
struct	residue_config_default
class	residue
class	sideset
	WARNING! Temporary implimentation. Only facets with vertices indexes. More...
struct	smith_norm
	Normalize for resulting elements of Smith form. More...
class	no_unique_solution
	An exception for non-one-point solution for a linear system. More...
class	monom
	Monom template definition. More...
struct	type_traits< monom< F, I > >
struct	factory< monom< F, I > >
struct	monom_degree_less
	Binary predicate for two monoms for degrees comparision. More...
struct	monom_degree_equal
	Binary predicate for two monoms for equality degrees determination. More...
struct	coef_extractor
	Óíàðíûé ôóíêòîð: ïî ìîíîìó âîçâðàùàåò ññûëêó íà åãî êîýôôèöèåíò. More...
struct	degree_extractor
	Óíàðíûé ôóíêòîð: ïî ìîíîìó âîçâðàùàåò ññûëêó íà åãî ñòåïåíü. More...
struct	norm_monom_seq_t
	Type for helper object norm_monom_seq. More...
struct	any_monom_seq_t
	Type for helper object any_monom_seq. More...
struct	sparse_polynom_base
	Base for all sparse polynomials. More...
class	sparse_polynom
struct	factory< sparse_polynom< F, I, REFCNT > >
struct	type_traits< sparse_polynom< F, I, REFCNT > >
struct	matrix_line
	A line descriptor for matrix output. More...
struct	matrix_box
	A box (or frame) descriptor for matrix output. More...
struct	matrix_frames
	Contains information about horizontals and verticals lines and boxes for matrix output. More...
struct	true_type
struct	false_type
struct	bool_type< false >
struct	bool_type< true >
struct	equal_types
	General form for defferent types. More...
struct	equal_types< T, T >
	Specialized form for the same type. More...
struct	omit_const
	General form (for types without exterior const). More...
struct	omit_const < const T >
	Specialized form (for types with exterior const). More...
struct	omit_asterisk
	General form (for types without exterior *). More...
struct	omit_asterisk< T * >
	Specialized form (for types with exterior const). More...
struct	omit_ref
	General form (for types without exterior *). More...
struct	omit_ref< T & >
	Specialized form (for types with exterior const). More...
struct	omit_const_ref
	Omitting const &. More...
struct	type_pair_traits_default
	Minimal specialization for type_pair_traits. More...
struct	type_pair_traits_helper< T1, T2, true, true >
struct	type_pair_traits_helper< T1, T2, true, false >
struct	type_pair_traits_helper< T1, T2, false, true >
struct	type_pair_traits_helper< T1, T2, false, false >
struct	type_pair_traits
	Generic implementation of type_pair_traits --- information about two types. More...
struct	type_pair_traits_for_the_same
	Pattern for type_pair_traits in case two identical types. More...
struct	type_pair_traits< T, T >
	Specialization of type_pair_traits for two identical types. More...
struct	auto_type_category_by_numeric_limits
	Determines type category for particular type. More...
struct	type_traits_default
	Minimal implementation for each specialization of type_traits. More...
struct	type_traits
	General specialization of root of additional information service about type. More...
struct	type_traits_iterator
struct	type_traits< T * >
struct	type_traits< T[Size]>
struct	type_traits_string
struct	type_traits< const char * >
struct	type_traits< char * >
struct	type_traits< const char[Size]>
struct	type_traits< char[Size]>
struct	type_traits< const wchar_t * >
struct	type_traits< wchar_t * >
struct	type_traits< const wchar_t[Size]>
struct	type_traits< wchar_t[Size]>
struct	type_traits_iostream
struct	vec_binary_function_traits
struct	fromseq_t
struct	fromval_t
struct	fromvec_t
struct	fromsize_t
struct	fromstr_t
struct	_element_type_vec_val_1
struct	_element_type_vec_val_1< X, true >
struct	_element_type_vec_val
class	vector
	Template class vector definition. More...
struct	type_traits< vector< T, REFCNT > >
struct	unary_function_traits< Tag, vector< T, REFCNT > >
struct	bfgs_vector_helper_1
struct	bfgs_vector_helper_1< Tag, V1, V2, false, false, Tag_class >
struct	bfgs_vector_helper_1< Tag, V1, V2, false, true, Tag_class >
struct	bfgs_vector_helper_1< Tag, V1, V2, true, false, Tag_class >
struct	bfgs_vector_helper_2
struct	bfgs_vector_helper_3
struct	binary_function_gate_slot< Tag, vector< T, REFCNT >, T1, T2 >
struct	binary_function_gate_slot< Tag, const vector< T, REFCNT >, T1, T2 >
struct	binary_function_gate_slot< Tag, vector< T, REFCNT > &, T1, T2 >
struct	binary_function_gate_slot< Tag, const vector< T, REFCNT > &, T1, T2 >
struct	factory< vector< T, REFCNT > >
	Specialization of the template 'factory' for the Arageli::vector template. More...
struct	factory< std::complex< T2 > >
	Specialization of common factory template for std::complex. More...
struct	unary_function_traits< function_tag::address, Arg >
struct	unary_function_traits< function_tag::unary_plus, Arg >
struct	unary_function_traits< function_tag::unary_minus, Arg >
struct	unary_function_traits< function_tag::logical_not, Arg >
struct	unary_function_traits< function_tag::bitwise_not, Arg >
struct	unary_function_traits< function_tag::prefix_increment, Arg >
struct	unary_function_traits< function_tag::prefix_decrement, Arg >
struct	unary_function_traits< function_tag::parentheses_0, Arg >
struct	binary_function_traits< function_tag::parentheses_1, Arg1, Arg2 >
struct	ternary_function_traits< function_tag::parentheses_2, Arg1, Arg2, Arg3 >
struct	binary_function_traits< function_tag::plus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::minus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::multiplies, Arg1, Arg2 >
struct	binary_function_traits< function_tag::divides, Arg1, Arg2 >
struct	binary_function_traits< function_tag::modulus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::logical_or, Arg1, Arg2 >
struct	binary_function_traits< function_tag::logical_and, Arg1, Arg2 >
struct	binary_function_traits< function_tag::equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::not_equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::greater, Arg1, Arg2 >
struct	binary_function_traits< function_tag::less, Arg1, Arg2 >
struct	binary_function_traits< function_tag::greater_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::less_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::bitwise_or, Arg1, Arg2 >
struct	binary_function_traits< function_tag::bitwise_and, Arg1, Arg2 >
struct	binary_function_traits< function_tag::bitwise_xor, Arg1, Arg2 >
struct	binary_function_traits< function_tag::shift_left, Arg1, Arg2 >
struct	binary_function_traits< function_tag::shift_right, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_not_equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_greater, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_less, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_greater_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::all_less_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_not_equal_to, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_greater, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_less, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_greater_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::each_less_equal, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_plus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_minus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_multiplies, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_divides, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_modulus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_bitwise_or, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_bitwise_and, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_bitwise_xor, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_shift_left, Arg1, Arg2 >
struct	binary_function_traits< function_tag::assign_shift_right, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_plus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_minus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_multiplies, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_modulus, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_bitwise_or, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_bitwise_and, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_bitwise_xor, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_shift_left, Arg1, Arg2 >
struct	binary_function_traits< function_tag::left_assign_shift_right, Arg1, Arg2 >
struct	type_traits< std::complex< T > >
	Specialization of type_traits template class for std::complex. More...
struct	type_traits< std::basic_string< Char, CharTr, A > >
struct	type_traits< std::basic_istream< Ch, ChT > >
struct	type_traits< std::basic_ostream< Ch, ChT > >
struct	binary_function_traits< function_tag::subscript, vector< T, REFCNT >, Index >
struct	binary_function_traits< function_tag::subscript, const vector< T, REFCNT >, Index >
struct	binary_function_traits< function_tag::parentheses_1, vector< T, REFCNT >, Index >
struct	binary_function_traits< function_tag::parentheses_1, const vector< T, REFCNT >, Index >
struct	bfgs_vector_helper_1< function_tag::cmp, V1, V2, false, false, Tag_class >
struct	bfgs_vector_helper_1< function_tag::cmp, V1, V2, false, true, Tag_class >
struct	bfgs_vector_helper_1< function_tag::cmp, V1, V2, true, false, Tag_class >
struct	bfgs_vector_helper_1< function_tag::each_cmp, V1, V2, false, false, Tag_class >
struct	bfgs_vector_helper_1< function_tag::each_cmp, V1, V2, false, true, Tag_class >
struct	bfgs_vector_helper_1< function_tag::each_cmp, V1, V2, true, false, Tag_class >
struct	bfgs_vector_helper_1< Tag, V1, V2, false, false, function_tag::each_compare >
struct	bfgs_vector_helper_1< Tag, V1, V2, false, true, function_tag::each_compare >
struct	bfgs_vector_helper_1< Tag, V1, V2, true, false, function_tag::each_compare >
struct	bfgs_vector_helper_1< Tag, V1, V2, false, false, function_tag::all_compare >
struct	bfgs_vector_helper_1< Tag, V1, V2, false, true, function_tag::all_compare >
struct	bfgs_vector_helper_1< Tag, V1, V2, true, false, function_tag::all_compare >
Namespaces
namespace	_Internal
namespace	ctrl
namespace	func
	Function representations as classes.
namespace	function_tag
namespace	gfunc
namespace	iomanip
namespace	simplex_method
namespace	type_category
	Category of type.
Sorted and nonsorted helper objects.
enum	monoms_order { mo_inc, mo_dec }
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	diff (const sparse_polynom< F, I, REFCNT > &x)
	Pefrorms differentiation of polynomial x by common symbolic rules.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_list (std::basic_ostream< Ch, ChT > &out, const sparse_polynom< F, I, REFCNT > &x, monoms_order mo=mo_inc, const char *first_bracket=monom_output_list_first_bracket_default, const char *second_bracket=monom_output_list_second_bracket_default, const char *separator=monom_output_list_separator_default)
	Simple outputting as monom list.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_var (std::basic_ostream< Ch, ChT > &out, const sparse_polynom< F, I, REFCNT > &x, monoms_order mo=mo_inc, const char *var=monom_output_var_var_default, const char *mul=monom_output_var_mul_default, const char *pow=monom_output_var_pow_default)
	Outputting of polynomial with variable symbol.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_list (std::basic_istream< Ch, ChT > &in, sparse_polynom< F, I, REFCNT > &x, const char *first_bracket=monom_input_list_first_bracket_default, const char *second_bracket=monom_input_list_second_bracket_default, const char *separator=monom_input_list_separator_default)
	Simple inputting of a polynomial.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT, typename Coef_factory>
std::basic_istream< Ch, ChT > &	input_var (std::basic_istream< Ch, ChT > &in, sparse_polynom< F, I, REFCNT > &x, const Coef_factory &fctr, const char *var=monom_input_var_var_default, const char *mul=monom_input_var_mul_default, const char *pow=monom_input_var_pow_default)
	Inputting of a polynomial with variable symbol.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_var (std::basic_istream< Ch, ChT > &in, sparse_polynom< F, I, REFCNT > &x, const char *var=monom_input_var_var_default, const char *mul=monom_input_var_mul_default, const char *pow=monom_input_var_pow_default)
	Inputting of a polynomial with variable symbol.
template<typename Ch, typename ChT, typename F, typename I, bool REFCNT>
std::basic_ostream< Ch, ChT > &	output_aligned (std::basic_ostream< Ch, ChT > &out, const sparse_polynom< F, I, REFCNT > &x, monoms_order mo=mo_inc, const char *var=monom_output_var_var_default, const char *mul=monom_output_var_mul_default, const char *pow=monom_output_var_pow_default)
	Oputputs polynomial in aligned form. (Restricted implementation.).
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	operator<< (std::basic_ostream< Ch, ChT > &out, const sparse_polynom< F, I, REFCNT > &x)
	Ñòàíàðòíûé âûâîä ïîëèíîìà. Ñîâïàäàåò ñ sparse_polynom_output_var.
template<typename F, typename I, bool REFCNT, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	operator>> (std::basic_istream< Ch, ChT > &in, sparse_polynom< F, I, REFCNT > &x)
	Ñòàíàðòíûé âûâîä ïîëèíîìà. Ñîâïàäàåò ñ sparse_polynom_input_var.
static const norm_monom_seq_t	norm_monom_seq = norm_monom_seq_t()
	Helper object for choosing method that gives sorted monom sequence.
static const any_monom_seq_t	any_monom_seq = any_monom_seq_t()
	Helper object for choosing method that gives unsorted monom sequence.
Standard integer mathematical operations.
big_int	operator+ (const big_int &b, const big_int &c)
big_int	operator- (const big_int &b, const big_int &c)
big_int	operator * (const big_int &b, const big_int &c)
big_int	operator% (const big_int &b, const big_int &c)
big_int	operator/ (const big_int &b, const big_int &c)
big_int	operator<< (const big_int &a, std::size_t n)
big_int	operator>> (const big_int &a, std::size_t n)
big_int	operator & (const big_int &a, const big_int &b)
big_int	operator| (const big_int &a, const big_int &b)
big_int	operator^ (const big_int &a, const big_int &b)
template<typename T>
big_int	operator<< (const big_int &a, const T &b)
template<typename T>
big_int	operator>> (const big_int &a, const T &b)
template<typename T>
big_int &	operator<<= (big_int &a, const T &b)
big_int &	operator>>= (big_int &a, std::size_t b)
template<typename T>
big_int &	operator>>= (big_int &a, const T &b)
Standard comparision operations.
bool	operator== (const big_int &a, const big_int &b)
bool	operator!= (const big_int &a, const big_int &b)
bool	operator< (const big_int &a, const big_int &b)
bool	operator> (const big_int &a, const big_int &b)
bool	operator<= (const big_int &a, const big_int &b)
bool	operator>= (const big_int &a, const big_int &b)
Computed assignment operators.
big_int &	operator+= (big_int &b, const big_int &c)
big_int &	operator-= (big_int &b, const big_int &c)
big_int &	operator *= (big_int &b, const big_int &c)
big_int &	operator/= (big_int &b, const big_int &c)
big_int &	operator%= (big_int &b, const big_int &c)
Helper functions for the factory class.
template<typename T>
const T &	unit ()
	åäèíè÷íûé ýëåìåíò
template<typename T>
T	unit (const T &x)
	åäèíè÷íûé ýëåìåíò
template<typename T>
bool	is_unit (const T &x)
	ïðîâåðêà íà ðàâåíñòâî åäèíè÷íîìó ýëåìåíòó
template<typename T>
const T &	opposite_unit ()
	ïðîòèâîïîëîæíûé ê åäèíè÷íîìó ýëåìåíòó (-1)
template<typename T>
T	opposite_unit (const T &x)
	ïðîòèâîïîëîæíûé ê åäèíè÷íîìó ýëåìåíòó (-1)
template<typename T>
bool	is_opposite_unit (const T &x)
	ïðîâåðêà íà ðàâåíñòâî -1
template<typename T>
const T &	null ()
	íóëåâîé ýëåìåíò
template<typename T>
T	null (const T &)
	íóëåâîé ýëåìåíò
template<typename T>
bool	is_null (const T &x)
	ïðîâåðêà íà ðàâåíñòâî íóëåâîìó ýëåìåíòó
template<typename T>
T	opposite (const T &x)
	ïðîòèâîïîëîæíûé ýëåìåíò
template<typename T>
T &	opposite (const T &x, T *y)
	ïðîòèâîïîëîæíûé ýëåìåíò
template<typename T>
T &	opposite (T *x)
	ïðîòèâîïîëîæíûé ýëåìåíò
template<typename T>
T	inverse (const T &x)
	îáðàòíûé ýëåìåíò ê äàííîìó
template<typename T>
T &	inverse (const T &x, T *y)
	îáðàòíûé ýëåìåíò ê äàííîìó
template<typename T>
T &	inverse (T *x)
	îáðàòíûé ýëåìåíò ê äàííîìó
A test for primality.
template<typename T>
bool	is_prime (const T &x)
	Determines if x is prime via appropriate algorithm for T.
template<typename T, typename T_factory>
bool	is_prime_division (const T &x, const T_factory &tfctr)
	Determines if x is prime via consecutive division by sample divisors.
template<typename T>
bool	is_prime_division (const T &x)
	Determines if x is prime via consecutive division by sample divisors.
template<typename T, typename N, typename T_factory>
bool	is_pseudoprime_miller_rabin (const T &x, const N &n, const T_factory &tfctr)
	Determines if x is prime via Miller-Rabin algorithm.
template<typename T>
bool	is_prime_AKS_classic (const T &n)
	Determines if x is prime.
template<typename T>
bool	is_prime_AKS (const T &n)
	Determines if x is prime.
template<typename T, typename N>
bool	is_pseudoprime_miller_rabin (const T &x, const N &n)
	Determines if x is prime via Miller-Rabin algorithm.
template<typename T, typename N, typename T_factory>
bool	is_pseudoprime_solovay_strassen (const T &x, const N &n, const T_factory &tfctr)
	Determines if x is prime via Solovey-Strassen algorithm.
template<typename T, typename N>
bool	is_prime_solovey_strassen (const T &x, const N &n)
	Determines if x is prime via Solovey-Strassen algorithm.
template<typename T, typename T_factory>
bool	is_prime (const T &x, const T_factory &tfctr)
	Determines if x is prime via appropriate algorithm for T.
template<typename T, typename T_factory>
bool	is_probably_prime (const T &x, const T_factory &tfctr)
	Determines if x is probably prime via appropriate algorithm for T.
template<typename T>
bool	is_probably_prime (const T &x)
	Determines if x is probably prime via appropriate algorithm for T.
template<typename Out, typename T>
Out	small_primes (Out primes, const T &N)
	Fills sequence with first N primes.
template<typename T, typename N>
int	is_prime_small_primes_division (const T &n, const N &np)
template<typename T>
int	is_prime_small_primes_division (const T &n)
template<typename T, typename T_factory>
bool	is_composite (const T &x, const T_factory &tfctr)
	Determines if x is composite.
template<typename T>
bool	is_composite (const T &x)
	Determines if x is composite.
The Euclidean algorithm.
template<typename T, typename T_factory>
T	euclid (T a, T b, const T_factory &tfctr)
	Processes the Euclidean algorithm on a and b.
template<typename T>
T	euclid (const T &a, const T &b)
	Processes the Euclidean algorithm on a and b.
template<typename T, typename T_factory>
T	euclid_binary (T a, T b, const T_factory &tfctr)
	Processes the Euclidean algorithm on a and b.
template<typename T>
T	euclid_binary (const T &a, const T &b)
	Processes the Euclidean algorithm on a and b.
template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>
vector< T, REFCNT >	euclid (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b, const T_factory &tfctr)
	Computes Euclidean algorithm for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T1, bool REFCNT1>
vector< T, REFCNT >	euclid (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b)
	Computes Euclidean algorithm for each corresponding pair of a and b.
template<typename T, typename T_factory>
T	euclid_bezout (const T &a, const T &b, T &u, T &v, const T_factory &tfctr)
	The greatest common divisor and Bezout's coefficients.
template<typename T>
T	euclid_bezout (const T &a, const T &b, T &u, T &v)
	The greatest common divisor and Bezout's coefficients.
The GCD and LCM algorithms.
template<typename T, typename T_factory>
T	gcd (const T &a, const T &b, const T_factory &tfctr, const type_category::type &)
template<typename T, typename T_factory>
T	gcd (const T &a, const T &b, const T_factory &tfctr, const type_category::integer &)
template<typename T, typename T_factory>
T	gcd (const T &a, const T &b, const T_factory &tfctr)
	Computes GCD for a and b.
template<typename T>
T	gcd (const T &a, const T &b)
	Computes GCD for a and b.
template<typename T1, typename T2>
T1	gcd (const T1 &a, const T2 &b)
	Computes GCD for a and b.
template<typename T, bool REFCNT, typename T_factory>
T	gcd (const vector< T, REFCNT > &x, const T_factory &tfctr)
	Computes GCD for all items of vector 'x'.
template<typename T, bool REFCNT>
T	gcd (const vector< T, REFCNT > &x)
	Computes GCD for all items of vector 'x'.
template<typename T>
T	gcd3 (const T &a, const T &b, const T &c)
	Compute GCD(a, b, c).
template<typename T>
T	gcdex (const T &a, const T &b, T &u, T &v, T &w, T &z)
	Extended GCD; abs(u*z - w*v) == 1; a*w + b*z == 0.
template<typename T>
T	gcdex (const T &a, const T &b, const T &N, T &u, T &v, T &w, T &z)
template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>
vector< T, REFCNT >	gcd_vec (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b, const T_factory &tfctr)
	Computes GCD for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>
vector< T, REFCNT >	gcd (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b, const T_factory &tfctr)
	Computes GCD for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T_factory>
vector< T, REFCNT >	gcd (const vector< T, REFCNT > &a, const vector< T, REFCNT > &b, const T_factory &tfctr)
	Computes GCD for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T1, bool REFCNT1>
vector< T, REFCNT >	gcd (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b)
	Computes GCD for each corresponding pair of a and b.
template<typename T, bool REFCNT>
vector< T, REFCNT >	gcd (const vector< T, REFCNT > &a, const vector< T, REFCNT > &b)
	Computes GCD for each corresponding pair of a and b.
template<typename T, typename T_factory>
T	lcm (const T &a, const T &b, const T_factory &tfctr)
	Computes LCM for a and b.
template<typename T>
T	lcm (const T &a, const T &b)
	Computes LCM for a and b.
template<typename T, bool REFCNT, typename T_factory>
T	lcm (const vector< T, REFCNT > &x, const T_factory &tfctr)
	Computes LCM for all items of vector 'x'.
template<typename T, bool REFCNT>
T	lcm (const vector< T, REFCNT > &x)
	Computes LCM for all items of vector 'x'.
template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>
vector< T, REFCNT >	lcm_vec (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b, const T_factory &tfctr)
	Computes LCM for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>
vector< T, REFCNT >	lcm (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b, const T_factory &tfctr)
	Computes LCM for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T_factory>
vector< T, REFCNT >	lcm (const vector< T, REFCNT > &a, const vector< T, REFCNT > &b, const T_factory &tfctr)
	Computes LCM for each corresponding pair of a and b.
template<typename T, bool REFCNT, typename T1, bool REFCNT1>
vector< T, REFCNT >	lcm (const vector< T, REFCNT > &a, const vector< T1, REFCNT1 > &b)
	Computes LCM for each corresponding pair of a and b.
template<typename T, bool REFCNT>
vector< T, REFCNT >	lcm (const vector< T, REFCNT > &a, const vector< T, REFCNT > &b)
A test for relative primality.
template<typename T, typename T_factory>
bool	is_coprime (const T &a, const T &b, const T_factory &tfctr)
	Returns true if two objects are coprime.
template<typename T>
bool	is_coprime (const T &a, const T &b)
	Returns true if two objects are coprime.
template<typename T, bool REFCNT, typename T_factory>
bool	is_coprime (const vector< T, REFCNT > &x, const T_factory &tfctr)
	Returns true if all objects in the vector are coprime.
template<typename T, bool REFCNT>
bool	is_coprime (const vector< T, REFCNT > &x)
	Returns true if all objects in the vector are coprime.
Jacobi symbol.
template<typename T, typename T_factory>
int	jacobi (T a, T n, const T_factory &tfctr)
	Computes the Jacobi symbol (a/n).
template<typename T>
int	jacobi (const T &a, const T &n)
	Computes the Jacobi symbol (a/n).
Standard comparision operators.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator<= (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator<= (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator<= (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator>= (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator>= (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator>= (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator< (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator< (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator< (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator> (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator> (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator> (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator== (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator== (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator== (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
bool	operator!= (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
bool	operator!= (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
bool	operator!= (const T1 &a, const matrix< T2, REFCNT2 > &b)
Binary operators with matrices and scalars.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator+ (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator+ (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator+ (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator+ (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator+ (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator+ (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator+ (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator+ (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator+ (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator- (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator- (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator- (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator- (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator- (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator- (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator- (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator- (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator- (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator * (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator * (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator * (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator * (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator * (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator * (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator * (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator * (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator * (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator/ (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator/ (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator/ (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator/ (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator/ (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator/ (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator/ (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator/ (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator/ (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator% (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator% (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator% (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator% (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator% (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator% (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator% (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator% (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator% (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator & (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator & (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator & (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator & (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator & (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator & (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator & (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator & (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator & (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator| (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator| (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator| (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator| (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator| (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator| (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator| (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator| (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator| (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator^ (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator^ (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator^ (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator^ (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator^ (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator^ (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator^ (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator^ (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator^ (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator<< (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator<< (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator<< (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator<< (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator<< (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator<< (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator<< (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator<< (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator<< (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
matrix< T1, REFCNT1 >	operator>> (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename T2>
matrix< T1, REFCNT1 >	operator>> (const matrix< T1, REFCNT1 > &a, const T2 &b)
template<typename T1, typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator>> (const T1 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< T1, REFCNT1 >	operator>> (const matrix< T1, REFCNT1 > &a, const T1 &b)
template<typename T2, bool REFCNT2>
matrix< T2, REFCNT2 >	operator>> (const T2 &a, const matrix< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1>
matrix< rational< T1 >, REFCNT1 >	operator>> (const matrix< rational< T1 >, REFCNT1 > &a, const rational< T1 > &b)
template<typename T2, bool REFCNT2>
matrix< rational< T2 >, REFCNT2 >	operator>> (const rational< T2 > &a, const matrix< rational< T2 >, REFCNT2 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator>> (const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &a, const sparse_polynom< T1, D1, REFCNT1 > &b)
template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>
matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 >	operator>> (const sparse_polynom< T1, D1, REFCNT1 > &a, const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &b)
Factorization.
template<typename T1, typename T2, bool REFCNT2, typename T_factory>
vector< T2, REFCNT2 > &	factorize_division (T1 x, vector< T2, REFCNT2 > &res, const T_factory &tfctr)
	Factorizes x into a set of prime factors via consecutive division.
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	factorize_division (const T1 &x, vector< T2, REFCNT2 > &res)
	Factorizes x into a set of prime factors via consecutive division.
template<typename T, typename T_factory>
vector< T, true >	factorize_division (const T &x, const T_factory &tfctr)
	Factorizes x into a set of prime factors via consecutive division.
template<typename T>
vector< T, true >	factorize_division (const T &x)
	Factorizes x into a set of prime factors via consecutive division.
template<typename T1, typename T2, bool REFCNT2, typename T_factory>
vector< T2, REFCNT2 > &	factorize (const T1 &x, vector< T2, REFCNT2 > &res, const T_factory &tfctr)
	Factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	factorize (const T1 &x, vector< T2, REFCNT2 > &res)
	Factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T, typename T_factory>
vector< T, true >	factorize (const T &x, const T_factory &tfctr)
	Factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T>
vector< T, true >	factorize (const T &x)
	Factorizes x into a set of prime factors via appropriate algorithm for T.
Partial factorization.
template<typename T1, typename T2, bool REFCNT2, typename T3, typename T4>
vector< T2, REFCNT2 > &	partial_factorize_division (T1 x, vector< T2, REFCNT2 > &res, const T3 &max, T4 &rest)
	Partialy factorizes x into a set of prime factors via test division.
template<typename T, typename N, typename T_factory>
T	pollard_pm1 (const T &n, const N &no_of_iter, const T_factory &tfctr)
	Pollard p-1 method (Simple variant).
template<typename T, typename N>
T	pollard_pm1 (const T &n, const N &no_of_iter=10000)
	Pollard p-1 method (Simple variant).
template<typename T, typename T_factory>
T	rho_pollard (const T &n, const T_factory &tfctr)
	Pollard's rho algorithm.
template<typename T>
T	rho_pollard (const T &n)
	Pollard's rho algorithm.
template<typename T, typename N, typename T_factory>
T	brent (const T &n, N no_of_iter, const T_factory &tfctr)
	Pollard's rho algorithm.
template<typename T, typename N>
T	brent (const T &n, N no_of_iter)
	Pollard's rho algorithm.
template<typename T, typename T3, typename T4>
vector< T, true >	partial_factorize_division (const T &x, const T3 &max, T4 &rest)
	Partialy factorizes x into a set of prime factors via test division.
template<typename T1, typename TT1, typename T2, bool REFCNT2, typename T3>
vector< T2, REFCNT2 > &	partial_factorize_division (const T1 &x, vector< T2, REFCNT2 > &res, const T3 &max)
	Partialy factorizes x into a set of prime factors via test division.
template<typename T, typename T3>
vector< T, true >	partial_factorize_division (const T &x, const T3 &max)
	Partialy factorizes x into a set of prime factors via test division.
template<typename T1, typename T2, bool REFCNT2, typename T3, typename T4>
vector< T2, REFCNT2 > &	partial_factorize (const T1 &x, vector< T2, REFCNT2 > &res, const T3 &max, T4 &rest)
	Partialy factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T, typename T3, typename T4>
vector< T, true >	partial_factorize (const T &x, const T3 &max, T4 &rest)
	Partialy factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T1, typename TT1, typename T2, bool REFCNT2, typename T3>
vector< T2, REFCNT2 > &	partial_factorize (const T1 &x, vector< T2, REFCNT2 > &res, const T3 &max)
	Partialy factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T, typename T3>
vector< T, true >	partial_factorize (const T &x, const T3 &max)
	Partialy factorizes x into a set of prime factors via appropriate algorithm for T.
template<typename T1, typename T2, typename T3, typename T4>
const T4 &	factorize_multiplier (T1 x, const T2 &m, T3 &rest, T4 &nm)
	Finds rest and nm such that x = rest * m^nm and rest is not divisible by m; returns reference to nm.
template<typename T1, typename T2, typename T3>
T1	factorize_multiplier (const T1 &x, const T2 &m, T3 &rest)
	Finds rest and nm such that x = rest * m^nm and rest is not divisible by m; returns nm.
template<typename T1, typename T2>
T1	factorize_multiplier (const T1 &x, const T2 &m)
	Finds rest and nm such that x = rest * m^nm and rest is not divisible by m; returns nm.
Prime number generators.
template<typename T>
T	next_prime_successive_checking (T x)
	Finds the next after x prime number via successive test for each number.
template<typename T>
T	prev_prime_successive_checking (T x)
	Finds the previous before x prime number via successive test for each number.
template<typename T>
T	next_prime (const T &x)
	Finds the next after x prime number via appropriate algorithm.
template<typename T>
T	prev_prime (const T &x)
	Finds the previous before x prime number via appropriate algorithm.
template<typename T>
T	next_probably_prime (T x)
	Finds the next after x probably prime number via appropriate algorithm.
template<typename T>
T	prev_probably_prime (T x)
	Finds the previous before x probably prime number via appropriate algorithm.
template<typename T, typename N>
void	rsa_generate_keys (N l, T &c, T &public_key, T &d)
	algorithms.
template<typename T>
T	rsa_encyph (const T &x, const T &c, const T &key)
template<typename T>
T	rsa_decyph (const T &y, const T &d, const T &key)
template<typename T>
bool	is_mersen_prime_degree (const T &n)
	Determines if 2^n-1 is Mersenn prime number.
template<typename T>
T	next_mersen_prime_degree (const T &n)
	Gives such k > n that 2^k-1 is Mersenn prime number, and for all k > m > n, 2^m-1 is not.
Standard arithmetic operations.
template<typename T1, typename T2>
rational< T1 >	operator+ (const rational< T1 > &b, const rational< T2 > &c)
template<typename T1, typename T2>
rational< T1 >	operator- (const rational< T1 > &b, const rational< T2 > &c)
template<typename T1, typename T2>
rational< T1 >	operator * (const rational< T1 > &b, const rational< T2 > &c)
template<typename T1, typename T2>
rational< T1 >	operator/ (const rational< T1 > &b, const rational< T2 > &c)
template<typename T1, typename T2>
rational< T1 >	operator% (const rational< T1 > &b, const rational< T2 > &c)
Standard arithmetic operations.
template<typename T1, typename T2>
rational< T1 > &	operator+= (rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator+= (rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator+ (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator+ (const T2 &a, const rational< T1 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator-= (rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator-= (rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator- (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator- (const T2 &a, const rational< T1 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator *= (rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator *= (rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator * (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator * (const T2 &a, const rational< T1 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator/= (rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator/= (rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator/ (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator/ (const T2 &a, const rational< T1 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator%= (rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
rational< T1 > &	operator%= (rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator% (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
rational< T1 >	operator% (const T2 &a, const rational< T1 > &b)
Standard comparision operators.
template<typename T1, typename T2>
bool	operator< (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator< (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator< (const T1 &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator> (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator> (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator> (const T1 &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator== (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator== (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator== (const T1 &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator!= (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator!= (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator!= (const T1 &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator<= (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator<= (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator<= (const T1 &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator>= (const rational< T1 > &a, const rational< T2 > &b)
template<typename T1, typename T2>
bool	operator>= (const rational< T1 > &a, const T2 &b)
template<typename T1, typename T2>
bool	operator>= (const T1 &a, const rational< T2 > &b)
Standard comparision operators that based on cmp function.
template<typename F1, typename I1, typename F2, typename I2>
bool	operator== (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator== (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator== (const F1 &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2>
bool	operator!= (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator!= (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator!= (const F1 &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2>
bool	operator<= (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator<= (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator<= (const F1 &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2>
bool	operator>= (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator>= (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator>= (const F1 &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2>
bool	operator< (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator< (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator< (const F1 &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2>
bool	operator> (const monom< F1, I1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2>
bool	operator> (const monom< F1, I1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2>
bool	operator> (const F1 &a, const monom< F2, I2 > &b)
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template<typename F1, typename I1, typename F2, typename I2>
monom< F1, I1 >	operator+ (const monom< F1, I1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2>
monom< F1, I1 >	operator+ (const monom< F1, I1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2>
monom< F2, I2 >	operator+ (const F1 &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2>
monom< F1, I1 >	operator- (const monom< F1, I1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2>
monom< F1, I1 >	operator- (const monom< F1, I1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2>
monom< F2, I2 >	operator- (const F1 &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2>
monom< F1, I1 >	operator * (const monom< F1, I1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2>
monom< F1, I1 >	operator * (const monom< F1, I1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2>
monom< F2, I2 >	operator * (const F1 &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2>
monom< F1, I1 >	operator/ (const monom< F1, I1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2>
monom< F1, I1 >	operator/ (const monom< F1, I1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2>
monom< F2, I2 >	operator/ (const F1 &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2>
monom< F1, I1 >	operator% (const monom< F1, I1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2>
monom< F1, I1 >	operator% (const monom< F1, I1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2>
monom< F2, I2 >	operator% (const F1 &x, const monom< F2, I2 > &y)
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template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F1, I1, REFCNT1 >	operator+ (const sparse_polynom< F1, I1, REFCNT1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	operator+ (const sparse_polynom< F1, I1, REFCNT1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator+ (const monom< F1, I1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2>
sparse_polynom< F1, I1, REFCNT1 >	operator+ (const sparse_polynom< F1, I1, REFCNT1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator+ (const F1 &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator+ (const sparse_polynom< rational< F1 >, I1, REFCNT1 > &x, const rational< F1 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator+ (const rational< F1 > &x, const sparse_polynom< rational< F1 >, I1, REFCNT1 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F1, I1, REFCNT1 >	operator- (const sparse_polynom< F1, I1, REFCNT1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	operator- (const sparse_polynom< F1, I1, REFCNT1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator- (const monom< F1, I1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2>
sparse_polynom< F1, I1, REFCNT1 >	operator- (const sparse_polynom< F1, I1, REFCNT1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator- (const F1 &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator- (const sparse_polynom< rational< F1 >, I1, REFCNT1 > &x, const rational< F1 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator- (const rational< F1 > &x, const sparse_polynom< rational< F1 >, I1, REFCNT1 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F1, I1, REFCNT1 >	operator * (const sparse_polynom< F1, I1, REFCNT1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	operator * (const sparse_polynom< F1, I1, REFCNT1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator * (const monom< F1, I1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2>
sparse_polynom< F1, I1, REFCNT1 >	operator * (const sparse_polynom< F1, I1, REFCNT1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator * (const F1 &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator * (const sparse_polynom< rational< F1 >, I1, REFCNT1 > &x, const rational< F1 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator * (const rational< F1 > &x, const sparse_polynom< rational< F1 >, I1, REFCNT1 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F1, I1, REFCNT1 >	operator/ (const sparse_polynom< F1, I1, REFCNT1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	operator/ (const sparse_polynom< F1, I1, REFCNT1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator/ (const monom< F1, I1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2>
sparse_polynom< F1, I1, REFCNT1 >	operator/ (const sparse_polynom< F1, I1, REFCNT1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator/ (const F1 &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator/ (const sparse_polynom< rational< F1 >, I1, REFCNT1 > &x, const rational< F1 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator/ (const rational< F1 > &x, const sparse_polynom< rational< F1 >, I1, REFCNT1 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F1, I1, REFCNT1 >	operator% (const sparse_polynom< F1, I1, REFCNT1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	operator% (const sparse_polynom< F1, I1, REFCNT1 > &x, const monom< F2, I2 > &y)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator% (const monom< F1, I1 > &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1, typename F2>
sparse_polynom< F1, I1, REFCNT1 >	operator% (const sparse_polynom< F1, I1, REFCNT1 > &x, const F2 &y)
template<typename F1, typename F2, typename I2, bool REFCNT2>
sparse_polynom< F2, I2, REFCNT2 >	operator% (const F1 &x, const sparse_polynom< F2, I2, REFCNT2 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator% (const sparse_polynom< rational< F1 >, I1, REFCNT1 > &x, const rational< F1 > &y)
template<typename F1, typename I1, bool REFCNT1>
sparse_polynom< rational< F1 >, I1, REFCNT1 >	operator% (const rational< F1 > &x, const sparse_polynom< rational< F1 >, I1, REFCNT1 > &y)
Standard comparision operators that based on cmp function.
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator== (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator== (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator== (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator== (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator== (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator!= (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator!= (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator!= (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator!= (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator!= (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator<= (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator<= (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator<= (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator<= (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator<= (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator>= (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator>= (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator>= (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator>= (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator>= (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator< (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator< (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator< (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator< (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator< (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
bool	operator> (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2>
bool	operator> (const sparse_polynom< F1, I1, REFCNT1 > &a, const monom< F2, I2 > &b)
template<typename F1, typename I1, typename F2, typename I2, bool REFCNT2>
bool	operator> (const monom< F1, I1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
template<typename F1, typename I1, bool REFCNT1, typename F2>
bool	operator> (const sparse_polynom< F1, I1, REFCNT1 > &a, const F2 &b)
template<typename F1, typename F2, typename I2, bool REFCNT2>
bool	operator> (const F1 &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
LaTeX output for built-in types and big_int
template<typename Out>
void	output_latex (Out &out, const signed int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const unsigned int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const signed short int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const unsigned short int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const signed long int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const unsigned long int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const float &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const double &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const long double &x, bool in_math=false, ex_environ_priority eep=eep_alone)
template<typename Out>
void	output_latex (Out &out, const big_int &x, bool in_math=false, ex_environ_priority eep=eep_alone)
Matrix frames maker functions.
template<typename In_hor, typename In_ver, typename In_box>
matrix_frames< In_hor, In_ver, In_box >	make_matrix_frames (In_hor hf, In_hor hl, In_ver vf, In_ver vl, In_box bf, In_box bl)
template<typename In_hor, typename In_ver>
matrix_frames< In_hor, In_ver >	make_matrix_frames (In_hor hf, In_hor hl, In_ver vf, In_ver vl)
template<typename In_hor>
matrix_frames< In_hor >	make_matrix_frames (In_hor hf, In_hor hl)
matrix_frames	make_matrix_frames ()
template<typename In_ver>
matrix_frames< const matrix_line *, In_ver >	make_matrix_vers (In_ver vf, In_ver vl)
template<typename In_box>
matrix_frames< const matrix_line *, const matrix_line *, In_box >	make_matrix_boxes (In_box bf, In_box bl)
template<typename In_ver, typename In_box>
matrix_frames< const matrix_line *, In_ver, In_box >	make_matrix_vers_boxes (In_ver vf, In_ver vl, In_box bf, In_box bl)
Boolean as type.
std::ostream &	operator<< (std::ostream &out, const true_type &)
std::ostream &	operator<< (std::ostream &out, const false_type &)
Standard mathematical functions on vector.
template<typename T, bool REFCNT>
vector< T, true >	sin (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	cos (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	tan (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	sinh (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	cosh (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	tanh (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	asin (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	acos (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	atan (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	abs (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	exp (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	floor (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	ceil (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	log (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	log10 (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, true >	sqrt (const vector< T, REFCNT > &x)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
vector< T1, REFCNT1 >	pow (const vector< T1, REFCNT1 > &a, const vector< T2, REFCNT2 > &b)
template<typename T1, bool REFCNT1, typename P>
vector< T1, REFCNT1 >	pow (const vector< T1, REFCNT1 > &a, const P &b)
Rounding Modes for big_float
const int	EXACT = 1
	Rounds to the closest value.
const int	ROUND = 2
	Uses rules of `'manual'' computations.
const int	TO_NEAREST = 3
	Rounds towards the nearest number.
const int	TO_ZERO = 4
	Rounds towards zero.
const int	TO_P_INF = 5
	Rounds towards +infinity.
const int	TO_M_INF = 6
	Rounds towards -infinity.
const int	TO_INF = 7
	Rounds outwards zero.
Special big_float numbers
const int	NAN = 1
const int	PINF = 2
const int	M_INF = 3
const int	P_ZERO = 4
const int	M_ZERO = 5
Helper types and constants to choose a particular cone class constructor.
const fromnull_t	fromnull = fromnull_t()
	Helper constant to create cone as one point (null).
const fromspace_t	fromspace = fromspace_t()
	Helper constant to create cone from dimention.
const fromineq_t	fromineq = fromineq_t()
	Helper constant to create cone from the set of inequalities.
const fromeq_t	fromeq = fromeq_t()
	Helper constant to create cone from the set of equalities.
const fromgen_t	fromgen = fromgen_t()
	Helper constant to create cone from the set of generatrices.
const frombasis_t	frombasis = frombasis_t()
	Helper constant to create cone from the set of basis vectors.
const fromdual_t	fromdual = fromdual_t()
Typedefs
typedef unsigned long long	counter_t
Enumerations
enum	interval_kind { interval_empty = 0, interval_point = 1, interval_length = 2 }
	Kind of interval. More...
enum	solve_linsys_result { SLR_EMPTY, SLR_UNIQUE, SLR_MULTIPLE }
enum	ex_environ_priority { eep_alone, eep_add, eep_mul }
	Type of environment (context) for an expression. More...
enum	matrix_line_type { mlt_solid, mlt_dot, mlt_hatch, mlt_chain }
	Type of a line that used in matrix output functions with boxes and dividing lines. More...
Functions
template<typename D1, typename T1>
bool	is_null (const _Internal::module_2pm1< D1, T1 > &a)
template<typename D1, typename T1>
bool	is_unit (const _Internal::module_2pm1< D1, T1 > &a)
template<typename T1, typename D2, typename T2>
T1	prrem (const T1 &aa, const _Internal::module_2pm1< D2, T2 > &b)
template<typename Out, typename D, typename T>
Out &	operator<< (Out &out, const _Internal::module_2pm1< D, T > &x)
template<typename In, typename D, typename T>
In &	operator>> (In &in, _Internal::module_2pm1< D, T > &x)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	operator+ (algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	operator- (algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	operator * (algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	operator/ (algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	operator% (algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator== (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator== (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator== (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator!= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator!= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator!= (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator< (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator< (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator< (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator<= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator<= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator<= (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator> (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator> (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator> (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator>= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>
bool	operator>= (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TS2 &b)
template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
bool	operator>= (const TS1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
int	cmp (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2>
int	cmp (const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &a, const TP2 &b)
template<typename TP1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>
int	cmp (const TP1 &a, const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &b)
template<typename Out, typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1>
Out &	operator<< (Out &out, const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &x)
template<typename PolyVec, typename SegVec, typename Rslt, typename P, typename Seg, typename F>
void	algebraic_func_rslt (const PolyVec &polyvec, SegVec segvec, Rslt rslt, P &p, Seg &seg, F f)
	Arbitrary function on algebraic numbers based on precomputed resultant.
template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>
void	algebraic_plus (const P1 &p1, const Seg1 &seg1, const P2 &p2, const Seg2 &seg2, P3 &p3, Seg3 &seg3)
template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>
void	algebraic_minus (const P1 &p1, const Seg1 &seg1, const P2 &p2, const Seg2 &seg2, P3 &p3, Seg3 &seg3)
template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>
void	algebraic_multiplies (const P1 &p1, const Seg1 &seg1, const P2 &p2, const Seg2 &seg2, P3 &p3, Seg3 &seg3)
template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>
void	algebraic_divides (const P1 &p1, const Seg1 &seg1, const P2 &p2, Seg2 seg2, P3 &p3, Seg3 &seg3)
template<typename MA, typename MB, typename MQ, typename Basis, typename T_det>
void	bareiss (const MA &A, MB &B, MQ &Q, Basis &basis, T_det &det)
	Produces the Gauss-Jordan form B of an integer matrix A.
template<typename MA, typename MP, typename MQ, typename Rank, typename T_det>
void	bareiss_pq (const MA &A, MP &P, MQ &Q, Rank &rank, T_det &det)
	Produces the Gauss form B of an integer matrix A.
template<typename MA>
MA	adjoint (const MA &A)
template<typename MA, typename MP, typename T_det>
void	adjoint (const MA &A, MP &P, T_det &det)
template<typename MA>
MA::element_type	det_brs (const MA &A)
template<typename MA>
MA::size_type	rank_brs (const MA &A)
template<typename T, typename Res>
Res &	indirection (const T &x, Res &res)
template<typename T, typename Res>
Res &	address (const T &x, Res &res)
template<typename T, typename Res>
Res &	unary_plus (const T &x, Res &res)
template<typename T, typename Res>
Res &	unary_minus (const T &x, Res &res)
template<typename T, typename Res>
Res &	logical_not (const T &x, Res &res)
template<typename T, typename Res>
Res &	bitwise_not (const T &x, Res &res)
template<typename T, typename Res>
Res &	prefix_increment (T &x, Res &res)
template<typename T, typename Res>
Res &	prefix_decrement (T &x, Res &res)
template<typename T, typename Res>
Res &	postfix_increment (T &x, Res &res)
template<typename T, typename Res>
Res &	postfix_decrement (T &x, Res &res)
template<typename T1, typename T2, typename Res>
Res &	plus (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	minus (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	multiplies (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	divides (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	modulus (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	logical_or (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	logical_and (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	equal_to (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	not_equal_to (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	greater (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	less (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	greater_equal (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	less_equal (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	bitwise_or (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	bitwise_and (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	bitwise_xor (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	shift_left (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2, typename Res>
Res &	shift_right (const T1 &x, const T2 &y, Res &res)
template<typename T1, typename T2>
T1 &	right_assign_plus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_plus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_minus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_minus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_multiplies (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_multiplies (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_divides (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_divides (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_modulus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_modulus (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_bitwise_or (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_bitwise_or (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_bitwise_and (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_bitwise_and (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_bitwise_xor (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_bitwise_xor (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_shift_left (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_shift_left (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_shift_right (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_shift_right (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_logical_or (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_logical_or (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_logical_and (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_logical_and (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_equal_to (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_equal_to (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_not_equal_to (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_not_equal_to (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_greater (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_greater (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_less (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_less (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_greater_equal (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_greater_equal (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	right_assign_less_equal (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	assign_less_equal (T1 &x, const T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_plus (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_minus (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_multiplies (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_divides (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_modulus (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_logical_or (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_logical_and (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_equal_to (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_not_equal_to (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_greater (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_less (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_greater_equal (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_less_equal (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_bitwise_or (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_bitwise_and (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_bitwise_xor (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_shift_left (const T1 &x, T2 &y)
template<typename T1, typename T2>
T1 &	left_assign_shift_right (const T1 &x, T2 &y)
template<typename T>
T &	assign_indirection (T &x)
template<typename T>
T &	assign_address (T &x)
template<typename T>
T &	assign_unary_plus (T &x)
template<typename T>
T &	assign_unary_minus (T &x)
template<typename T>
T &	assign_logical_not (T &x)
template<typename T>
T &	assign_bitwise_not (T &x)
big_int	ln1_25 (std::size_t nbits)
	Returns ln(1.25) with nbits significant bits.
big_int	ln1_25_o (std::size_t nbits)
	Returns ln(1.25) with nbits significant bits with overflow.
big_int	ln1_25_u (std::size_t nbits)
	Returns ln(1.25) with nbits significant bits with imperfection.
big_int	ln2 (std::size_t nbits)
	Returns ln(2) with nbits significant bits.
big_int	ln2_u (std::size_t nbits)
	Returns ln(2) with nbits significant bits with imperfection.
big_int	ln2_o (std::size_t nbits)
	Returns ln(2) with nbits significant bits with oveflow.
big_int	log2_10 (std::size_t nbits)
	Returns log2_10 with nbits significant bits.
big_int	log2_10_o (std::size_t nbits)
	Returns log2_10 with nbits significant bits with oveflow.
big_int	log2_10_u (std::size_t nbits)
	Returns log2_10 with nbits significant bits with imperfection.
big_int	lg_2_o (std::size_t nbits)
	Returns lg2 with nbits significant bits with oveflow.
big_int	lg_2_u (std::size_t nbits)
	Returns lg2 with nbits significant bits with imperfection.
big_int	lg_2 (std::size_t nbits)
	Returns lg2 with nbits significant bits.
big_int	exp_u (big_int arg, std::size_t nbits, int factor=0)
	Returns exp(arg/2^factor) with nbits significant bits with imperfection.
big_int	exp_o (big_int arg, std::size_t nbits, int factor=0)
	Returns exp(arg/2^factor) with nbits significant bits with oveflow.
big_int	exp (big_int arg, std::size_t nbits, int factor=0)
	Returns exp(arg/2^factor) with nbits significant bits.
big_int	exp_2_u (big_int arg, std::size_t nbits, int factor=0)
	Returns 2^(arg/2^factor) with nbits significant bits with imperfection.
big_int	exp_2_o (big_int arg, std::size_t nbits, int factor=0)
	Returns 2^(arg/2^factor) with nbits significant bits with oveflow.
big_int	exp_2 (big_int arg, std::size_t nbits, int factor=0)
	Returns 2^(arg/2^factor) with nbits significant bits.
big_int	e_u (std::size_t nbits)
	Returns e number with nbits significant bits with imperfection.
big_int	e_o (std::size_t nbits)
	Returns e number with nbits significant bits with oveflow.
big_int	e (std::size_t nbits)
	Returns e number with nbits significant bits.
big_int	ln10 (std::size_t nbits)
	Returns ln10 with nbits significant bits.
big_int	ln10_u (std::size_t nbits)
	Returns ln10 with nbits significant bits with imperfection.
big_int	ln10_o (std::size_t nbits)
	Returns ln10 with nbits significant bits with oveflow.
void	big_float_warning (const char *s)
void	big_float_error (const char *s)
void	big_float_fatal_error (const char *s)
unsigned	fracsion (int n, unsigned m)
int	get_exponent_of_double (double d)
_Internal::digit *	get_mantissa_of_double (double d)
int	get_sign (big_int s)
int	cmp (const big_float &a, const big_float &b)
int	operator== (const big_float &a, const big_float &b)
int	operator!= (const big_float &a, const big_float &b)
int	operator> (const big_float &a, const big_float &b)
int	operator>= (const big_float &a, const big_float &b)
int	operator< (const big_float &a, const big_float &b)
int	operator<= (const big_float &a, const big_float &b)
big_float	operator+ (const big_float &a)
big_float	operator- (const big_float &a)
big_float	operator+ (const big_float &b, const big_float &c)
big_float	operator- (const big_float &b, const big_float &c)
big_float	operator * (const big_float &b, const big_float &c)
big_float	operator/ (const big_float &b, const big_float &c)
big_float	add (const big_float &b, const big_float &c)
big_float	sub (const big_float &b, const big_float &c)
big_float	mul (const big_float &b, const big_float &c)
big_float	div (const big_float &b, const big_float &c)
big_float	add (const big_float &b, const big_float &c, long prec)
big_float	sub (const big_float &b, const big_float &c, long prec)
big_float	mul (const big_float &b, const big_float &c, long prec)
big_float	div (const big_float &b, const big_float &c, long prec)
big_float	add (const big_float &b, const big_float &c, long prec, int mode)
big_float	sub (const big_float &b, const big_float &c, long prec, int mode)
big_float	mul (const big_float &b, const big_float &c, long prec, int mode)
big_float	div (const big_float &b, const big_float &c, long prec, int mode)
big_float	divnu (const big_float &b, const big_float &c, long prec, int mode)
big_float	div_i (const big_int &c)
void	reduce_final_zeros (std::basic_string< char > &str)
std::istream &	operator>> (std::istream &is, big_float &fnum)
std::ostream &	operator<< (std::ostream &os, const big_float &fnum)
big_float	ceil (const big_float &a)
big_float	floor (const big_float &a)
big_float	frac (const big_float &a)
big_int	iceil (const big_float &a)
big_int	ifloor (const big_float &a)
big_float	fsqrt (const big_float &b)
big_float	fsqrt (const big_float &bf, long prec)
big_float	fsqrt (const big_float &bf, long prec, int mode)
big_float	nfsqrt (const big_float &bf, long prec, int mode)
big_float	frandom (long prec)
big_float	frandom ()
big_float	frandom1 (long bits, const big_int &exp)
big_float	abs (const big_float &x)
template<typename Outiter>
void	generate_range_helper (big_float &t1, const big_float &t2, Outiter outiter)
big_float &	operator+= (big_float &b, const big_float &c)
big_float &	operator-= (big_float &b, const big_float &c)
big_float &	operator *= (big_float &b, const big_float &c)
big_float &	operator/= (big_float &b, const big_float &c)
void	big_arith_error (const char *s)
void	calc_bdn_radix (digit radix, digit &bdn_radix, std::size_t &chars_per_digit)
int	cmp (const big_int &a, const big_int &b)
	Compares two big integers.
digit	random_digit ()
digit	stream_radix (std::ios &s)
std::ostream &	operator<< (std::ostream &s, const big_int &x)
	Reads a number from a string notation.
void	set_stream_radix (std::ios &s, digit radix)
std::istream &	operator>> (std::istream &s, big_int &x)
	Writes a number to a string notation.
std::size_t	nbits (const big_int &x)
	Returns the number of bits in number. The same as big_int::length.
template<typename TT>
int	sign (const big_int &x)
void	divide (const big_int &a, const big_int &b, big_int &q, big_int &r)
	Divizion with quotient and remainder.
big_int &	operator+= (big_int &b, char c)
char &	operator+= (char &b, const big_int &c)
big_int &	operator+= (big_int &b, signed char c)
signed char &	operator+= (signed char &b, const big_int &c)
big_int &	operator+= (big_int &b, unsigned char c)
unsigned char &	operator+= (unsigned char &b, const big_int &c)
big_int &	operator+= (big_int &b, signed short c)
signed short &	operator+= (signed short &b, const big_int &c)
big_int &	operator+= (big_int &b, unsigned short c)
unsigned short &	operator+= (unsigned short &b, const big_int &c)
big_int &	operator+= (big_int &b, signed int c)
signed int &	operator+= (signed int &b, const big_int &c)
big_int &	operator+= (big_int &b, unsigned int c)
unsigned int &	operator+= (unsigned int &b, const big_int &c)
big_int &	operator+= (big_int &b, signed long c)
signed long &	operator+= (signed long &b, const big_int &c)
big_int &	operator+= (big_int &b, unsigned long c)
unsigned long &	operator+= (unsigned long &b, const big_int &c)
big_int &	operator+= (big_int &b, bool c)
bool &	operator+= (bool &b, const big_int &c)
big_int &	operator-= (big_int &b, char c)
char &	operator-= (char &b, const big_int &c)
big_int &	operator-= (big_int &b, signed char c)
signed char &	operator-= (signed char &b, const big_int &c)
big_int &	operator-= (big_int &b, unsigned char c)
unsigned char &	operator-= (unsigned char &b, const big_int &c)
big_int &	operator-= (big_int &b, signed short c)
signed short &	operator-= (signed short &b, const big_int &c)
big_int &	operator-= (big_int &b, unsigned short c)
unsigned short &	operator-= (unsigned short &b, const big_int &c)
big_int &	operator-= (big_int &b, signed int c)
signed int &	operator-= (signed int &b, const big_int &c)
big_int &	operator-= (big_int &b, unsigned int c)
unsigned int &	operator-= (unsigned int &b, const big_int &c)
big_int &	operator-= (big_int &b, signed long c)
signed long &	operator-= (signed long &b, const big_int &c)
big_int &	operator-= (big_int &b, unsigned long c)
unsigned long &	operator-= (unsigned long &b, const big_int &c)
big_int &	operator-= (big_int &b, bool c)
bool &	operator-= (bool &b, const big_int &c)
big_int &	operator *= (big_int &b, char c)
char &	operator *= (char &b, const big_int &c)
big_int &	operator *= (big_int &b, signed char c)
signed char &	operator *= (signed char &b, const big_int &c)
big_int &	operator *= (big_int &b, unsigned char c)
unsigned char &	operator *= (unsigned char &b, const big_int &c)
big_int &	operator *= (big_int &b, signed short c)
signed short &	operator *= (signed short &b, const big_int &c)
big_int &	operator *= (big_int &b, unsigned short c)
unsigned short &	operator *= (unsigned short &b, const big_int &c)
big_int &	operator *= (big_int &b, signed int c)
signed int &	operator *= (signed int &b, const big_int &c)
big_int &	operator *= (big_int &b, unsigned int c)
unsigned int &	operator *= (unsigned int &b, const big_int &c)
big_int &	operator *= (big_int &b, signed long c)
signed long &	operator *= (signed long &b, const big_int &c)
big_int &	operator *= (big_int &b, unsigned long c)
unsigned long &	operator *= (unsigned long &b, const big_int &c)
big_int &	operator *= (big_int &b, bool c)
bool &	operator *= (bool &b, const big_int &c)
big_int &	operator/= (big_int &b, char c)
char &	operator/= (char &b, const big_int &c)
big_int &	operator/= (big_int &b, signed char c)
signed char &	operator/= (signed char &b, const big_int &c)
big_int &	operator/= (big_int &b, unsigned char c)
unsigned char &	operator/= (unsigned char &b, const big_int &c)
big_int &	operator/= (big_int &b, signed short c)
signed short &	operator/= (signed short &b, const big_int &c)
big_int &	operator/= (big_int &b, unsigned short c)
unsigned short &	operator/= (unsigned short &b, const big_int &c)
big_int &	operator/= (big_int &b, signed int c)
signed int &	operator/= (signed int &b, const big_int &c)
big_int &	operator/= (big_int &b, unsigned int c)
unsigned int &	operator/= (unsigned int &b, const big_int &c)
big_int &	operator/= (big_int &b, signed long c)
signed long &	operator/= (signed long &b, const big_int &c)
big_int &	operator/= (big_int &b, unsigned long c)
unsigned long &	operator/= (unsigned long &b, const big_int &c)
big_int &	operator/= (big_int &b, bool c)
bool &	operator/= (bool &b, const big_int &c)
big_int &	operator+= (big_int &b, float c)
float &	operator+= (float &b, const big_int &c)
big_int &	operator+= (big_int &b, double c)
double &	operator+= (double &b, const big_int &c)
big_int &	operator+= (big_int &b, long double c)
long double &	operator+= (long double &b, const big_int &c)
big_int &	operator-= (big_int &b, float c)
float &	operator-= (float &b, const big_int &c)
big_int &	operator-= (big_int &b, double c)
double &	operator-= (double &b, const big_int &c)
big_int &	operator-= (big_int &b, long double c)
long double &	operator-= (long double &b, const big_int &c)
big_int &	operator *= (big_int &b, float c)
float &	operator *= (float &b, const big_int &c)
big_int &	operator *= (big_int &b, double c)
double &	operator *= (double &b, const big_int &c)
big_int &	operator *= (big_int &b, long double c)
long double &	operator *= (long double &b, const big_int &c)
big_int &	operator/= (big_int &b, float c)
float &	operator/= (float &b, const big_int &c)
big_int &	operator/= (big_int &b, double c)
double &	operator/= (double &b, const big_int &c)
big_int &	operator/= (big_int &b, long double c)
long double &	operator/= (long double &b, const big_int &c)
big_int &	operator%= (big_int &b, char c)
char &	operator%= (char &b, const big_int &c)
big_int &	operator%= (big_int &b, signed char c)
signed char &	operator%= (signed char &b, const big_int &c)
big_int &	operator%= (big_int &b, unsigned char c)
unsigned char &	operator%= (unsigned char &b, const big_int &c)
big_int &	operator%= (big_int &b, signed short c)
signed short &	operator%= (signed short &b, const big_int &c)
big_int &	operator%= (big_int &b, unsigned short c)
unsigned short &	operator%= (unsigned short &b, const big_int &c)
big_int &	operator%= (big_int &b, signed int c)
signed int &	operator%= (signed int &b, const big_int &c)
big_int &	operator%= (big_int &b, unsigned int c)
unsigned int &	operator%= (unsigned int &b, const big_int &c)
big_int &	operator%= (big_int &b, signed long c)
signed long &	operator%= (signed long &b, const big_int &c)
big_int &	operator%= (big_int &b, unsigned long c)
unsigned long &	operator%= (unsigned long &b, const big_int &c)
big_int &	operator%= (big_int &b, bool c)
bool &	operator%= (bool &b, const big_int &c)
big_int	operator+ (char b, const big_int &c)
big_int	operator+ (const big_int &b, char c)
big_int	operator+ (signed char b, const big_int &c)
big_int	operator+ (const big_int &b, signed char c)
big_int	operator+ (unsigned char b, const big_int &c)
big_int	operator+ (const big_int &b, unsigned char c)
big_int	operator+ (signed short b, const big_int &c)
big_int	operator+ (const big_int &b, signed short c)
big_int	operator+ (unsigned short b, const big_int &c)
big_int	operator+ (const big_int &b, unsigned short c)
big_int	operator+ (signed int b, const big_int &c)
big_int	operator+ (const big_int &b, signed int c)
big_int	operator+ (unsigned int b, const big_int &c)
big_int	operator+ (const big_int &b, unsigned int c)
big_int	operator+ (signed long b, const big_int &c)
big_int	operator+ (const big_int &b, signed long c)
big_int	operator+ (unsigned long b, const big_int &c)
big_int	operator+ (const big_int &b, unsigned long c)
big_int	operator+ (bool b, const big_int &c)
big_int	operator+ (const big_int &b, bool c)
big_int	operator- (char b, const big_int &c)
big_int	operator- (const big_int &b, char c)
big_int	operator- (signed char b, const big_int &c)
big_int	operator- (const big_int &b, signed char c)
big_int	operator- (unsigned char b, const big_int &c)
big_int	operator- (const big_int &b, unsigned char c)
big_int	operator- (signed short b, const big_int &c)
big_int	operator- (const big_int &b, signed short c)
big_int	operator- (unsigned short b, const big_int &c)
big_int	operator- (const big_int &b, unsigned short c)
big_int	operator- (signed int b, const big_int &c)
big_int	operator- (const big_int &b, signed int c)
big_int	operator- (unsigned int b, const big_int &c)
big_int	operator- (const big_int &b, unsigned int c)
big_int	operator- (signed long b, const big_int &c)
big_int	operator- (const big_int &b, signed long c)
big_int	operator- (unsigned long b, const big_int &c)
big_int	operator- (const big_int &b, unsigned long c)
big_int	operator- (bool b, const big_int &c)
big_int	operator- (const big_int &b, bool c)
big_int	operator * (char b, const big_int &c)
big_int	operator * (const big_int &b, char c)
big_int	operator * (signed char b, const big_int &c)
big_int	operator * (const big_int &b, signed char c)
big_int	operator * (unsigned char b, const big_int &c)
big_int	operator * (const big_int &b, unsigned char c)
big_int	operator * (signed short b, const big_int &c)
big_int	operator * (const big_int &b, signed short c)
big_int	operator * (unsigned short b, const big_int &c)
big_int	operator * (const big_int &b, unsigned short c)
big_int	operator * (signed int b, const big_int &c)
big_int	operator * (const big_int &b, signed int c)
big_int	operator * (unsigned int b, const big_int &c)
big_int	operator * (const big_int &b, unsigned int c)
big_int	operator * (signed long b, const big_int &c)
big_int	operator * (const big_int &b, signed long c)
big_int	operator * (unsigned long b, const big_int &c)
big_int	operator * (const big_int &b, unsigned long c)
big_int	operator * (bool b, const big_int &c)
big_int	operator * (const big_int &b, bool c)
big_int	operator/ (char b, const big_int &c)
big_int	operator/ (const big_int &b, char c)
big_int	operator/ (signed char b, const big_int &c)
big_int	operator/ (const big_int &b, signed char c)
big_int	operator/ (unsigned char b, const big_int &c)
big_int	operator/ (const big_int &b, unsigned char c)
big_int	operator/ (signed short b, const big_int &c)
big_int	operator/ (const big_int &b, signed short c)
big_int	operator/ (unsigned short b, const big_int &c)
big_int	operator/ (const big_int &b, unsigned short c)
big_int	operator/ (signed int b, const big_int &c)
big_int	operator/ (const big_int &b, signed int c)
big_int	operator/ (unsigned int b, const big_int &c)
big_int	operator/ (const big_int &b, unsigned int c)
big_int	operator/ (signed long b, const big_int &c)
big_int	operator/ (const big_int &b, signed long c)
big_int	operator/ (unsigned long b, const big_int &c)
big_int	operator/ (const big_int &b, unsigned long c)
big_int	operator/ (bool b, const big_int &c)
big_int	operator/ (const big_int &b, bool c)
big_int	operator+ (float b, const big_int &c)
big_int	operator+ (const big_int &b, float c)
big_int	operator+ (double b, const big_int &c)
big_int	operator+ (const big_int &b, double c)
big_int	operator+ (long double b, const big_int &c)
big_int	operator+ (const big_int &b, long double c)
big_int	operator- (float b, const big_int &c)
big_int	operator- (const big_int &b, float c)
big_int	operator- (double b, const big_int &c)
big_int	operator- (const big_int &b, double c)
big_int	operator- (long double b, const big_int &c)
big_int	operator- (const big_int &b, long double c)
big_int	operator * (float b, const big_int &c)
big_int	operator * (const big_int &b, float c)
big_int	operator * (double b, const big_int &c)
big_int	operator * (const big_int &b, double c)
big_int	operator * (long double b, const big_int &c)
big_int	operator * (const big_int &b, long double c)
big_int	operator/ (float b, const big_int &c)
big_int	operator/ (const big_int &b, float c)
big_int	operator/ (double b, const big_int &c)
big_int	operator/ (const big_int &b, double c)
big_int	operator/ (long double b, const big_int &c)
big_int	operator/ (const big_int &b, long double c)
big_int	operator% (char b, const big_int &c)
big_int	operator% (const big_int &b, char c)
big_int	operator% (signed char b, const big_int &c)
big_int	operator% (const big_int &b, signed char c)
big_int	operator% (unsigned char b, const big_int &c)
big_int	operator% (const big_int &b, unsigned char c)
big_int	operator% (signed short b, const big_int &c)
big_int	operator% (const big_int &b, signed short c)
big_int	operator% (unsigned short b, const big_int &c)
big_int	operator% (const big_int &b, unsigned short c)
big_int	operator% (signed int b, const big_int &c)
big_int	operator% (const big_int &b, signed int c)
big_int	operator% (unsigned int b, const big_int &c)
big_int	operator% (const big_int &b, unsigned int c)
big_int	operator% (signed long b, const big_int &c)
big_int	operator% (const big_int &b, signed long c)
big_int	operator% (unsigned long b, const big_int &c)
big_int	operator% (const big_int &b, unsigned long c)
big_int	operator% (bool b, const big_int &c)
big_int	operator% (const big_int &b, bool c)
bool	operator== (char b, const big_int &c)
bool	operator== (const big_int &b, char c)
bool	operator!= (char b, const big_int &c)
bool	operator!= (const big_int &b, char c)
bool	operator<= (char b, const big_int &c)
bool	operator<= (const big_int &b, char c)
bool	operator>= (char b, const big_int &c)
bool	operator>= (const big_int &b, char c)
bool	operator< (char b, const big_int &c)
bool	operator< (const big_int &b, char c)
bool	operator> (char b, const big_int &c)
bool	operator> (const big_int &b, char c)
bool	operator== (signed char b, const big_int &c)
bool	operator== (const big_int &b, signed char c)
bool	operator!= (signed char b, const big_int &c)
bool	operator!= (const big_int &b, signed char c)
bool	operator<= (signed char b, const big_int &c)
bool	operator<= (const big_int &b, signed char c)
bool	operator>= (signed char b, const big_int &c)
bool	operator>= (const big_int &b, signed char c)
bool	operator< (signed char b, const big_int &c)
bool	operator< (const big_int &b, signed char c)
bool	operator> (signed char b, const big_int &c)
bool	operator> (const big_int &b, signed char c)
bool	operator== (unsigned char b, const big_int &c)
bool	operator== (const big_int &b, unsigned char c)
bool	operator!= (unsigned char b, const big_int &c)
bool	operator!= (const big_int &b, unsigned char c)
bool	operator<= (unsigned char b, const big_int &c)
bool	operator<= (const big_int &b, unsigned char c)
bool	operator>= (unsigned char b, const big_int &c)
bool	operator>= (const big_int &b, unsigned char c)
bool	operator< (unsigned char b, const big_int &c)
bool	operator< (const big_int &b, unsigned char c)
bool	operator> (unsigned char b, const big_int &c)
bool	operator> (const big_int &b, unsigned char c)
bool	operator== (signed short b, const big_int &c)
bool	operator== (const big_int &b, signed short c)
bool	operator!= (signed short b, const big_int &c)
bool	operator!= (const big_int &b, signed short c)
bool	operator<= (signed short b, const big_int &c)
bool	operator<= (const big_int &b, signed short c)
bool	operator>= (signed short b, const big_int &c)
bool	operator>= (const big_int &b, signed short c)
bool	operator< (signed short b, const big_int &c)
bool	operator< (const big_int &b, signed short c)
bool	operator> (signed short b, const big_int &c)
bool	operator> (const big_int &b, signed short c)
bool	operator== (unsigned short b, const big_int &c)
bool	operator== (const big_int &b, unsigned short c)
bool	operator!= (unsigned short b, const big_int &c)
bool	operator!= (const big_int &b, unsigned short c)
bool	operator<= (unsigned short b, const big_int &c)
bool	operator<= (const big_int &b, unsigned short c)
bool	operator>= (unsigned short b, const big_int &c)
bool	operator>= (const big_int &b, unsigned short c)
bool	operator< (unsigned short b, const big_int &c)
bool	operator< (const big_int &b, unsigned short c)
bool	operator> (unsigned short b, const big_int &c)
bool	operator> (const big_int &b, unsigned short c)
bool	operator== (signed int b, const big_int &c)
bool	operator== (const big_int &b, signed int c)
bool	operator!= (signed int b, const big_int &c)
bool	operator!= (const big_int &b, signed int c)
bool	operator<= (signed int b, const big_int &c)
bool	operator<= (const big_int &b, signed int c)
bool	operator>= (signed int b, const big_int &c)
bool	operator>= (const big_int &b, signed int c)
bool	operator< (signed int b, const big_int &c)
bool	operator< (const big_int &b, signed int c)
bool	operator> (signed int b, const big_int &c)
bool	operator> (const big_int &b, signed int c)
bool	operator== (unsigned int b, const big_int &c)
bool	operator== (const big_int &b, unsigned int c)
bool	operator!= (unsigned int b, const big_int &c)
bool	operator!= (const big_int &b, unsigned int c)
bool	operator<= (unsigned int b, const big_int &c)
bool	operator<= (const big_int &b, unsigned int c)
bool	operator>= (unsigned int b, const big_int &c)
bool	operator>= (const big_int &b, unsigned int c)
bool	operator< (unsigned int b, const big_int &c)
bool	operator< (const big_int &b, unsigned int c)
bool	operator> (unsigned int b, const big_int &c)
bool	operator> (const big_int &b, unsigned int c)
bool	operator== (signed long b, const big_int &c)
bool	operator== (const big_int &b, signed long c)
bool	operator!= (signed long b, const big_int &c)
bool	operator!= (const big_int &b, signed long c)
bool	operator<= (signed long b, const big_int &c)
bool	operator<= (const big_int &b, signed long c)
bool	operator>= (signed long b, const big_int &c)
bool	operator>= (const big_int &b, signed long c)
bool	operator< (signed long b, const big_int &c)
bool	operator< (const big_int &b, signed long c)
bool	operator> (signed long b, const big_int &c)
bool	operator> (const big_int &b, signed long c)
bool	operator== (unsigned long b, const big_int &c)
bool	operator== (const big_int &b, unsigned long c)
bool	operator!= (unsigned long b, const big_int &c)
bool	operator!= (const big_int &b, unsigned long c)
bool	operator<= (unsigned long b, const big_int &c)
bool	operator<= (const big_int &b, unsigned long c)
bool	operator>= (unsigned long b, const big_int &c)
bool	operator>= (const big_int &b, unsigned long c)
bool	operator< (unsigned long b, const big_int &c)
bool	operator< (const big_int &b, unsigned long c)
bool	operator> (unsigned long b, const big_int &c)
bool	operator> (const big_int &b, unsigned long c)
bool	operator== (bool b, const big_int &c)
bool	operator== (const big_int &b, bool c)
bool	operator!= (bool b, const big_int &c)
bool	operator!= (const big_int &b, bool c)
bool	operator<= (bool b, const big_int &c)
bool	operator<= (const big_int &b, bool c)
bool	operator>= (bool b, const big_int &c)
bool	operator>= (const big_int &b, bool c)
bool	operator< (bool b, const big_int &c)
bool	operator< (const big_int &b, bool c)
bool	operator> (bool b, const big_int &c)
bool	operator> (const big_int &b, bool c)
bool	operator== (float b, const big_int &c)
bool	operator== (const big_int &b, float c)
bool	operator!= (float b, const big_int &c)
bool	operator!= (const big_int &b, float c)
bool	operator<= (float b, const big_int &c)
bool	operator<= (const big_int &b, float c)
bool	operator>= (float b, const big_int &c)
bool	operator>= (const big_int &b, float c)
bool	operator< (float b, const big_int &c)
bool	operator< (const big_int &b, float c)
bool	operator> (float b, const big_int &c)
bool	operator> (const big_int &b, float c)
bool	operator== (double b, const big_int &c)
bool	operator== (const big_int &b, double c)
bool	operator!= (double b, const big_int &c)
bool	operator!= (const big_int &b, double c)
bool	operator<= (double b, const big_int &c)
bool	operator<= (const big_int &b, double c)
bool	operator>= (double b, const big_int &c)
bool	operator>= (const big_int &b, double c)
bool	operator< (double b, const big_int &c)
bool	operator< (const big_int &b, double c)
bool	operator> (double b, const big_int &c)
bool	operator> (const big_int &b, double c)
bool	operator== (long double b, const big_int &c)
bool	operator== (const big_int &b, long double c)
bool	operator!= (long double b, const big_int &c)
bool	operator!= (const big_int &b, long double c)
bool	operator<= (long double b, const big_int &c)
bool	operator<= (const big_int &b, long double c)
bool	operator>= (long double b, const big_int &c)
bool	operator>= (const big_int &b, long double c)
bool	operator< (long double b, const big_int &c)
bool	operator< (const big_int &b, long double c)
bool	operator> (long double b, const big_int &c)
bool	operator> (const big_int &b, long double c)
bool	is_null (const big_int &x)
bool	is_unit (const big_int &x)
bool	is_opposite_unit (const big_int &x)
bool	is_positive (const big_int &x)
bool	is_negative (const big_int &x)
bool	is_even (const big_int &x)
bool	is_odd (const big_int &x)
template<typename T>
T	intsqrt (const T &a)
	Integer square root of a.
big_int	sqrt (const big_int &a)
big_int	abs (const big_int &x)
	Returns absolutly value of x.
big_int	pow (const big_int &x, int p)
	Raise x in to a power p.
big_int	pow (const big_int &x, const big_int &p)
	Raise x in to a power p.
big_int	log2 (const big_int &x)
	Returns the base-2 logarithm of abs(x). If x == 0, returns -1.
template<typename T1, typename T2>
int	cmp (const T1 &a, const T2 &b)
	Performs Arageli like comparision.
template<typename T>
int	sign (const T &x)
	Sign of element.
template<typename T>
bool	is_even (const T &x)
	Returns true if x is even.
template<typename T>
bool	is_odd (const T &x)
	Returns true if x is odd.
template<typename T1, typename T2>
bool	is_divisible (const T1 &a, const T2 &b)
	Returns true if a is divisible by b.
template<typename T>
bool	is_positive (const T &x)
	Returns true if x is greater then null.
template<typename T>
bool	is_negative (const T &x)
	Returns true if x is less then null.
template<typename T>
bool	is_integer (const T &x)
	Returns true if x is integer.
template<typename Out, typename T, typename M, typename CFG>
void	output_list (Out &out, const cone< T, M, CFG > &x)
template<typename Out, typename T, typename M, typename CFG>
Out &	operator<< (Out &out, const cone< T, M, CFG > &x)
template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>
cone< T1, M1, CFG1 >	intersection (cone< T1, M1, CFG1 > a, const cone< T2, M2, CFG2 > &b)
template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>
cone< T1, M1, CFG1 >	cone_union (cone< T1, M1, CFG1 > a, const cone< T2, M2, CFG2 > &b)
template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>
int	cmp (const cone< T1, M1, CFG1 > &a, const cone< T2, M2, CFG2 > &b)
std::ostream &	operator<< (std::ostream &out, const exception &e)
	ARAGELI_UNARY_FUNCTION_TRAITS (indirection, typename omit_asterisk< Arg >::type, false, false)
	ARAGELI_UNARY_FUNCTION_TRAITS (postfix_increment, typename omit_ref< Arg >::type, true, false)
	ARAGELI_UNARY_FUNCTION_TRAITS (postfix_decrement, typename omit_ref< Arg >::type, true, false)
	ARAGELI_BINARY_FUNCTION_TRAITS (subscript, typename omit_asterisk< Arg1 >::type, false, false, false)
template<typename M>
void	gauss_field_row_iter (M &a, typename M::size_type row, typename M::size_type col)
	Gauss elimination of column col with row manipulation.
template<typename M>
void	gauss_field_col_iter (M &a, typename M::size_type row, typename M::size_type col)
	Gauss elimination of row with column manipulation.
template<typename M, typename T>
void	gauss_bareiss_row_iter (M &a, typename M::size_type row, typename M::size_type col, T &det, T &det_denom)
	Gauss-Bareiss elimination of column col with row manipulation.
template<typename M, typename T>
void	gauss_bareiss_col_iter (M &a, typename M::size_type row, typename M::size_type col, T &det, T &det_denom)
	Gauss-Bareiss elimination of row with column manipulation.
template<typename M>
void	gauss_bareiss_row_iter (M &a, typename M::size_type row, typename M::size_type col)
	Gauss-Bareiss elimination of column col with row manipulation.
template<typename M>
void	gauss_bareiss_col_iter (M &a, typename M::size_type row, typename M::size_type col)
	Gauss-Bareiss elimination of row with column manipulation.
template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>
void	rref_gauss_field (const A &a, B &b, Q &q, Basis &basis, T &det, const T_factory &tfctr, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>
void	rref_gauss_field (const A &a, B &b, Q &q, Basis &basis, T &det, Ctrler ctrler)
	Produces the reduced row echelon form B of a matrix A.
template<typename A, typename B, typename Q, typename Basis, typename T>
void	rref_gauss_field (const A &a, B &b, Q &q, Basis &basis, T &det)
	Produces the reduced row echelon form B of a matrix A.
template<typename A, typename B, typename Q, typename Basis>
void	rref_gauss_field (const A &a, B &b, Q &q, Basis &basis)
	Produces the reduced row echelon form B of a matrix A.
template<typename A, typename B, typename Q>
void	rref_gauss_field (const A &a, B &b, Q &q)
	Produces the reduced row echelon form B of a matrix A.
template<typename A, typename B>
void	rref_gauss_field (const A &a, B &b)
	Produces the reduced row echelon form B of a matrix A.
template<typename A>
A	rref_gauss_field (const A &a)
	Produces the reduced row echelon form B of a matrix A.
template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>
void	rref_field (const A &a, B &b, Q &q, Basis &basis, T &det, const T_factory &tfctr, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>
void	rref_field (const A &a, B &b, Q &q, Basis &basis, T &det, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B, typename Q, typename Basis, typename T>
void	rref_field (const A &a, B &b, Q &q, Basis &basis, T &det)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B, typename Q, typename Basis>
void	rref_field (const A &a, B &b, Q &q, Basis &basis)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B, typename Q>
void	rref_field (const A &a, B &b, Q &q)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A, typename B>
void	rref_field (const A &a, B &b)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A>
A	rref_field (const A &a)
	Produces the reduced row echelon form B of the matrix a over a field.
template<typename A1, typename A2, typename I>
void	mat_col_copy_order (const A1 &a1, A2 &a2, const I &idx)
	Copies columns from a1 to a2 in order indexes in idx then tails the rest.
template<typename A1, typename A2, typename I>
void	vec_copy_order (const A1 &a1, A2 &a2, const I &idx)
	Copies elements from a1 to a2 in order indexes in idx then tails the rest.
template<typename A, typename B>
void	vec_inverse_permutation (const A &a, B &b)
	Inverses permutation vector.
template<typename A, typename B, typename Q, typename Basis_in, typename Basis_out, typename Det>
void	rref_order (const A &a, B &b, Q &q, const Basis_in &basis_in, Basis_out &basis_out, Det &det)
	Produces the reduced row echelon from B of the matrix A with a specific column order.
template<typename T, bool REFCNT>
matrix< T, REFCNT >	inverse (const matrix< T, REFCNT > &A)
	Matrix inversion.
template<typename T, bool REFCNT>
T	det (const matrix< T, REFCNT > &A)
	Returns determinant of A.
template<typename T, bool REFCNT>
matrix< T, REFCNT >::size_type	rank (const matrix< T, REFCNT > &A)
	Returns a rank of a matrix.
template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>
void	rref_gauss_bareiss (const A &a, B &b, Q &q, Basis &basis, T &det, const T_factory &tfctr, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>
void	rref_gauss_bareiss (const A &a, B &b, Q &q, Basis &basis, T &det, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T>
void	rref_gauss_bareiss (const A &a, B &b, Q &q, Basis &basis, T &det)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis>
void	rref_gauss_bareiss (const A &a, B &b, Q &q, Basis &basis)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q>
void	rref_gauss_bareiss (const A &a, B &b, Q &q)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B>
void	rref_gauss_bareiss (const A &a, B &b)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A>
A	rref_gauss_bareiss (const A &a)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>
void	rref_int (const A &a, B &b, Q &q, Basis &basis, T &det, const T_factory &tfctr, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>
void	rref_int (const A &a, B &b, Q &q, Basis &basis, T &det, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T>
void	rref_int (const A &a, B &b, Q &q, Basis &basis, T &det)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis>
void	rref_int (const A &a, B &b, Q &q, Basis &basis)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q>
void	rref_int (const A &a, B &b, Q &q)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B>
void	rref_int (const A &a, B &b)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A>
A	rref_int (const A &a)
	Produces the reduced row echelon form B of the matrix a over an integer domain.
template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>
void	rref (const A &a, B &b, Q &q, Basis &basis, T &det, const T_factory &tfctr, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a.
template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>
void	rref (const A &a, B &b, Q &q, Basis &basis, T &det, Ctrler ctrler)
	Produces the reduced row echelon form B of the matrix a.
template<typename A, typename B, typename Q, typename Basis, typename T>
void	rref (const A &a, B &b, Q &q, Basis &basis, T &det)
	Produces the reduced row echelon form B of the matrix a.
template<typename A, typename B, typename Q, typename Basis>
void	rref (const A &a, B &b, Q &q, Basis &basis)
	Produces the reduced row echelon form B of the matrix a.
template<typename A, typename B, typename Q>
void	rref (const A &a, B &b, Q &q)
	Produces the reduced row echelon form B of the matrix a.
template<typename A, typename B>
void	rref (const A &a, B &b)
	Produces the reduced row echelon form B of the matrix a.
template<typename A>
A	rref (const A &a)
	Produces the reduced row echelon form B of the matrix a.
template<typename T, bool REFCNT>
T	det_int (const matrix< T, REFCNT > &A)
	Returns determinant of integer matrix A.
template<typename T, bool REFCNT>
matrix< T, REFCNT >::size_type	rank_int (const matrix< T, REFCNT > &A)
	Returns a rank of integer matrix.
template<class T>
matrix< T >	hermite_old (const matrix< T > &m_)
	The old original function for producing Hermite form.
template<typename MA, typename MH, typename MU>
void	hermite_upper (const MA &A, MH &H, MU &U)
	Produces the upper Hermite form H of an integer matrix A.
template<typename MA, typename MH, typename MU>
void	hermite_lower (const MA &A, MH &H, MU &U)
	Produces the lower Hermite form H of an integer matrix A.
template<typename M>
M	hermite (const M &A)
	Produces the upper Hermite form H of an integer matrix A.
template<typename M>
M	hermite_transform_matrix (const M &A)
	Produces the unimodular princpal left transform U such that U*A is a Hermite form of an integer matrix A.
template<typename T, typename T_factory>
T	inverse_mod (const T &a, const T &m, const T_factory &tfctr)
	Returns inversion of a modulo n.
template<typename T>
T	inverse_mod (const T &a, const T &n)
	Returns inversion of a modulo n.
template<typename T, typename I, typename T_factory>
T	power_mod (T a, I n, const T &m, const T_factory &tfctr)
	Exponentiates a in to power n modulo m via squaring and adding.
template<typename T, typename I>
T	power_mod (const T &a, const I &n, const T &m)
	Exponentiates a in to power n modulo m via squaring and adding.
template<typename T1, typename T2, typename T3>
T3	mod (const T1 &a, const T2 &b, const T3 &d)
template<typename T1, typename T2>
T2	mod (const T1 &a, const T2 &b)
	Compute a modulo b.
template<typename T1, typename T2, typename T3>
T3	div_mod (const T1 &a, const T2 &b, const T3 &d)
	Compute a/b modulo d.
template<typename T1, typename T2, typename T3>
T3	rem_mod (const T1 &a, const T2 &b, const T3 &d)
	Compute residue of division a by b modulo d.
template<typename T1, typename T2>
T2	ann (const T1 &a, const T2 &n)
	Compute n/gcd(a, n).
template<typename T1, typename T2, typename T3>
T3	quo_mod (const T1 &a, const T2 &b, const T3 &d)
template<typename T>
T	split (const T &a, const T &d)
template<typename T>
T	stab (const T &a, const T &b, const T &N)
template<typename T>
T	split_stab (const T &a, const T &b, const T &N)
template<typename T>
T	unit (const T &a, const T &N)
template<typename T>
T	stab (const T &a, const T &b, const T &N, const T &d)
template<typename T>
T	split_stab (const T &a, const T &b, const T &N, const T &d)
template<typename T>
T	split_mod (const T &a, const T &d)
template<typename T>
T	stab_mod (const T &a, const T &b, const T &N)
template<typename T>
T	stab_mod (const T &a, const T &b, const T &N, const T &d)
template<typename T>
bool	is_invertible_mod (const T &a, const T &N)
	Returns true iff a is invertible element modulo N.
template<typename T>
std::size_t	nbits (const T &a)
	Compute number of bit in binary notation of a.
template<typename T, typename T_factory>
std::size_t	nbits (T a, const T_factory &tfctr)
	Compute number of bit in binary notation of a.
template<typename T, typename T_factory>
T	factorial_successive_multiplication (T a, const T_factory &tfctr)
	Computes factorial via just successive multiplication (by definition).
template<typename T>
T	factorial_successive_multiplication (const T &a)
	Computes factorial via just successive multiplication (by definition).
template<typename T, typename T_factory>
T	factorial_even_odd_multiplication (T a, const T_factory &tfctr)
	Computes factorial via even and odd multiplier separation.
template<typename T>
T	factorial_even_odd_multiplication (const T &a)
	Computes factorial via even and odd multiplier separation.
template<typename T, typename T_factory>
T	factorial (const T &a, const T_factory &tfctr)
	Computes factorial of a via apropriate algorithm.
template<typename T>
T	factorial (const T &a)
	Computes factorial of a via apropriate algorithm.
template<typename T, typename TT>
T	sqrt_mod_shenks (const T &a, const T &n, const TT &tt)
	The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).
template<typename T>
T	sqrt_mod_shenks (const T &a, const T &n)
	The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).
template<typename Gen, typename IntGen>
void	intconvex_simple (const Gen &gen, IntGen &intgen)
	A convex hull of integer points of a polyhedron.
template<typename A, typename T, typename Ctrler>
void	intcount_barvinok (const A &a, T &res, Ctrler ctrler)
	Counts all integer points in bodily polytope.
template<typename A, typename T>
void	intcount_barvinok (const A &a, T &res)
	Counts all integer points in bodily polytope.
template<typename A>
A::element_type	intcount_barvinok (const A &a)
	Counts all integer points in bodily polytope.
template<typename T>
interval< T >	operator+ (const interval< T > &a, const interval< T > &b)
template<typename T>
interval< T >	operator- (const interval< T > &a, const interval< T > &b)
template<typename T>
interval< T >	operator * (const interval< T > &a, const interval< T > &b)
template<typename T>
interval< T >	operator/ (const interval< T > &a, const interval< T > &b)
template<typename T1, typename T2>
bool	are_overlap_intervals_oooo (const T1 &a, const T2 &b)
template<typename Seg1, typename Seg2>
bool	is_overlap_segs (const Seg1 &a, const Seg2 &b)
template<typename Out, typename T>
Out &	operator<< (Out &out, const interval< T > &x)
template<typename In, typename T>
In &	operator>> (In &in, interval< T > &x)
template<typename T1, typename T2>
bool	are_comparable_oooo (const interval< T1 > &a, const interval< T2 > &b)
	Determines if a and b are exactly comparable as two open intervals.
template<typename T1, typename T2>
int	cmp (const interval< T1 > &a, const interval< T2 > &b)
	Semi-lexicographical comparision between two intervals.
template<typename T1, typename T2>
bool	operator< (const interval< T1 > &a, const interval< T2 > &b)
template<typename T1, typename T2>
bool	operator> (const interval< T1 > &a, const interval< T2 > &b)
template<typename T1, typename T2>
bool	operator<= (const interval< T1 > &a, const interval< T2 > &b)
template<typename T1, typename T2>
bool	operator>= (const interval< T1 > &a, const interval< T2 > &b)
template<typename T1, typename T2>
bool	operator== (const interval< T1 > &a, const interval< T2 > &b)
template<typename T1, typename T2>
bool	operator!= (const interval< T1 > &a, const interval< T2 > &b)
template<typename T>
interval< T >	abs (const interval< T > &x)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_polynom_first_default (std::basic_ostream< Ch, ChT > &out, const T &x)
	Default ouputting method for subexpression as the first coefficient in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_polynom_internal_default (std::basic_ostream< Ch, ChT > &out, const T &x)
	Default ouputting method for subexpression as an internal coefficient in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_pow_default (std::basic_ostream< Ch, ChT > &out, const T &x)
	Default ouputting method for subexpression as a degree of variable in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_polynom_first_default (std::basic_istream< Ch, ChT > &in, T &x)
	Default inputting method for subexpression as the first coefficient in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_polynom_internal_default (std::basic_istream< Ch, ChT > &in, T &x)
	Default inputting method for subexpression as an internal coefficient in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_pow_default (std::basic_istream< Ch, ChT > &in, T &x)
	Default inutting method for subexpression as a degree of variable in a polynomial.
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_polynom_first (std::basic_ostream< Ch, ChT > &out, const T &x)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_polynom_internal (std::basic_ostream< Ch, ChT > &out, const T &x)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_pow (std::basic_ostream< Ch, ChT > &out, const T &x)
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_polynom_first (std::basic_istream< Ch, ChT > &in, T &x)
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_polynom_internal (std::basic_istream< Ch, ChT > &in, T &x)
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_pow (std::basic_istream< Ch, ChT > &in, T &x)
template<typename T, typename TB, typename F>
apply_iterator< T, TB, F >	operator+ (apply_iterator< T, TB, F > x, typename apply_iterator< T, TB, F >::difference_type n)
template<typename T, typename TB, typename F>
apply_iterator< T, TB, F >	operator- (apply_iterator< T, TB, F > x, typename apply_iterator< T, TB, F >::difference_type n)
template<typename T, typename TB, typename F>
std::iterator_traits< TB >::difference_type	operator- (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator== (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator!= (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator< (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator> (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator<= (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB, typename F>
bool	operator>= (const apply_iterator< T, TB, F > &a, const apply_iterator< T, TB, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
std::iterator_traits< TB1 >::difference_type	operator- (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator== (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator!= (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator< (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator> (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator<= (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename T, typename TB1, typename TB2, typename F>
bool	operator>= (const Iterpair< T, TB1, TB2, F > &a, const Iterpair< T, TB1, TB2, F > &b)
template<typename B_type, typename H_type>
bool	lll_reduction (B_type &B, H_type &H)
	LLL basis reduction.
big_int	entier (const big_int &de)
big_int	frac (const big_int &de, std::size_t kbits)
std::size_t	lg10 (const big_int &b)
	Returns lg (b).
std::size_t	lg10 (std::size_t b)
	Returns lg (b).
big_int	power_of_ten (std::size_t pow)
	Returns 10^pow.
big_int	entier_1 (const big_int &be)
big_int	frac_1 (const big_int &de, std::size_t kbits)
	Returns 10 ^ {de/log2_10} with kbits - 1 precision.
void	do_bin_convert (const big_int &dm, const big_int &de, std::size_t p, big_int &bm, big_int &be)
std::size_t	do_dec_convert (big_int &dm, big_int &de, std::size_t p, const big_int &bm, const big_int &be)
template<typename T, bool REFCNT>
matrix< T, true >	transpose (const matrix< T, REFCNT > &a)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
int	cmp (const matrix< T1, REFCNT1 > &a, const matrix< T2, REFCNT2 > &b)
	Lexicographical comparision of two matrix.
template<typename T1, typename T2, typename T3>
T3 &	each_add_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	add_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	add_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_sub_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	sub_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	sub_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_mul_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mul_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mul_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_div_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	div_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	div_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_mod_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mod_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mod_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_bitand_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitand_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitand_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_bitor_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitor_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitor_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_bitxor_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitxor_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitxor_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_shl_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shl_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shl_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	each_shr_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shr_matrix_scalar (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shr_scalar_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mul_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	div_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	add_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	sub_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	mod_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitand_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitor_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	bitxor_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shl_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, typename T2, typename T3>
T3 &	shr_matrix_matrix (const T1 &a, const T2 &b, T3 &res)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 >	operator * (const matrix< T1, REFCNT1 > &m, const vector< T2, REFCNT2 > &x)
	Matrix by vector multiplication.
template<typename T2, bool REFCNT2, typename T1, bool REFCNT1>
vector< T2, REFCNT2 >	operator * (const vector< T2, REFCNT2 > &x, const matrix< T1, REFCNT1 > &m)
	Vector by matrix multiplication.
template<typename T, bool REFCNT>
std::ostream &	output_list (std::ostream &out, const matrix< T, REFCNT > &x, const char *first_bracket=matrix_output_list_first_bracket_default, const char *second_bracket=matrix_output_list_second_bracket_default, const char *row_separator=matrix_output_list_row_separator_default, const char *first_row_bracket=matrix_output_list_first_row_bracket_default, const char *second_row_bracket=matrix_output_list_second_row_bracket_default, const char *col_separator=matrix_output_list_col_separator_default)
	Simple output of the matrix.
template<typename T, bool REFCNT>
std::istream &	input_list (std::istream &out, matrix< T, REFCNT > &x, const char *first_bracket=matrix_input_list_first_bracket_default, const char *second_bracket=matrix_input_list_second_bracket_default, const char *row_separator=matrix_input_list_row_separator_default, const char *first_row_bracket=matrix_input_list_first_row_bracket_default, const char *second_row_bracket=matrix_input_list_second_row_bracket_default, const char *col_separator=matrix_input_list_col_separator_default)
	Simple input of the matrix.
template<typename T, bool REFCNT>
std::ostream &	output_aligned (std::ostream &out, const matrix< T, REFCNT > &x, const char *left_col=matrix_output_aligned_left_col_default, const char *right_col=matrix_output_aligned_right_col_default, const char *inter_col=matrix_output_aligned_inter_col_default)
	Aligned output of the matrix.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
std::ostream &	output_aligned_ver_pair (std::ostream &out, const matrix< T1, REFCNT1 > &m1, const matrix< T2, REFCNT2 > &m2, const char *left_col="|| ", const char *right_col=" ||", const char *inter_col=" ", const char *hsplitter="-")
	Vertical aligned output of a pair of matrices.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
std::ostream &	output_aligned_hor_pair (std::ostream &out, const matrix< T1, REFCNT1 > &m1, const matrix< T2, REFCNT2 > &m2, const char *left_col="|| ", const char *right_col=" ||", const char *inter_col=" ", const char *vsplitter=" | ")
	Horizontal aligned output of a pair of matrices.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2, typename T3, bool REFCNT3>
std::ostream &	output_aligned_corner_triplet_br (std::ostream &out, const matrix< T1, REFCNT1 > &m1, const matrix< T2, REFCNT2 > &m2, const matrix< T3, REFCNT3 > &m3, const char *left_col="|| ", const char *right_col=" ||", const char *inter_col=" ", const char *vsplitter=" | ", const char *hsplitter="-")
	Aligned output of a triplet of matrices.
template<typename T, bool REFCNT>
std::ostream &	operator<< (std::ostream &out, const matrix< T, REFCNT > &x)
	Standard output routine (default type of outputting) for the matrix.
template<typename T, bool REFCNT>
std::istream &	operator>> (std::istream &out, matrix< T, REFCNT > &x)
	Standard input routine (default type of inputting) for the matrix.
template<typename T, bool REFCNT>
std::ofstream &	operator<< (std::ofstream &out, const matrix< T, REFCNT > &x)
	WARNING! TEMPORARY DEFINITION!!!
template<typename T, bool REFCNT>
std::ifstream &	operator>> (std::ifstream &out, matrix< T, REFCNT > &x)
	WARNING! TEMPORARY DEFINITION!!!
template<typename T, bool REFCNT>
std::ostream &	operator<< (std::ostringstream &out, const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	operator>> (std::istringstream &out, matrix< T, REFCNT > &x)
	Standard input routine (default type of inputting) for the matrix.
template<typename T, bool REFCNT>
matrix< T, REFCNT >	opposite (const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
matrix< T, REFCNT > &	opposite (const matrix< T, REFCNT > &x, matrix< T, REFCNT > *y)
template<typename T, bool REFCNT>
matrix< T, REFCNT > &	opposite (matrix< T, REFCNT > *x)
template<typename T, bool REFCNT>
matrix< T, REFCNT > &	inverse (const matrix< T, REFCNT > &x, matrix< T, REFCNT > *y)
template<typename T, bool REFCNT>
matrix< T, REFCNT > &	inverse (matrix< T, REFCNT > *x)
template<typename T, bool REFCNT>
bool	is_unit (const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
bool	is_opposite_unit (const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
bool	is_null (const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_polynom_first (std::ostream &out, const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_polynom_internal (std::ostream &out, const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_pow (std::ostream &out, const matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_polynom_first (std::istream &in, matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_polynom_internal (std::istream &in, matrix< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_pow (std::istream &in, matrix< T, REFCNT > &x)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2, typename T3, bool REFCNT3>
void	fill_submatrix_col (const matrix< T1, REFCNT1 > &orig, const vector< T2, REFCNT2 > &indexes, matrix< T3, REFCNT3 > &res)
	Makes submatrix from columns of another matrix with particular indexes.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2, typename T3, bool REFCNT3>
void	fill_submatrix_row (const matrix< T1, REFCNT1 > &orig, const vector< T2, REFCNT2 > &indexes, matrix< T3, REFCNT3 > &res)
	Makes submatrix from rows of another matrix with particular indexes.
template<typename T>
T	safe_reference (const T &x)
	Makes and returns a temporary copy of the argument.
template<typename T1, typename T2, typename Outiter>
void	generate_range_helper (T1 &t1, const T2 &t2, Outiter outiter)
template<typename T1, typename T2, typename T3, typename Outiter>
void	generate_range_helper (T1 &t1, const T2 &t2, const T3 &t3, Outiter outiter)
template<typename T1, typename T2, typename Outiter>
void	generate_range_helper_wo_inc (T1 &t1, const T2 &t2, Outiter outiter)
template<typename Outiter>
void	generate_range_helper (bool &t1, bool t2, Outiter outiter)
template<typename Outiter>
void	generate_range_helper (float &t1, float t2, Outiter outiter)
template<typename Outiter>
void	generate_range_helper (double &t1, double t2, Outiter outiter)
template<typename Outiter>
void	generate_range_helper (long double &t1, long double t2, Outiter outiter)
template<typename A, typename F, typename Q, typename E, typename Ctrler>
void	skeleton_motzkin_burger (A &a, F &f, Q &q, E &e, Ctrler ctrler)
	The Motzkin-Burger algorithm without modifications.
template<typename A, typename F, typename Q, typename E>
void	skeleton_motzkin_burger (A &a, F &f, Q &q, E &e)
	The Motzkin-Burger algorithm without modifications.
template<typename A, typename F, typename Q, typename E, typename Ctrler>
void	skeleton_motzkin_burger_min (A &a, F &f, Q &q, E &e, Ctrler ctrler)
	The Motzkin-Burger algorithm with selecting minimum elements.
template<typename A, typename F, typename Q, typename E>
void	skeleton_motzkin_burger_min (A &a, F &f, Q &q, E &e)
	The Motzkin-Burger algorithm with selecting minimum elements.
template<typename A, typename F, typename Q, typename E, typename Ctrler>
void	skeleton_motzkin_burger_max (A &a, F &f, Q &q, E &e, Ctrler ctrler)
	The Motzkin-Burger algorithm with selecting maximum elements.
template<typename A, typename F, typename Q, typename E>
void	skeleton_motzkin_burger_max (A &a, F &f, Q &q, E &e)
	The Motzkin-Burger algorithm with selecting maximum elements.
template<typename A, typename F, typename Q, typename E>
void	integer_conv_motzkin_burger (A &a, F &f, Q &q, E &e)
template<typename P1, typename P2, typename PQ, typename PR>
void	polynom_divide_simple (const P1 &p1, const P2 &p2, PQ &pq, PR &pr)
	Division of two univariate polynomials with quotient and remainder.
template<typename P1, typename P2, typename PQ, typename PR, typename T>
void	polynom_pseudodivide_simple (const P1 &p1, const P2 &p2, PQ &pq, PR &pr, T &multiplier)
template<typename P, typename T>
T &	polynom_rational_to_int_value (const P &p, T &res)
template<typename Pr, typename Pi, typename X>
void	polynom_rational_to_int (const Pr &pr, Pi &pi, const X &x)
template<typename P1, typename P2, typename PQ, typename PR>
void	polynom_divide_rational_simple (P1 p1, P2 p2, PQ &pq, PR &pr)
template<typename P1, typename P2, typename PQ, typename PR>
void	polynom_divide (const P1 &p1, const P2 &p2, PQ &pq, PR &pr, const type_category::type &)
template<typename P1, typename P2, typename PQ, typename PR>
void	polynom_divide (const P1 &p1, const P2 &p2, PQ &pq, PR &pr, const type_category::rational &)
template<typename P1, typename P2, typename PQ, typename PR>
void	polynom_divide (const P1 &p1, const P2 &p2, PQ &pq, PR &pr)
template<typename P, typename M>
void	sparse_polynom_reduction_mod (P &p, const M &m)
	Polynom coefficients reduction modulo m.
template<typename P>
P::coef_type	max_abs_coef (const P &p)
	Computes maximum of absolute values of coefficients of polynom p.
template<typename P>
P::coef_type	max_abs_coef_wo_leading (const P &p)
	Computes maximum of absolute values of coefficients of polynom p without leading coef.
template<typename P>
P::coef_type	polynom_content (const P &x)
template<typename P>
P	polynom_primpart (const P &x)
template<typename T, typename P>
T	root_upper_bound_cauchy (const P &p)
template<typename P, typename V>
V &	squarefree_factorize_poly_rational (const P &h, V &res)
template<typename P>
P	reciprocal_poly (const P &p)
template<typename Out, typename T, typename R, typename M, typename CFG>
void	output_vrml (Out &out, const polyhedron< T, R, M, CFG > &p)
	VRML Output. WARNING! The view will be correct only in wired mode.
template<typename Out, typename P, typename X1, typename Y1, typename X2, typename Y2, typename Viewdir, typename Colormap>
void	output_polytope_pstricks_3d (Out &out, const P &p, double x1, double y1, double x2, double y2, double linewidth, const Viewdir &viewdir, const Colormap &colormap)
	PostScript LaTeX Output with pstricks package. WARNING! Only for 3-dim polytopes.
template<typename F, typename FT>
std::ostream &	operator<< (std::ostream &s, const polynom< F > &v)
template<typename F, typename FT>
polynom< F >	abs (const polynom< F > &maxVal)
template<typename F, typename FT>
polynom< F >	normalize (const polynom< F > &val)
template<typename T, typename I, typename T_factory>
T	power (T a, I n, const T_factory &tfctr)
	Exponentiates a in to positive integer power n via squaring and adding.
template<typename T, typename I>
T	power (const T &a, const I &n)
	Exponentiates a in to positive integer power n via squaring and adding.
template<typename T, typename I, typename T_factory>
T	pow2 (I n, const T_factory &tfctr)
	Exponentiates 2 in to positive integer power n via left shift operator.
template<typename T, typename I>
T	pow2 (I n)
	Exponentiates 2 in to positive integer power n via left shift operator.
template<typename T>
T	log2 (T x)
	Returns the base-2 logarithm of x. The default version.
template<typename T1, typename T2, typename Q, typename R>
void	divide (const T1 &a, const T2 &b, Q &q, R &r)
	Performs division produced quotient and remainder.
template<typename T1, typename T2, typename Q, typename R>
void	prdivide (const T1 &a, const T2 &b, Q &q, R &r)
	Performs division produced quotient and POSITIVE remainder (pr).
template<typename T1, typename T2>
T1	prquot (const T1 &a, const T2 &b)
	Returns quotient of pr-division of a by b.
template<typename T1, typename T2>
T2	prrem (const T1 &a, const T2 &b)
	Returns remainder of pr-division of a by b.
template<typename T>
T	square (const T &a)
	Returns square of a.
int	pow (int x, int y)
char	rand (char maxVal)
unsigned char	rand (unsigned char maxVal)
short	rand (short maxVal)
unsigned short	rand (unsigned short maxVal)
int	rand (int maxVal)
unsigned int	rand (unsigned int maxVal)
long	rand (long maxVal)
unsigned long	rand (unsigned long maxVal)
big_int	rand (big_int maxVal)
template<typename T>
rational< T >	rand (const rational< T > &maxVal)
template<typename F, typename I>
monom< F, I >	rand (const monom< F, I > &maxVal)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	rand (const sparse_polynom< F, I, REFCNT > &maxVal)
template<typename T, bool REFCNT>
matrix< T, REFCNT >	rand (const matrix< T, REFCNT > &maxVal)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_list (std::basic_ostream< Ch, ChT > &out, const rational< T > &x, const Ch *first_bracket=rational_output_list_first_bracket_default, const Ch *second_bracket=rational_output_list_second_bracket_default, const Ch *separator=rational_output_list_separator_default)
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_list (std::basic_istream< Ch, ChT > &in, rational< T > &x, const Ch *first_bracket=rational_input_list_first_bracket_default, const Ch *second_bracket=rational_input_list_second_bracket_default, const Ch *separator=rational_input_list_separator_default)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	output_default (std::basic_ostream< Ch, ChT > &out, const rational< T > &x, const Ch *oblique=rational_output_default_oblique_default)
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	input_default (std::basic_istream< Ch, ChT > &in, rational< T > &x, const Ch *oblique=rational_input_default_oblique_default)
template<typename T, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	operator<< (std::basic_ostream< Ch, ChT > &out, const rational< T > &x)
	Reads a rational from a string notation.
template<typename T, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	operator>> (std::basic_istream< Ch, ChT > &in, rational< T > &x)
	Writes a rational to a string notation.
template<typename T1, typename T2>
int	cmp (const rational< T1 > &a, const rational< T2 > &b)
	Comparison of two rationals.
template<typename T>
int	sign (const rational< T > &x)
template<typename T>
bool	is_coprime (const rational< T > &a, const rational< T > &b)
template<typename T>
rational< T >	gcd (const rational< T > &a, const rational< T > &b)
template<typename T>
T	ifloor (const rational< T > &x)
	Floor of x.
template<typename T>
T	iceil (const rational< T > &x)
	Ceiling of x.
template<typename T>
rational< T >	frac (const rational< T > &x)
	Fractional part of x.
template<typename T1>
bool	is_null (const rational< T1 > &x)
template<typename T1>
rational< T1 >	opposite (const rational< T1 > &x)
template<typename T1>
rational< T1 > &	opposite (const rational< T1 > &x, rational< T1 > *y)
template<typename T1>
rational< T1 > &	opposite (rational< T1 > *x)
template<typename T1>
rational< T1 >	inverse (const rational< T1 > &x)
template<typename T1>
rational< T1 > &	inverse (const rational< T1 > &x, rational< T1 > *y)
template<typename T1>
rational< T1 > &	inverse (rational< T1 > *x)
template<typename T1>
std::ostream &	output_polynom_first (std::ostream &out, const rational< T1 > &x)
template<typename T1>
std::ostream &	output_polynom_internal (std::ostream &out, const rational< T1 > &x)
template<typename T1>
std::ostream &	output_pow (std::ostream &out, const rational< T1 > &x)
template<typename T1>
std::istream &	input_polynom_first (std::istream &in, rational< T1 > &x)
template<typename T1>
std::istream &	input_polynom_internal (std::istream &in, rational< T1 > &x)
template<typename T1>
std::istream &	input_pow (std::istream &in, rational< T1 > &x)
template<typename T>
rational< T >	abs (const rational< T > &x)
	Absolute value of x.
template<typename T>
rational< T >	floor (const rational< T > &x)
	Floor of x.
template<typename T>
rational< T >	ceil (const rational< T > &x)
	Ceiling of x.
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
residue< T1, M1, Config1 >	operator+ (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
residue< T1, M1, Config1 >	operator- (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
residue< T1, M1, Config1 >	operator * (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
residue< T1, M1, Config1 >	operator/ (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
residue< T1, M1, Config1 >	operator% (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator== (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator== (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator== (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator!= (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator!= (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator!= (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator< (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator< (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator< (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator<= (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator<= (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator<= (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator> (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator> (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator> (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
bool	operator>= (const residue< T1, M1, Config1 > &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2>
bool	operator>= (const residue< T1, M1, Config1 > &a, const T2 &b)
template<typename T1, typename T2, typename M2, typename Config2>
bool	operator>= (const T1 &a, const residue< T2, M2, Config2 > &b)
template<typename T1, typename M1, typename Config1, typename T2, typename M2, typename Config2>
int	cmp (residue< T1, M1, Config1 > a, const residue< T2, M2, Config2 > &b)
template<typename T, typename M, typename Config>
std::ostream &	operator<< (std::ostream &out, const residue< T, M, Config > &x)
template<typename T, typename M, typename Config>
std::istream &	operator>> (std::istream &in, residue< T, M, Config > &x)
template<typename T, typename M, typename Config>
const residue< T, M, Config > &	abs (const residue< T, M, Config > &x)
template<typename P1, typename P2, typename M>
M &	sylvester_fill (const P1 &p1, const P2 &p2, M &res)
	Fills non-zero elements in Sylvester matrix from two polynomials.
template<typename P1, typename P2, typename M, typename MTFactory>
M &	sylvester (const P1 &p1, const P2 &p2, M &res, MTFactory fctr)
	Creates Sylvester matrix from two polynomials.
template<typename P1, typename P2, typename M>
M &	sylvester (const P1 &p1, const P2 &p2, M &res)
	Creates Sylvester matrix from two polynomials.
template<typename P1, typename P2>
matrix< typename P1::coef_type >	sylvester (const P1 &p1, const P2 &p2)
	Creates Sylvester matrix from two polynomials.
template<typename P1, typename P2, typename SRChain, typename PCFactory>
void	subresultants_nonmodular (const P1 &p1, const P2 &p2, SRChain &s, PCFactory fctr)
	Computes the chain of subresultants of two polynomials.
template<typename P1, typename P2, typename SRChain>
void	subresultants_nonmodular (const P1 &p1, const P2 &p2, SRChain &s)
	Computes the chain of subresultants of two polynomials.
template<typename P1, typename P2, typename PCFactory>
P1::coef_type	resultant_nonmodular (const P1 &p1, const P2 &p2, PCFactory fctr)
	Computes the resultant of two polynomials.
template<typename P1, typename P2>
P1::coef_type	resultant_nonmodular (const P1 &p1, const P2 &p2)
	Computes the resultant of two polynomials.
template<typename P1, typename P2, typename PCFactory>
P1::coef_type	resultant (const P1 &p1, const P2 &p2, PCFactory fctr)
	Computes the resultant of two polynomials.
template<typename P1, typename P2>
P1::coef_type	resultant (const P1 &p1, const P2 &p2)
	Computes the resultant of two polynomials.
template<typename A, typename F, typename Q, typename E, typename Ctrler>
void	skeleton (A &a, F &f, Q &q, E &e, const Ctrler &ctrler)
	The algorithm for double-description of a polyhedal cone.
template<typename A, typename F, typename Q, typename E>
void	skeleton (A &a, F &f, Q &q, E &e)
	The algorithm for double-description of a polyhedal cone.
template<typename MA, typename MB, typename MP, typename MQ, typename Rank, typename T_det, typename T_factory, typename Ctrler, typename Norm>
void	smith (const MA &A, MB &B, MP &P, MQ &Q, Rank &rank, T_det &det, const T_factory &tfctr, Ctrler ctrler, Norm norm)
	Produces normal diagonal form B of integer matrix A.
template<typename MA, typename MB, typename MP, typename MQ, typename Rank, typename T_det, typename Ctrler>
void	smith (const MA &A, MB &B, MP &P, MQ &Q, Rank &rank, T_det &det, Ctrler ctrler)
	Produces normal diagonal form B of integer matrix A.
template<typename MA, typename MB, typename MP, typename MQ, typename Rank, typename T_det>
void	smith (const MA &A, MB &B, MP &P, MQ &Q, Rank &rank, T_det &det)
	Produces normal diagonal form B of integer matrix A.
template<typename M>
M	smith (const M &a)
	Produces normal diagonal form B of integer matrix A.
template<typename MA, typename MB, typename MP, typename MQ, typename Rank, typename T_det>
void	smith_storjohann (const MA &A, MB &B, MP &P, MQ &Q, Rank &rank, T_det &det)
	Produces normal diagonal form B of integer matrix A.
template<typename MA, typename MB, typename MP, typename MQ, typename Rank, typename T_det>
void	smith_near_optimal (const MA &A, MB &B, MP &P, MQ &Q, Rank &rank, T_det &det)
	Produces normal diagonal form B of integer matrix A.
template<typename A, typename B, typename GX, typename Offset>
solve_linsys_result	solve_linsys (const A &a, const B &b, Offset &offset, GX &gx)
	Solve heterogeneous linear system.
template<typename A, typename B, typename X>
solve_linsys_result	solve_linsys (const A &a, const B &b, X &x)
	Solve a heterogeneous linear system.
template<typename A, typename B>
B	solve_linsys (const A &a, const B &b)
	Solve a heterogeneous linear system.
template<typename A>
A	solve_linsys (const A &a)
	Solve a homogeneous linear system.
template<typename F, typename I>
bool	is_unit (const monom< F, I > &x)
template<typename F, typename I>
bool	is_opposite_unit (const monom< F, I > &x)
template<typename F, typename I>
bool	is_null (const monom< F, I > &x)
template<typename F, typename I>
monom< F, I >	opposite (const monom< F, I > &x)
template<typename F, typename I>
monom< F, I > &	opposite (const monom< F, I > &x, monom< F, I > *y)
template<typename F, typename I>
monom< F, I > &	opposite (monom< F, I > *x)
template<typename F, typename I>
monom< F, I >	inverse (const monom< F, I > &x)
template<typename F, typename I>
monom< F, I > &	inverse (const monom< F, I > &x, monom< F, I > *y)
template<typename F, typename I>
monom< F, I > &	inverse (monom< F, I > *x)
template<typename F, typename I>
std::ostream &	output_polynom_first (std::ostream &out, const monom< F, I > &x)
template<typename F, typename I>
std::ostream &	output_polynom_internal (std::ostream &out, const monom< F, I > &x)
template<typename F, typename I>
std::ostream &	output_pow (std::ostream &out, const monom< F, I > &x)
template<typename F, typename I>
std::istream &	input_polynom_first (std::istream &in, monom< F, I > &x)
template<typename F, typename I>
std::istream &	input_polynom_internal (std::istream &in, monom< F, I > &x)
template<typename F, typename I>
std::istream &	input_pow (std::istream &in, monom< F, I > &x)
template<typename F1, typename I1, typename F2, typename I2>
int	cmp (const monom< F1, I1 > &m1, const monom< F2, I2 > &m2)
template<typename F1, typename I1, typename F2>
int	cmp (const monom< F1, I1 > &m1, const F2 &b)
template<typename F1, typename F2, typename I2>
int	cmp (const F1 &a, const monom< F2, I2 > &m2)
template<typename F, typename I, typename Factory_coef>
int	sign (const monom< F, I > &x)
	Determines the sign of monom, i.e. sign of the its coefficient.
template<typename Ch, typename ChT, typename F, typename I>
std::basic_ostream< Ch, ChT > &	output_list (std::basic_ostream< Ch, ChT > &out, const monom< F, I > &x, const char *first_bracket=monom_output_list_first_bracket_default, const char *second_bracket=monom_output_list_second_bracket_default, const char *separator=monom_output_list_separator_default)
	Simple outputting of monom.
template<typename Ch, typename ChT, typename F, typename I>
std::basic_ostream< Ch, ChT > &	output_var (std::basic_ostream< Ch, ChT > &out, const monom< F, I > &x, bool first_a=true, const char *var=monom_output_var_var_default, const char *mul=monom_output_var_mul_default, const char *pow=monom_output_var_pow_default)
	Âûâîäèò ìîíîì â ïðèâû÷íîì âèäå, ñ óêàçàíèåì ôîðìàëüíîé ïåðåìåííîé.
template<typename Ch, typename ChT, typename F, typename I>
std::basic_istream< Ch, ChT > &	input_list (std::basic_istream< Ch, ChT > &in, monom< F, I > &x, const char *first_bracket=monom_input_list_first_bracket_default, const char *second_bracket=monom_input_list_second_bracket_default, const char *separator=monom_input_list_separator_default)
	Simple intputting for monom.
template<typename Ch, typename ChT, typename F, typename I, typename Factory_coef>
std::basic_istream< Ch, ChT > &	input_var (std::basic_istream< Ch, ChT > &in, monom< F, I > &x, bool first_a, const Factory_coef &fctr, const char *var=monom_input_var_var_default, const char *mul=monom_input_var_mul_default, const char *pow=monom_input_var_pow_default)
	Inputting with variable symbol for monom.
template<typename Ch, typename ChT, typename F, typename I>
std::basic_istream< Ch, ChT > &	input_var (std::basic_istream< Ch, ChT > &in, monom< F, I > &x, bool first_a=true, const char *var=monom_input_var_var_default, const char *mul=monom_input_var_mul_default, const char *pow=monom_input_var_pow_default)
	Inputting with variable symbol for monom.
template<typename Ch, typename ChT, typename F, typename I>
std::basic_ostream< Ch, ChT > &	output_aligned (std::basic_ostream< Ch, ChT > &out, const monom< F, I > &x, bool first_a=true, const char *var=monom_output_var_var_default, const char *mul=monom_output_var_mul_default, const char *pow=monom_output_var_pow_default)
	Oputputs monom in aligned form. (Restricted implementation.).
template<typename F, typename I, typename Ch, typename ChT>
std::basic_ostream< Ch, ChT > &	operator<< (std::basic_ostream< Ch, ChT > &out, const monom< F, I > &x)
	Ñòàíäàðòíûé ñïîñîá âûâîäà ìîíîìà: ñîâïàäàåò ñ output_var.
template<typename F, typename I, typename Ch, typename ChT>
std::basic_istream< Ch, ChT > &	operator>> (std::basic_istream< Ch, ChT > &in, monom< F, I > &x)
	Ñòàíäàðòíûé ñïîñîá ââîäà ìîíîìà: ñîâïàäàåò ñ input_var.
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2>
int	cmp (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b)
	Lexicographical comparision of two polynomials.
template<typename F, typename I, bool REFCNT>
bool	is_primitive (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
bool	is_unit (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
bool	is_opposite_unit (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
bool	is_null (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	opposite (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT > &	opposite (const sparse_polynom< F, I, REFCNT > &x, sparse_polynom< F, I, REFCNT > *y)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT > &	opposite (sparse_polynom< F, I, REFCNT > *x)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	inverse (const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT > &	inverse (const sparse_polynom< F, I, REFCNT > &x, sparse_polynom< F, I, REFCNT > *y)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT > &	inverse (sparse_polynom< F, I, REFCNT > *x)
template<typename F, typename I, bool REFCNT>
std::ostream &	output_polynom_first (std::ostream &out, const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
std::ostream &	output_polynom_internal (std::ostream &out, const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
std::ostream &	output_pow (std::ostream &out, const sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
std::istream &	input_polynom_first (std::istream &in, sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
std::istream &	input_polynom_internal (std::istream &in, sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
std::istream &	input_pow (std::istream &in, sparse_polynom< F, I, REFCNT > &x)
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	euclid (sparse_polynom< F, I, REFCNT > a, sparse_polynom< F, I, REFCNT > b)
	Specialization of euclid for sparse_polynom.
template<typename F, typename I, bool REFCNT>
bool	is_coprime (const sparse_polynom< F, I, REFCNT > &a, const sparse_polynom< F, I, REFCNT > &b)
	Specialization of is_coprime for sparse_polynom.
template<typename F1, typename I1, bool REFCNT1, typename F2, typename I2, bool REFCNT2, typename Q, typename R>
void	prdivide (const sparse_polynom< F1, I1, REFCNT1 > &a, const sparse_polynom< F2, I2, REFCNT2 > &b, Q &q, R &r)
template<typename F1, typename I1, bool REFCNT1, typename I2>
sparse_polynom< F1, I1, REFCNT1 >	pow (const sparse_polynom< F1, I1, REFCNT1 > &a, const I2 &n)
template<typename F, typename I>
monom< F, I >	abs (const monom< F, I > &x)
	Absolute value for monom.
template<typename F, typename I, bool REFCNT>
sparse_polynom< F, I, REFCNT >	abs (const sparse_polynom< F, I, REFCNT > &x)
	Absolute value for polynomial.
template<typename T>
T	sin (const T &x)
template<typename T>
T	cos (const T &x)
template<typename T>
T	tan (const T &x)
template<typename T>
T	sinh (const T &x)
template<typename T>
T	cosh (const T &x)
template<typename T>
T	tanh (const T &x)
template<typename T>
T	asin (const T &x)
template<typename T>
T	acos (const T &x)
template<typename T>
T	atan (const T &x)
template<typename T>
T	abs (const T &x)
template<typename T>
T	exp (const T &x)
template<typename T>
T	floor (const T &x)
template<typename T>
T	ceil (const T &x)
template<typename T>
T	log (const T &x)
template<typename T>
T	log10 (const T &x)
template<typename T>
T	sqrt (const T &x)
template<typename T1, typename T2>
T1	pow (const T1 &x, const T2 &y)
template<typename T1, typename T2>
void	swap (T1 &x, T2 &y)
template<typename P, typename SS>
void	sturm_diff_sys (const P &p, SS &ss)
	Builds full Sturm system for polynomial.
template<typename SS, typename T>
SS::size_type	sturm_sign_changes (const SS &ss, const T &x, int signpx)
	Number of sign changes for Sturm system in point 'x' with precomputed sign.
template<typename SS, typename T>
SS::size_type	sturm_sign_changes (const SS &ss, const T &x)
	Number of sign changes for Sturm system in point 'x'.
template<typename SS, typename Seg>
SS::size_type	sturm_number_roots (const SS &ss, const Seg &seg)
	Number of roots of polynomial ss.front() on segment 'seg' by Sturm system 'ss'.
template<typename SS, typename SegT, bool SegREFCNT>
vector< typename SS::size_type >	sturm_number_roots (const SS &ss, const vector< SegT, SegREFCNT > &lims)
	Vector version of simple sturm_number_roots.
template<typename T, typename P, typename LIMS, typename SegBound>
void	sturm (const P &p, LIMS &lims, SegBound bs)
	Real root location for polynomial by the Sturm algorithm on segment bs.
template<typename T, typename P, typename LIMS>
void	sturm (const P &p, LIMS &lims)
	All real root location for polynomial by the Sturm algorithm.
template<typename P, typename Lims>
bool	interval_root_dichotomy (const P &p, int lsign, Lims &lims)
	Dichotomy of an interval with one root of a polynomial to double precision.
template<typename P, typename Lims, typename T>
bool	interval_root_precise (const P &p, Lims &lims, const T &e)
	Fits intervals that located the roots to 'e' precision.
template<typename T, typename P, typename Roots, typename Prec>
void	roots_poly_real (const P &p, Roots &roots, Prec &prec, const T &e=null< T >())
	Computes all real roots of polynomial with precision 'e'.
template<typename Out, typename T>
void	output_latex_verb (Out &out, const T &x, bool in_math=false, ex_environ_priority eep=eep_alone)
	Verbativ output in LaTeX.
template<typename Out, typename T>
void	output_latex (Out &out, const T &x, bool in_math=false, ex_environ_priority eep=eep_alone)
	Outputs the object in LaTeX notation. Common case.
template<typename Out, typename T>
void	output_latex_math (Out &out, const T &x, bool in_math=false, ex_environ_priority eep=eep_alone)
	Encloses the standard output of x in $ brackets.
template<typename Out, typename T>
void	output_latex (Out &out, const rational< T > &x, bool in_math, ex_environ_priority eep, std::size_t minlensimple, bool externsign=true)
	Outputs a rational in LaTeX notation.
template<typename Out, typename T>
void	output_latex (Out &out, const rational< T > &x, bool in_math, ex_environ_priority eep)
template<typename Out, typename T>
void	output_latex (Out &out, const rational< T > &x, bool in_math)
template<typename Out, typename T>
void	output_latex (Out &out, const rational< T > &x)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const vector< T, REFCNT > &x, bool in_math, ex_environ_priority eep, bool hor, const char *first_bracket="(", const char *second_bracket=")", const char *delim=",")
	Outputs a vector in LaTeX notation.
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const vector< T, REFCNT > &x, bool in_math, ex_environ_priority eep)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const vector< T, REFCNT > &x, bool in_math)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const vector< T, REFCNT > &x)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const matrix< T, REFCNT > &x, bool in_math, ex_environ_priority eep, bool transposed, const char *first_bracket="(", const char *second_bracket=")")
	Outputs a matrix in LaTeX notation.
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const matrix< T, REFCNT > &x)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const matrix< T, REFCNT > &x, bool in_math)
template<typename Out, typename T, bool REFCNT>
void	output_latex (Out &out, const matrix< T, REFCNT > &x, bool in_math, ex_environ_priority eep)
template<typename Out, typename F, typename I>
void	output_latex (Out &out, const monom< F, I > &x, bool in_math, ex_environ_priority eep, bool first, const char *var="x")
	Outputs a monom in LaTeX notation.
template<typename Out, typename F, typename I>
void	output_latex (Out &out, const monom< F, I > &x, bool in_math, ex_environ_priority eep)
template<typename Out, typename F, typename I>
void	output_latex (Out &out, const monom< F, I > &x, bool in_math)
template<typename Out, typename F, typename I>
void	output_latex (Out &out, const monom< F, I > &x)
template<typename Out, typename F, typename I, bool REFCNT>
void	output_latex (Out &out, const sparse_polynom< F, I, REFCNT > &x, bool in_math, ex_environ_priority eep, const char *var)
	Outputs a sparse_polynom in LaTeX notation.
template<typename Out, typename F, typename I, bool REFCNT>
void	output_latex (Out &out, const sparse_polynom< F, I, REFCNT > &x, bool in_math, ex_environ_priority eep)
template<typename Out, typename F, typename I, bool REFCNT>
void	output_latex (Out &out, const sparse_polynom< F, I, REFCNT > &x, bool in_math)
template<typename Out, typename F, typename I, bool REFCNT>
void	output_latex (Out &out, const sparse_polynom< F, I, REFCNT > &x)
template<typename T, bool REFCNT, typename Ch, typename ChT, typename In_hor, typename In_ver, typename In_box>
void	output_latex_matrix_frames (std::basic_ostream< Ch, ChT > &out, const matrix< T, REFCNT > &x, const matrix_frames< In_hor, In_ver, In_box > &mf, bool in_math=false, bool transposed=false, const char *first_bracket="(", const char *second_bracket=")")
	Outputs a matrix in LaTeX notation with lines and boxes.
template<typename Q, typename Dim1, typename TR, typename Dim2, typename Ctrler>
void	triangulate_simple_1 (const Q &q, const Dim1 &dim, TR &tr, const Dim2 &subspdim, Ctrler ctrler)
	Triangulates a cone with structure matrix q.
template<typename Q, typename Dim1, typename TR, typename Dim2>
void	triangulate_simple_1 (const Q &q, const Dim1 &dim, TR &tr, const Dim2 &subspdim)
	Triangulates a cone with the relations matrix q.
template<typename Q, typename Dim1, typename TR>
void	triangulate_simple_1 (const Q &q, const Dim1 &dim, TR &tr)
	Triangulates a pointed cone with the relations matrix q.
template<typename Vec, typename Index>
cnc_reference< Vec >::type	vec_operator_sqbrackets_index_vector (Vec *vec, const Index &ind, const type_category::integer &)
template<typename Vec, typename Index>
indexed_subvector< Vec, vector< typename Vec::size_type > >	vec_operator_sqbrackets_index_vector (Vec *vec, const Index &ind, const type_category::string &)
template<typename Vec, typename Index>
indexed_subvector< Vec, Index >	vec_operator_sqbrackets_index_vector (Vec *vec, const Index &ind, const type_category::type &)
template<typename Vec, typename UFunc>
void	apply1_wores_vec (Vec &a, UFunc f)
template<typename Vec1, typename Vec2, typename BinOp>
void	apply2_wores_vec_by_vec (Vec1 &a, Vec2 &b, BinOp f)
template<typename Vec, typename Val, typename BinOp>
void	apply2_wores_vec_by_val (Vec &a, Val &b, BinOp f)
template<typename Val, typename Vec, typename BinOp>
void	apply2_wores_val_by_vec (Val &a, Vec &b, BinOp f)
template<typename Vec1, typename Vec2, typename VecRes, typename Func2>
VecRes &	apply2_vec_by_vec (const Vec1 &a, const Vec2 &b, VecRes &res, Func2 f)
template<typename Vec1, typename Vec2, typename Func2>
Vec1	apply2_vec_by_vec (const Vec1 &a, const Vec2 &b, Func2 f)
template<typename Vec, typename Val, typename VecRes, typename Func2>
VecRes &	apply2_vec_by_val (const Vec &a, const Val &b, VecRes &res, Func2 f)
template<typename Vec, typename Val, typename Func2>
Vec	apply2_vec_by_val (const Vec &a, const Val &b, Func2 f)
template<typename Val, typename Vec, typename VecRes, typename Func2>
VecRes &	apply2_val_by_vec (const Val &a, const Vec &b, VecRes &res, Func2 f)
template<typename Val, typename Vec, typename Func2>
Vec	apply2_val_by_vec (const Val &a, const Vec &b, Func2 f)
template<typename Vec1, typename Vec2, typename VecRes, typename Func3>
VecRes &	apply3_vec_by_vec (const Vec1 &a, const Vec2 &b, VecRes &res, Func3 f)
template<typename Vec1, typename Vec2, typename Func3>
Vec1	apply3_vec_by_vec (const Vec1 &a, const Vec2 &b, Func3 f)
template<typename Vec, typename Val, typename VecRes, typename Func3>
VecRes &	apply3_vec_by_val (const Vec &a, const Val &b, VecRes &res, Func3 f)
template<typename Vec, typename Val, typename Func3>
Vec	apply3_vec_by_val (const Vec &a, const Val &b, Func3 f)
template<typename Val, typename Vec, typename VecRes, typename Func3>
VecRes &	apply3_val_by_vec (const Val &a, const Vec &b, VecRes &res, Func3 f)
template<typename Val, typename Vec, typename Func3>
Vec	apply3_val_by_vec (const Val &a, const Vec &b, Func3 f)
template<typename Vec1, typename Vec2, typename Cmp>
int	cmp_vec_by_vec (const Vec1 &a, const Vec2 &b, Cmp cmp)
template<typename Vec, typename Val, typename Cmp>
int	cmp_vec_by_val (const Vec &a, const Val &val, Cmp cmp)
template<typename Val, typename Vec, typename Cmp>
int	cmp_val_by_vec (const Val &val, const Vec &a, Cmp cmp)
template<typename Vec1, typename Vec2>
int	cmpdef_vec_by_vec (const Vec1 &a, const Vec2 &b)
template<typename Vec, typename Val>
int	cmpdef_vec_by_val (const Vec &a, const Val &val)
template<typename Val, typename Vec>
int	cmpdef_val_by_vec (const Val &val, const Vec &a)
template<typename Vec1, typename Vec2, typename Cmp>
bool	allcmp_vec_by_vec (const Vec1 &a, const Vec2 &b, Cmp cmp)
template<typename Vec, typename Val, typename Cmp>
bool	allcmp_vec_by_val (const Vec &a, const Val &val, Cmp cmp)
template<typename Val, typename Vec, typename Cmp>
bool	allcmp_val_by_vec (const Val &val, const Vec &a, Cmp cmp)
template<typename Vec1, typename Vec2, typename Cmp>
Vec1::template other_element_type_refcnt< bool, true >::type	eachcmp_vec_by_vec (const Vec1 &a, const Vec2 &b, Cmp cmp)
template<typename Vec, typename Val, typename Cmp>
Vec::template other_element_type_refcnt< bool, true >::type	eachcmp_vec_by_val (const Vec &a, const Val &val, Cmp cmp)
template<typename Val, typename Vec, typename Cmp>
Vec::template other_element_type_refcnt< bool, true >::type	eachcmp_val_by_vec (const Val &val, const Vec &a, Cmp cmp)
template<typename Vec1, typename Vec2, typename Cmp>
Vec1::template other_element_type_refcnt< int, true >::type	elwisecmp_vec_by_vec (const Vec1 &a, const Vec2 &b, Cmp cmp)
template<typename Vec, typename Val, typename Cmp>
Vec::template other_element_type_refcnt< int, true >::type	elwisecmp_vec_by_val (const Vec &a, const Val &val, Cmp cmp)
template<typename Val, typename Vec, typename Cmp>
Vec::template other_element_type_refcnt< int, true >::type	elwisecmp_val_by_vec (const Val &val, const Vec &a, Cmp cmp)
template<typename Index, typename T>
bool	all_in_range (const Index &ind, const T &left, const T &right)
template<typename Out, typename Vec>
Out &	vec_output_list (Out &out, const Vec &x, const char *first_bracket=vector_output_list_first_bracket_default, const char *second_bracket=vector_output_list_second_bracket_default, const char *separator=vector_output_list_separator_default)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_plus (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_minus (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_multiplies (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_divides (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_modulus (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_bitwise_or (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_bitwise_and (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_bitwise_xor (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_shift_left (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, typename T2, bool REFCNT2>
vector< T2, REFCNT2 > &	left_assign_shift_right (const T1 &x, vector< T2, REFCNT2 > &y)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2, typename T1_factory>
T1	dotprod (const vector< T1, REFCNT1 > &a, const vector< T2, REFCNT2 > &b, const T1_factory &t1fctr)
	Dot product (scalar product) of two vectors.
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>
T1	dotprod (const vector< T1, REFCNT1 > &a, const vector< T2, REFCNT2 > &b)
	Dot product (scalar product) of two vectors.
template<typename T, bool REFCNT, typename T2, typename T2_factory>
T2 &	product (const vector< T, REFCNT > &x, T2 &res, const T2_factory &t2fctr)
	Multiplies all elements of vector.
template<typename T, bool REFCNT, typename T2, typename T2_factory>
T2 &	sum (const vector< T, REFCNT > &x, T2 &res, const T2_factory &t2fctr)
	Sums all elements of vector.
template<typename T, bool REFCNT, typename T2>
T2 &	product (const vector< T, REFCNT > &x, T2 &res)
	Multiplies all elements of vector.
template<typename T, bool REFCNT, typename T2>
T2 &	sum (const vector< T, REFCNT > &x, T2 &res)
	Sums all elements of vector.
template<typename T, bool REFCNT>
T	product (const vector< T, REFCNT > &x)
	Multiplies all elements of vector.
template<typename T, bool REFCNT>
T	sum (const vector< T, REFCNT > &x)
	Sums all elements of vector.
template<typename Out, typename T, bool REFCNT>
Out &	output_list (Out &out, const vector< T, REFCNT > &x, const char *first_bracket=vector_output_list_first_bracket_default, const char *second_bracket=vector_output_list_second_bracket_default, const char *separator=vector_output_list_separator_default)
	Simple output of the vector.
template<typename In, typename T, bool REFCNT>
In &	input_list (In &in, vector< T, REFCNT > &x, const char *first_bracket=vector_input_list_first_bracket_default, const char *second_bracket=vector_input_list_second_bracket_default, const char *separator=vector_input_list_separator_default, const char *range=vector_input_list_range_default)
	Simple input of the vector.
template<typename T, bool REFCNT>
std::ostream &	output_aligned (std::ostream &out, const vector< T, REFCNT > &x, const char *left_col=vector_output_aligned_left_col_default, const char *right_col=vector_output_aligned_right_col_default)
	Aligned output of the vector.
template<typename T, bool REFCNT>
std::ostream &	vector_output_row (std::ostream &out, const vector< T, REFCNT > &x)
	Prints vector as a row-vector.
template<typename T, bool REFCNT>
std::ostream &	vector_output_col (std::ostream &out, const vector< T, REFCNT > &x)
	Prints vector as a column-vector.
template<typename T, bool REFCNT>
std::ostream &	operator<< (std::ostream &out, const vector< T, REFCNT > &x)
	Standard output routine (default type of outputting) for the vector.
template<typename T, bool REFCNT>
std::istream &	operator>> (std::istream &in, vector< T, REFCNT > &x)
	Standard input routine (default type of inputting) for the vector.
template<typename T, bool REFCNT>
std::ofstream &	operator<< (std::ofstream &out, const vector< T, REFCNT > &x)
	WARNING! TEMPORARY!.
template<typename T, bool REFCNT>
std::ifstream &	operator>> (std::ifstream &in, vector< T, REFCNT > &x)
	WARNING! TEMPORARY!.
template<typename T, bool REFCNT>
std::ostringstream &	operator<< (std::ostringstream &out, const vector< T, REFCNT > &x)
	WARNING! TEMPORARY!.
template<typename T, bool REFCNT>
std::istringstream &	operator>> (std::istringstream &in, vector< T, REFCNT > &x)
	WARNING! TEMPORARY!.
template<typename T, bool REFCNT>
vector< T, REFCNT >	opposite (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, REFCNT > &	opposite (const vector< T, REFCNT > &x, vector< T, REFCNT > *y)
template<typename T, bool REFCNT>
vector< T, REFCNT > &	opposite (vector< T, REFCNT > *x)
template<typename T, bool REFCNT>
vector< T, REFCNT >	inverse (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
vector< T, REFCNT > &	inverse (const vector< T, REFCNT > &x, vector< T, REFCNT > *y)
template<typename T, bool REFCNT>
vector< T, REFCNT > &	inverse (vector< T, REFCNT > *x)
template<typename T, bool REFCNT>
bool	is_unit (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
bool	is_opposite_unit (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
bool	is_null (const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_polynom_first (std::ostream &out, const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_polynom_internal (std::ostream &out, const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::ostream &	output_pow (std::ostream &out, const vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_polynom_first (std::istream &in, vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_polynom_internal (std::istream &in, vector< T, REFCNT > &x)
template<typename T, bool REFCNT>
std::istream &	input_pow (std::istream &in, vector< T, REFCNT > &x)
template<typename T1, bool REFCNT1, typename T2, bool REFCNT2, typename T3, bool REFCNT3>
void	fill_subvector (const vector< T1, REFCNT1 > &orig, const vector< T2, REFCNT2 > &indexes, vector< T3, REFCNT3 > &res)
	Makes subvector from another vector and index vector.
Variables
const int	PREC_MIN = 2
const unsigned long	PREC_MAX = _Internal::max_digit
const unsigned long	D_PREC_MAX = ( long ) (_Internal::max_digit * log ( 2.0l ) / log ( 10.0l ))
CCounter	counter_big_int_sum_GC
CCounter	counter_big_int_mul_GC
CCounter	counter_big_int_div_GC
const char *	matrix_output_list_first_bracket_default = "("
const char *	matrix_output_list_second_bracket_default = ")"
const char *	matrix_output_list_row_separator_default = ", "
const char *	matrix_output_list_first_row_bracket_default = "("
const char *	matrix_output_list_second_row_bracket_default = ")"
const char *	matrix_output_list_col_separator_default = ", "
const char *	matrix_input_list_first_bracket_default = "("
const char *	matrix_input_list_second_bracket_default = ")"
const char *	matrix_input_list_row_separator_default = ","
const char *	matrix_input_list_first_row_bracket_default = "("
const char *	matrix_input_list_second_row_bracket_default = ")"
const char *	matrix_input_list_col_separator_default = ","
const char *	matrix_output_aligned_left_col_default = "||"
const char *	matrix_output_aligned_right_col_default = "||"
const char *	matrix_output_aligned_inter_col_default = " "
const colwise_t	colwise = colwise_t()
	Helper object for columnwise filling of the matrix.
const diag_t	diag = diag_t()
	Helper object for construct a diagonal matrix.
const eye_t	eye = eye_t()
	Helper object for construct an indentity matrix.
const frommat_t	frommat = frommat_t()
const char *	matrix_output_list_first_bracket_default
const char *	matrix_output_list_second_bracket_default
const char *	matrix_output_list_row_separator_default
const char *	matrix_output_list_first_row_bracket_default
const char *	matrix_output_list_second_row_bracket_default
const char *	matrix_output_list_col_separator_default
const char *	matrix_input_list_first_bracket_default
const char *	matrix_input_list_second_bracket_default
const char *	matrix_input_list_row_separator_default
const char *	matrix_input_list_first_row_bracket_default
const char *	matrix_input_list_second_row_bracket_default
const char *	matrix_input_list_col_separator_default
const char *	matrix_output_aligned_left_col_default
const char *	matrix_output_aligned_right_col_default
const char *	matrix_output_aligned_inter_col_default
const fromempty_t	fromempty = fromempty_t()
const fromivert_t	fromivert = fromivert_t()
const fromvert_t	fromvert = fromvert_t()
const char *	rational_output_list_first_bracket_default = "("
const char *	rational_output_list_second_bracket_default = ")"
const char *	rational_output_list_separator_default = ", "
const char *	rational_input_list_first_bracket_default = "("
const char *	rational_input_list_second_bracket_default = ")"
const char *	rational_input_list_separator_default = ","
const char *	rational_output_default_oblique_default = "/"
const char *	rational_input_default_oblique_default = "/"
const char *	rational_output_list_first_bracket_default
const char *	rational_output_list_second_bracket_default
const char *	rational_output_list_separator_default
const char *	rational_input_list_first_bracket_default
const char *	rational_input_list_second_bracket_default
const char *	rational_input_list_separator_default
const char *	rational_output_default_oblique_default
const char *	rational_input_default_oblique_default
const char *	monom_input_list_first_bracket_default = "("
const char *	monom_output_list_first_bracket_default = "("
const char *	monom_input_list_second_bracket_default = ")"
const char *	monom_output_list_second_bracket_default = ")"
const char *	monom_input_list_separator_default = ","
const char *	monom_output_list_separator_default = ", "
const char *	monom_input_var_mul_default = "*"
const char *	monom_output_var_mul_default = "*"
const char *	monom_input_var_var_default = "x"
const char *	monom_output_var_var_default = "x"
const char *	monom_input_var_pow_default = "^"
const char *	monom_output_var_pow_default = "^"
const char *	monom_input_list_first_bracket_default
const char *	monom_output_list_first_bracket_default
const char *	monom_input_list_second_bracket_default
const char *	monom_output_list_second_bracket_default
const char *	monom_input_list_separator_default
const char *	monom_output_list_separator_default
const char *	monom_input_var_mul_default
const char *	monom_output_var_mul_default
const char *	monom_input_var_var_default
const char *	monom_output_var_var_default
const char *	monom_input_var_pow_default
const char *	monom_output_var_pow_default
const char *	vector_output_list_first_bracket_default = "("
const char *	vector_output_list_second_bracket_default = ")"
const char *	vector_output_list_separator_default = ", "
const char *	vector_input_list_first_bracket_default = "("
const char *	vector_input_list_second_bracket_default = ")"
const char *	vector_input_list_separator_default = ","
const char *	vector_input_list_range_default = ":"
const char *	vector_output_aligned_left_col_default = "||"
const char *	vector_output_aligned_right_col_default = "||"
const char *	vector_output_list_first_bracket_default
const char *	vector_output_list_second_bracket_default
const char *	vector_output_list_separator_default
const char *	vector_input_list_first_bracket_default
const char *	vector_input_list_second_bracket_default
const char *	vector_input_list_separator_default
const char *	vector_input_list_range_default
const char *	vector_output_aligned_left_col_default
const char *	vector_output_aligned_right_col_default
const fromseq_t	fromseq = fromseq_t()
const fromval_t	fromval = fromval_t()
const fromvec_t	fromvec = fromvec_t()
const fromsize_t	fromsize = fromsize_t()
const fromstr_t	fromstr = fromstr_t()

---

Typedef Documentation

typedef unsigned long long Arageli::counter_t

Definition at line 17 of file counter.hpp.

---

Enumeration Type Documentation

enum Arageli::interval_kind

Kind of interval.

Enumerator:

interval_empty	empty as a segment
interval_point	point as a segment
interval_length	have a nonzero length

Definition at line 46 of file interval.hpp.

enum Arageli::solve_linsys_result

Enumerator:

SLR_EMPTY
SLR_UNIQUE
SLR_MULTIPLE

Definition at line 43 of file solve_linsys.hpp.

enum Arageli::monoms_order

Enumerator:

mo_inc
mo_dec

Definition at line 1733 of file sparse_polynom.hpp.

enum Arageli::ex_environ_priority

Type of environment (context) for an expression.

These values helps to bracket placing in nested expressions.

Enumerator:

eep_alone	an expression is alone (matrix or vector item, power of another expression and so on)
eep_add
eep_mul	multiplicative context (coefficient of monom with degree that greater than 0 and so on)

Definition at line 42 of file texout.hpp.

enum Arageli::matrix_line_type

Type of a line that used in matrix output functions with boxes and dividing lines.

Enumerator:

mlt_solid	Solid line "_______".
mlt_dot	Dotted line "......." (it's not supported for boxes yet).
mlt_hatch	Hatched line "_ _ _ _" (it's not supported for boxes yet).
mlt_chain	Chain line "_ . _ ." (it's not supported for boxes yet).

Definition at line 364 of file texout.hpp.

---

Function Documentation

template<typename D1, typename T1>

bool Arageli::is_null

(

const _Internal::module_2pm1< D1, T1 > &

a

)

[inline]

Definition at line 222 of file _utility.hpp.

template<typename D1, typename T1>

bool Arageli::is_unit

(

const _Internal::module_2pm1< D1, T1 > &

a

)

[inline]

Definition at line 226 of file _utility.hpp.

template<typename T1, typename D2, typename T2>

T1 Arageli::prrem	(	const T1 &	aa,
		const _Internal::module_2pm1< D2, T2 > &	b
	)			[inline]

Definition at line 231 of file _utility.hpp.

template<typename Out, typename D, typename T>

Out& Arageli::operator<<	(	Out &	out,
		const _Internal::module_2pm1< D, T > &	x
	)			[inline]

Definition at line 282 of file _utility.hpp.

template<typename In, typename D, typename T>

In& Arageli::operator>>	(	In &	in,
		_Internal::module_2pm1< D, T > &	x
	)			[inline]

Definition at line 290 of file _utility.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

algebraic<TP1, TS1, Poly1, Seg1, Cfg1> Arageli::operator+	(	algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 320 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

algebraic<TP1, TS1, Poly1, Seg1, Cfg1> Arageli::operator-	(	algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 321 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

algebraic<TP1, TS1, Poly1, Seg1, Cfg1> Arageli::operator *	(	algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 322 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

algebraic<TP1, TS1, Poly1, Seg1, Cfg1> Arageli::operator/	(	algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 323 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

algebraic<TP1, TS1, Poly1, Seg1, Cfg1> Arageli::operator%	(	algebraic< TP1, TS1, Poly1, Seg1, Cfg1 >	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 324 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator==	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 366 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator==	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 366 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator==	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 366 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator!=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 367 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator!=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 367 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator!=	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 367 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator<	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 368 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator<	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 368 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator<	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 368 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator<=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 369 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator<=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 369 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator<=	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 369 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator>	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 370 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator>	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 370 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator>	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 370 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator>=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 371 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TS2>

bool Arageli::operator>=	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TS2 &	b
	)			[inline]

Definition at line 371 of file algebraic.hpp.

template<typename TS1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

bool Arageli::operator>=	(	const TS1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 371 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

int Arageli::cmp	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)

Definition at line 380 of file algebraic.hpp.

template<typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1, typename TP2>

int Arageli::cmp	(	const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	a,
		const TP2 &	b
	)			[inline]

Definition at line 400 of file algebraic.hpp.

template<typename TP1, typename TP2, typename TS2, typename Poly2, typename Seg2, typename Cfg2>

int Arageli::cmp	(	const TP1 &	a,
		const algebraic< TP2, TS2, Poly2, Seg2, Cfg2 > &	b
	)			[inline]

Definition at line 413 of file algebraic.hpp.

template<typename Out, typename TP1, typename TS1, typename Poly1, typename Seg1, typename Cfg1>

Out& Arageli::operator<<	(	Out &	out,
		const algebraic< TP1, TS1, Poly1, Seg1, Cfg1 > &	x
	)			[inline]

Definition at line 425 of file algebraic.hpp.

template<typename PolyVec, typename SegVec, typename Rslt, typename P, typename Seg, typename F>

void Arageli::algebraic_func_rslt	(	const PolyVec &	polyvec,
		SegVec	segvec,
		Rslt	rslt,
		P &	p,
		Seg &	seg,
		F	f
	)

Arbitrary function on algebraic numbers based on precomputed resultant.

template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>

void Arageli::algebraic_plus	(	const P1 &	p1,
		const Seg1 &	seg1,
		const P2 &	p2,
		const Seg2 &	seg2,
		P3 &	p3,
		Seg3 &	seg3
	)

template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>

void Arageli::algebraic_minus	(	const P1 &	p1,
		const Seg1 &	seg1,
		const P2 &	p2,
		const Seg2 &	seg2,
		P3 &	p3,
		Seg3 &	seg3
	)

template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>

void Arageli::algebraic_multiplies	(	const P1 &	p1,
		const Seg1 &	seg1,
		const P2 &	p2,
		const Seg2 &	seg2,
		P3 &	p3,
		Seg3 &	seg3
	)

template<typename P1, typename Seg1, typename P2, typename Seg2, typename P3, typename Seg3>

void Arageli::algebraic_divides	(	const P1 &	p1,
		const Seg1 &	seg1,
		const P2 &	p2,
		Seg2	seg2,
		P3 &	p3,
		Seg3 &	seg3
	)

template<typename MA, typename MB, typename MQ, typename Basis, typename T_det>

void Arageli::bareiss	(	const MA &	A,
		MB &	B,
		MQ &	Q,
		Basis &	basis,
		T_det &	det
	)

Produces the Gauss-Jordan form B of an integer matrix A.

Returns B, Q, basis, det:

• Q is such that B = Q * A;
• r = basis.size() is a rank of A;
• B.sumbatrix(mesh_grid(1,r), basis) is the r-by-r non-singular diagonal matrix;
• det is the basis minor of A.

template<typename MA, typename MP, typename MQ, typename Rank, typename T_det>

void Arageli::bareiss_pq	(	const MA &	A,
		MP &	P,
		MQ &	Q,
		Rank &	rank,
		T_det &	det
	)

Produces the Gauss form B of an integer matrix A.

Returns P, Q, rank, det:

• P, Q permutation matrices: (P * A * Q).sumbatrix(mesh_grid(1,r), mesh_grid(1,r)) is the r-by-r non-singular matrix;
• rank is a rank of A;
• det is the basis minor of A.

template<typename MA>

MA Arageli::adjoint

(

const MA &

A

)

template<typename MA, typename MP, typename T_det>

void Arageli::adjoint	(	const MA &	A,
		MP &	P,
		T_det &	det
	)

template<typename MA>

MA::element_type Arageli::det_brs

(

const MA &

A

)

template<typename MA>

MA::size_type Arageli::rank_brs

(

const MA &

A

)

template<typename T, typename Res>

Res& Arageli::indirection	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 41 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::address	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 42 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::unary_plus	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 43 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::unary_minus	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 44 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::logical_not	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 45 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::bitwise_not	(	const T &	x,
		Res &	res
	)			[inline]

Definition at line 46 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::prefix_increment	(	T &	x,
		Res &	res
	)			[inline]

Definition at line 51 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::prefix_decrement	(	T &	x,
		Res &	res
	)			[inline]

Definition at line 55 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::postfix_increment	(	T &	x,
		Res &	res
	)			[inline]

Definition at line 59 of file basefuncs.hpp.

template<typename T, typename Res>

Res& Arageli::postfix_decrement	(	T &	x,
		Res &	res
	)			[inline]

Definition at line 63 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::plus	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 73 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::minus	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 74 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::multiplies	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 75 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::divides	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 76 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::modulus	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 77 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::logical_or	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 78 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::logical_and	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 79 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::equal_to	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 80 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::not_equal_to	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 81 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::greater	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 82 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::less	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 83 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::greater_equal	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 84 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::less_equal	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 85 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::bitwise_or	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 86 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::bitwise_and	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 87 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::bitwise_xor	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 88 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::shift_left	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 89 of file basefuncs.hpp.

template<typename T1, typename T2, typename Res>

Res& Arageli::shift_right	(	const T1 &	x,
		const T2 &	y,
		Res &	res
	)			[inline]

Definition at line 90 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_plus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 105 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_plus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 105 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_minus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 106 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_minus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 106 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_multiplies	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 107 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_multiplies	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 107 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_divides	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 108 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_divides	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 108 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_modulus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 109 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_modulus	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 109 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_bitwise_or	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 110 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_bitwise_or	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 110 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_bitwise_and	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 111 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_bitwise_and	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 111 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_bitwise_xor	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 112 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_bitwise_xor	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 112 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_shift_left	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 113 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_shift_left	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 113 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_shift_right	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 114 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_shift_right	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 114 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_logical_or	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 126 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_logical_or	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 126 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_logical_and	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 127 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_logical_and	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 127 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_equal_to	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 128 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_equal_to	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 128 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_not_equal_to	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 129 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_not_equal_to	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 129 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_greater	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 130 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_greater	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 130 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_less	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 131 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_less	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 131 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_greater_equal	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 132 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_greater_equal	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 132 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::right_assign_less_equal	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 133 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::assign_less_equal	(	T1 &	x,
		const T2 &	y
	)			[inline]

Definition at line 133 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_plus	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 141 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_minus	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 142 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_multiplies	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 143 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_divides	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 144 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_modulus	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 145 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_logical_or	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 146 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_logical_and	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 147 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_equal_to	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 148 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_not_equal_to	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 149 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_greater	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 150 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_less	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 151 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_greater_equal	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 152 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_less_equal	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 153 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_bitwise_or	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 154 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_bitwise_and	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 155 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_bitwise_xor	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 156 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_shift_left	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 157 of file basefuncs.hpp.

template<typename T1, typename T2>

T1& Arageli::left_assign_shift_right	(	const T1 &	x,
		T2 &	y
	)			[inline]

Definition at line 158 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_indirection

(

T &

x

)

[inline]

Definition at line 165 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_address

(

T &

x

)

[inline]

Definition at line 166 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_unary_plus

(

T &

x

)

[inline]

Definition at line 167 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_unary_minus

(

T &

x

)

[inline]

Definition at line 168 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_logical_not

(

T &

x

)

[inline]

Definition at line 169 of file basefuncs.hpp.

template<typename T>

T& Arageli::assign_bitwise_not

(

T &

x

)

[inline]

Definition at line 170 of file basefuncs.hpp.

big_int Arageli::ln1_25

(

std::size_t

kbits

)

Returns ln(1.25) with nbits significant bits.

Definition at line 30 of file big_const.cpp.

big_int Arageli::ln1_25_o

(

std::size_t

kbits

)

Returns ln(1.25) with nbits significant bits with overflow.

Definition at line 54 of file big_const.cpp.

big_int Arageli::ln1_25_u

(

std::size_t

kbits

)

Returns ln(1.25) with nbits significant bits with imperfection.

Definition at line 59 of file big_const.cpp.

big_int Arageli::ln2

(

std::size_t

kbits

)

Returns ln(2) with nbits significant bits.

Definition at line 65 of file big_const.cpp.

big_int Arageli::ln2_u

(

std::size_t

kbits

)

Returns ln(2) with nbits significant bits with imperfection.

Definition at line 87 of file big_const.cpp.

big_int Arageli::ln2_o

(

std::size_t

kbits

)

Returns ln(2) with nbits significant bits with oveflow.

Definition at line 92 of file big_const.cpp.

big_int Arageli::log2_10

(

std::size_t

nbits

)

Returns log2_10 with nbits significant bits.

Definition at line 99 of file big_const.cpp.

big_int Arageli::log2_10_o

(

std::size_t

nbits

)

Returns log2_10 with nbits significant bits with oveflow.

Definition at line 105 of file big_const.cpp.

big_int Arageli::log2_10_u

(

std::size_t

nbits

)

Returns log2_10 with nbits significant bits with imperfection.

Definition at line 110 of file big_const.cpp.

big_int Arageli::lg_2_o

(

std::size_t

nbits

)

Returns lg2 with nbits significant bits with oveflow.

Definition at line 117 of file big_const.cpp.

big_int Arageli::lg_2_u

(

std::size_t

nbits

)

Returns lg2 with nbits significant bits with imperfection.

Definition at line 122 of file big_const.cpp.

big_int Arageli::lg_2

(

std::size_t

nbits

)

Returns lg2 with nbits significant bits.

Definition at line 127 of file big_const.cpp.

big_int Arageli::exp_u	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns exp(arg/2^factor) with nbits significant bits with imperfection.

Definition at line 138 of file big_const.cpp.

big_int Arageli::exp_o	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns exp(arg/2^factor) with nbits significant bits with oveflow.

Definition at line 145 of file big_const.cpp.

big_int Arageli::exp	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns exp(arg/2^factor) with nbits significant bits.

Definition at line 152 of file big_const.cpp.

big_int Arageli::exp_2_u	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns 2^(arg/2^factor) with nbits significant bits with imperfection.

Definition at line 179 of file big_const.cpp.

big_int Arageli::exp_2_o	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns 2^(arg/2^factor) with nbits significant bits with oveflow.

Definition at line 184 of file big_const.cpp.

big_int Arageli::exp_2	(	big_int	arg,
		std::size_t	kbits,
		int	factor = 0
	)

Returns 2^(arg/2^factor) with nbits significant bits.

Definition at line 189 of file big_const.cpp.

big_int Arageli::e_u

(

std::size_t

kbits

)

Returns e number with nbits significant bits with imperfection.

Definition at line 213 of file big_const.cpp.

big_int Arageli::e_o

(

std::size_t

kbits

)

Returns e number with nbits significant bits with oveflow.

Definition at line 218 of file big_const.cpp.

big_int Arageli::e

(

std::size_t

kbits

)

Returns e number with nbits significant bits.

Definition at line 224 of file big_const.cpp.

big_int Arageli::ln10

(

std::size_t

nbits

)

Returns ln10 with nbits significant bits.

big_int Arageli::ln10_u

(

std::size_t

nbits

)

Returns ln10 with nbits significant bits with imperfection.

big_int Arageli::ln10_o

(

std::size_t

nbits

)

Returns ln10 with nbits significant bits with oveflow.

void Arageli::big_float_warning

(

const char *

s

)

Definition at line 34 of file big_float.cpp.

void Arageli::big_float_error

(

const char *

s

)

Definition at line 39 of file big_float.cpp.

void Arageli::big_float_fatal_error

(

const char *

s

)

Definition at line 44 of file big_float.cpp.

unsigned Arageli::fracsion	(	int	n,
		unsigned	m
	)

Definition at line 65 of file big_float.cpp.

int Arageli::get_exponent_of_double

(

double

d

)

Definition at line 72 of file big_float.cpp.

_Internal::digit* Arageli::get_mantissa_of_double

(

double

d

)

Definition at line 83 of file big_float.cpp.

int Arageli::get_sign

(

big_int

s

)

[inline]

Definition at line 120 of file big_float.cpp.

int Arageli::cmp	(	const big_float &	a,
		const big_float &	b
	)

Returns

• 0 if a = b,
• -1 if a < b,
• 1 if a > b

Definition at line 447 of file big_float.cpp.

int Arageli::operator==	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 453 of file big_float.cpp.

int Arageli::operator!=	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 458 of file big_float.cpp.

int Arageli::operator>	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 463 of file big_float.cpp.

int Arageli::operator>=	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 468 of file big_float.cpp.

int Arageli::operator<	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 473 of file big_float.cpp.

int Arageli::operator<=	(	const big_float &	a,
		const big_float &	b
	)

Definition at line 478 of file big_float.cpp.

big_float Arageli::operator+

(

const big_float &

a

)

Definition at line 499 of file big_float.cpp.

big_float Arageli::operator-

(

const big_float &

a

)

Definition at line 505 of file big_float.cpp.

big_float Arageli::operator+	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 514 of file big_float.cpp.

big_float Arageli::operator-	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 520 of file big_float.cpp.

big_float Arageli::operator *	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 526 of file big_float.cpp.

big_float Arageli::operator/	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 532 of file big_float.cpp.

big_float Arageli::add	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 538 of file big_float.cpp.

big_float Arageli::sub	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 544 of file big_float.cpp.

big_float Arageli::mul	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 550 of file big_float.cpp.

big_float Arageli::div	(	const big_float &	b,
		const big_float &	c
	)

Definition at line 556 of file big_float.cpp.

big_float Arageli::add	(	const big_float &	b,
		const big_float &	c,
		long	prec
	)

Definition at line 562 of file big_float.cpp.

big_float Arageli::sub	(	const big_float &	b,
		const big_float &	c,
		long	prec
	)

Definition at line 568 of file big_float.cpp.

big_float Arageli::mul	(	const big_float &	b,
		const big_float &	c,
		long	prec
	)

Definition at line 574 of file big_float.cpp.

big_float Arageli::div	(	const big_float &	b,
		const big_float &	c,
		long	prec
	)

Definition at line 580 of file big_float.cpp.

big_float Arageli::add	(	const big_float &	b,
		const big_float &	c,
		long	prec,
		int	mode
	)

Addition. Up to prec binary digits in rounding mode mode. The parameters prec and mode are optional and have the global defult values which can be set by set_global_precision and set_rounding_mode.

Definition at line 586 of file big_float.cpp.

big_float Arageli::sub	(	const big_float &	b,
		const big_float &	c,
		long	prec,
		int	mode
	)

Subtraction. Up to prec binary digits in rounding mode mode The parameters prec and mode are optional and have the global defult values which can be set by set_global_precision and set_rounding_mode.

Definition at line 659 of file big_float.cpp.

big_float Arageli::mul	(	const big_float &	b,
		const big_float &	c,
		long	prec,
		int	mode
	)

Multiplication. Up to prec binary digits in rounding mode mode The parameters prec and mode are optional and have the global defult values which can be set by set_global_precision and set_rounding_mode.

Definition at line 668 of file big_float.cpp.

big_float Arageli::div	(	const big_float &	b,
		const big_float &	c,
		long	prec,
		int	mode
	)

Divizion. Up to prec binary digits The parameters prec and mode are optional and have the global defult values which can be set by set_global_precision

Definition at line 714 of file big_float.cpp.

big_float Arageli::divnu	(	const big_float &	b,
		const big_float &	c,
		long	prec,
		int	mode
	)

Definition at line 731 of file big_float.cpp.

big_float Arageli::div_i

(

const big_int &

c

)

Definition at line 759 of file big_float.cpp.

void Arageli::reduce_final_zeros

(

std::basic_string< char > &

str

)

Definition at line 813 of file big_float.cpp.

std::istream& Arageli::operator>>	(	std::istream &	is,
		big_float &	fnum
	)

Definition at line 826 of file big_float.cpp.

std::ostream& Arageli::operator<<	(	std::ostream &	os,
		const big_float &	fnum
	)

Definition at line 914 of file big_float.cpp.

big_float Arageli::ceil

(

const big_float &

a

)

Definition at line 1128 of file big_float.cpp.

big_float Arageli::floor

(

const big_float &

a

)

Definition at line 1150 of file big_float.cpp.

big_float Arageli::frac

(

const big_float &

a

)

Definition at line 1173 of file big_float.cpp.

big_int Arageli::iceil

(

const big_float &

a

)

Definition at line 1187 of file big_float.cpp.

big_int Arageli::ifloor

(

const big_float &

a

)

Definition at line 1208 of file big_float.cpp.

big_float Arageli::fsqrt

(

const big_float &

b

)

Definition at line 1228 of file big_float.cpp.

big_float Arageli::fsqrt	(	const big_float &	bf,
		long	prec
	)

Definition at line 1235 of file big_float.cpp.

big_float Arageli::fsqrt	(	const big_float &	bf,
		long	prec,
		int	mode
	)

Square rooting. Up to prec binary digits The parameters prec and mode are optional and have the global defult values which can be set by set_global_precision.

Definition at line 1240 of file big_float.cpp.

big_float Arageli::nfsqrt	(	const big_float &	bf,
		long	prec,
		int	mode
	)

Definition at line 1271 of file big_float.cpp.

big_float Arageli::frandom

(

long

prec

)

Definition at line 1299 of file big_float.cpp.

big_float Arageli::frandom

(

)

Definition at line 1305 of file big_float.cpp.

big_float Arageli::frandom1	(	long	bits,
		const big_int &	exp = 0
	)

Definition at line 1310 of file big_float.cpp.

big_float Arageli::abs

(

const big_float &

x

)

[inline]

Definition at line 240 of file big_float.hpp.

template<typename Outiter>

void Arageli::generate_range_helper	(	big_float &	t1,
		const big_float &	t2,
		Outiter	outiter
	)			[inline]

Definition at line 245 of file big_float.hpp.

big_float& Arageli::operator+=	(	big_float &	b,
		const big_float &	c
	)			[inline]

Definition at line 249 of file big_float.hpp.

big_float& Arageli::operator-=	(	big_float &	b,
		const big_float &	c
	)			[inline]

Definition at line 252 of file big_float.hpp.

big_float& Arageli::operator *=	(	big_float &	b,
		const big_float &	c
	)			[inline]

Definition at line 255 of file big_float.hpp.

big_float& Arageli::operator/=	(	big_float &	b,
		const big_float &	c
	)			[inline]

Definition at line 258 of file big_float.hpp.

void Arageli::big_arith_error

(

const char *

s

)

Definition at line 333 of file big_int.cpp.

void Arageli::calc_bdn_radix	(	digit	radix,
		digit &	bdn_radix,
		std::size_t &	chars_per_digit
	)

Definition at line 425 of file big_int.cpp.

big_int Arageli::operator+	(	const big_int &	b,
		const big_int &	c
	)

Definition at line 550 of file big_int.cpp.

big_int Arageli::operator-	(	const big_int &	b,
		const big_int &	c
	)

Definition at line 625 of file big_int.cpp.

big_int Arageli::operator *	(	const big_int &	b,
		const big_int &	c
	)

Definition at line 636 of file big_int.cpp.

big_int Arageli::operator%	(	const big_int &	b,
		const big_int &	c
	)

Definition at line 762 of file big_int.cpp.

big_int Arageli::operator/	(	const big_int &	b,
		const big_int &	c
	)

Definition at line 770 of file big_int.cpp.

int Arageli::cmp	(	const big_int &	a,
		const big_int &	b
	)

Compares two big integers.

Returns

• 0 if a = b,
• -1 if a < b,
• 1 if a > b

Definition at line 785 of file big_int.cpp.

digit Arageli::random_digit

(

)

Definition at line 826 of file big_int.cpp.

digit Arageli::stream_radix

(

std::ios &

s

)

Definition at line 921 of file big_int.cpp.

std::ostream & Arageli::operator<<	(	std::ostream &	s,
		const big_int &	x
	)

Reads a number from a string notation.

Definition at line 930 of file big_int.cpp.

void Arageli::set_stream_radix	(	std::ios &	s,
		digit	radix
	)			[inline]

Definition at line 978 of file big_int.cpp.

std::istream & Arageli::operator>>	(	std::istream &	s,
		big_int &	x
	)

Writes a number to a string notation.

Definition at line 990 of file big_int.cpp.

big_int Arageli::operator<<	(	const big_int &	a,
		std::size_t	n
	)

Definition at line 1281 of file big_int.cpp.

big_int Arageli::operator>>	(	const big_int &	a,
		std::size_t	n
	)

Definition at line 1319 of file big_int.cpp.

big_int Arageli::operator &	(	const big_int &	a,
		const big_int &	b
	)

Definition at line 1355 of file big_int.cpp.

std::size_t Arageli::nbits

(

const big_int &

x

)

[inline]

Returns the number of bits in number. The same as big_int::length.

Definition at line 469 of file big_int.hpp.

template<typename TT>

int Arageli::sign

(

const big_int &

x

)

[inline]

Definition at line 489 of file big_int.hpp.

big_int Arageli::operator|	(	const big_int &	a,
		const big_int &	b
	)

big_int Arageli::operator^	(	const big_int &	a,
		const big_int &	b
	)

template<typename T>

big_int Arageli::operator<<	(	const big_int &	a,
		const T &	b
	)			[inline]

Requirements: b is representable as std::size_t.

Definition at line 512 of file big_int.hpp.

template<typename T>

big_int Arageli::operator>>	(	const big_int &	a,
		const T &	b
	)			[inline]

Requirements: b is representable as std::size_t.

Definition at line 517 of file big_int.hpp.

template<typename T>

big_int& Arageli::operator<<=	(	big_int &	a,
		const T &	b
	)			[inline]

Definition at line 521 of file big_int.hpp.

big_int& Arageli::operator>>=	(	big_int &	a,
		std::size_t	b
	)			[inline]

Definition at line 524 of file big_int.hpp.

template<typename T>

big_int& Arageli::operator>>=	(	big_int &	a,
		const T &	b
	)			[inline]

Definition at line 546 of file big_int.hpp.

void Arageli::divide	(	const big_int &	a,
		const big_int &	b,
		big_int &	q,
		big_int &	r
	)			[inline]

Divizion with quotient and remainder.

Divides a by b and stores quotient in q and remainder in r.

Parameters:

	a	a dividend
	b	a divizor, b must not be a zero
	q	a quotient
	r	a remainder

Definition at line 560 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 571 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 572 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 573 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 574 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 575 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	a,
		const big_int &	b
	)			[inline]

Definition at line 576 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		const big_int &	c
	)			[inline]

Definition at line 594 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		const big_int &	c
	)			[inline]

Definition at line 595 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		const big_int &	c
	)			[inline]

Definition at line 596 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		const big_int &	c
	)			[inline]

Definition at line 597 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		const big_int &	c
	)			[inline]

Definition at line 598 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		char	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

char& Arageli::operator+=	(	char &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		signed char	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

signed char& Arageli::operator+=	(	signed char &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

unsigned char& Arageli::operator+=	(	unsigned char &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		signed short	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

signed short& Arageli::operator+=	(	signed short &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

unsigned short& Arageli::operator+=	(	unsigned short &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		signed int	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

signed int& Arageli::operator+=	(	signed int &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

unsigned int& Arageli::operator+=	(	unsigned int &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		signed long	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

signed long& Arageli::operator+=	(	signed long &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

unsigned long& Arageli::operator+=	(	unsigned long &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		bool	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

bool& Arageli::operator+=	(	bool &	b,
		const big_int &	c
	)			[inline]

Definition at line 712 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		char	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

char& Arageli::operator-=	(	char &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		signed char	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

signed char& Arageli::operator-=	(	signed char &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

unsigned char& Arageli::operator-=	(	unsigned char &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		signed short	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

signed short& Arageli::operator-=	(	signed short &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

unsigned short& Arageli::operator-=	(	unsigned short &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		signed int	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

signed int& Arageli::operator-=	(	signed int &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

unsigned int& Arageli::operator-=	(	unsigned int &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		signed long	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

signed long& Arageli::operator-=	(	signed long &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

unsigned long& Arageli::operator-=	(	unsigned long &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		bool	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

bool& Arageli::operator-=	(	bool &	b,
		const big_int &	c
	)			[inline]

Definition at line 713 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		char	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

char& Arageli::operator *=	(	char &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		signed char	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

signed char& Arageli::operator *=	(	signed char &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

unsigned char& Arageli::operator *=	(	unsigned char &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		signed short	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

signed short& Arageli::operator *=	(	signed short &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

unsigned short& Arageli::operator *=	(	unsigned short &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		signed int	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

signed int& Arageli::operator *=	(	signed int &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

unsigned int& Arageli::operator *=	(	unsigned int &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		signed long	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

signed long& Arageli::operator *=	(	signed long &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

unsigned long& Arageli::operator *=	(	unsigned long &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		bool	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

bool& Arageli::operator *=	(	bool &	b,
		const big_int &	c
	)			[inline]

Definition at line 714 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		char	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

char& Arageli::operator/=	(	char &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		signed char	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

signed char& Arageli::operator/=	(	signed char &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

unsigned char& Arageli::operator/=	(	unsigned char &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		signed short	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

signed short& Arageli::operator/=	(	signed short &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

unsigned short& Arageli::operator/=	(	unsigned short &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		signed int	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

signed int& Arageli::operator/=	(	signed int &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

unsigned int& Arageli::operator/=	(	unsigned int &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		signed long	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

signed long& Arageli::operator/=	(	signed long &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

unsigned long& Arageli::operator/=	(	unsigned long &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		bool	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

bool& Arageli::operator/=	(	bool &	b,
		const big_int &	c
	)			[inline]

Definition at line 715 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		float	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

float& Arageli::operator+=	(	float &	b,
		const big_int &	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		double	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

double& Arageli::operator+=	(	double &	b,
		const big_int &	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

big_int& Arageli::operator+=	(	big_int &	b,
		long double	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

long double& Arageli::operator+=	(	long double &	b,
		const big_int &	c
	)			[inline]

Definition at line 717 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		float	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

float& Arageli::operator-=	(	float &	b,
		const big_int &	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		double	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

double& Arageli::operator-=	(	double &	b,
		const big_int &	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

big_int& Arageli::operator-=	(	big_int &	b,
		long double	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

long double& Arageli::operator-=	(	long double &	b,
		const big_int &	c
	)			[inline]

Definition at line 718 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		float	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

float& Arageli::operator *=	(	float &	b,
		const big_int &	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		double	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

double& Arageli::operator *=	(	double &	b,
		const big_int &	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

big_int& Arageli::operator *=	(	big_int &	b,
		long double	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

long double& Arageli::operator *=	(	long double &	b,
		const big_int &	c
	)			[inline]

Definition at line 719 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		float	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

float& Arageli::operator/=	(	float &	b,
		const big_int &	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		double	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

double& Arageli::operator/=	(	double &	b,
		const big_int &	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

big_int& Arageli::operator/=	(	big_int &	b,
		long double	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

long double& Arageli::operator/=	(	long double &	b,
		const big_int &	c
	)			[inline]

Definition at line 720 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		char	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

char& Arageli::operator%=	(	char &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		signed char	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

signed char& Arageli::operator%=	(	signed char &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

unsigned char& Arageli::operator%=	(	unsigned char &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		signed short	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

signed short& Arageli::operator%=	(	signed short &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

unsigned short& Arageli::operator%=	(	unsigned short &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		signed int	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

signed int& Arageli::operator%=	(	signed int &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

unsigned int& Arageli::operator%=	(	unsigned int &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		signed long	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

signed long& Arageli::operator%=	(	signed long &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

unsigned long& Arageli::operator%=	(	unsigned long &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int& Arageli::operator%=	(	big_int &	b,
		bool	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

bool& Arageli::operator%=	(	bool &	b,
		const big_int &	c
	)			[inline]

Definition at line 722 of file big_int.hpp.

big_int Arageli::operator+	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 731 of file big_int.hpp.

big_int Arageli::operator-	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 732 of file big_int.hpp.

big_int Arageli::operator *	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 733 of file big_int.hpp.

big_int Arageli::operator/	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 734 of file big_int.hpp.

big_int Arageli::operator+	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator+	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator+	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator+	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 736 of file big_int.hpp.

big_int Arageli::operator-	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator-	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator-	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator-	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 737 of file big_int.hpp.

big_int Arageli::operator *	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator *	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator *	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator *	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 738 of file big_int.hpp.

big_int Arageli::operator/	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator/	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator/	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator/	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 739 of file big_int.hpp.

big_int Arageli::operator%	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

big_int Arageli::operator%	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 741 of file big_int.hpp.

bool Arageli::operator==	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator!=	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator<=	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator>=	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator<	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator>	(	char	b,
		const big_int &	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		char	c
	)			[inline]

Definition at line 759 of file big_int.hpp.

bool Arageli::operator==	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator!=	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator<=	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator>=	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator<	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator>	(	signed char	b,
		const big_int &	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		signed char	c
	)			[inline]

Definition at line 760 of file big_int.hpp.

bool Arageli::operator==	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator!=	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator<=	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator>=	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator<	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator>	(	unsigned char	b,
		const big_int &	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		unsigned char	c
	)			[inline]

Definition at line 761 of file big_int.hpp.

bool Arageli::operator==	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator!=	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator<=	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator>=	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator<	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator>	(	signed short	b,
		const big_int &	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		signed short	c
	)			[inline]

Definition at line 762 of file big_int.hpp.

bool Arageli::operator==	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator!=	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator<=	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator>=	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator<	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator>	(	unsigned short	b,
		const big_int &	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		unsigned short	c
	)			[inline]

Definition at line 763 of file big_int.hpp.

bool Arageli::operator==	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator!=	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator<=	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator>=	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator<	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator>	(	signed int	b,
		const big_int &	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		signed int	c
	)			[inline]

Definition at line 764 of file big_int.hpp.

bool Arageli::operator==	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator!=	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator<=	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator>=	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator<	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator>	(	unsigned int	b,
		const big_int &	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		unsigned int	c
	)			[inline]

Definition at line 765 of file big_int.hpp.

bool Arageli::operator==	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator!=	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator<=	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator>=	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator<	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator>	(	signed long	b,
		const big_int &	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		signed long	c
	)			[inline]

Definition at line 766 of file big_int.hpp.

bool Arageli::operator==	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator!=	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator<=	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator>=	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator<	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator>	(	unsigned long	b,
		const big_int &	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		unsigned long	c
	)			[inline]

Definition at line 767 of file big_int.hpp.

bool Arageli::operator==	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator!=	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator<=	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator>=	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator<	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator>	(	bool	b,
		const big_int &	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		bool	c
	)			[inline]

Definition at line 768 of file big_int.hpp.

bool Arageli::operator==	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator!=	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator<=	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator>=	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator<	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator>	(	float	b,
		const big_int &	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		float	c
	)			[inline]

Definition at line 770 of file big_int.hpp.

bool Arageli::operator==	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator!=	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator<=	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator>=	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator<	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator>	(	double	b,
		const big_int &	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		double	c
	)			[inline]

Definition at line 771 of file big_int.hpp.

bool Arageli::operator==	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator==	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator!=	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator!=	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator<=	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator<=	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator>=	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator>=	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator<	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator<	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator>	(	long double	b,
		const big_int &	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::operator>	(	const big_int &	b,
		long double	c
	)			[inline]

Definition at line 772 of file big_int.hpp.

bool Arageli::is_null

(

const big_int &

x

)

[inline]

Definition at line 791 of file big_int.hpp.

bool Arageli::is_unit

(

const big_int &

x

)

[inline]

Definition at line 794 of file big_int.hpp.

bool Arageli::is_opposite_unit

(

const big_int &

x

)

[inline]

Definition at line 797 of file big_int.hpp.

bool Arageli::is_positive

(

const big_int &

x

)

[inline]

Definition at line 800 of file big_int.hpp.

bool Arageli::is_negative

(

const big_int &

x

)

[inline]

Definition at line 803 of file big_int.hpp.

bool Arageli::is_even

(

const big_int &

x

)

[inline]

Definition at line 806 of file big_int.hpp.

bool Arageli::is_odd

(

const big_int &

x

)

[inline]

Definition at line 810 of file big_int.hpp.

template<typename T>

T Arageli::intsqrt

(

const T &

a

)

Integer square root of a.

Returns the biggest x such that x^2 <= a. Requirement: a is positive.

big_int Arageli::sqrt

(

const big_int &

a

)

[inline]

Definition at line 823 of file big_int.hpp.

big_int Arageli::abs

(

const big_int &

x

)

[inline]

Returns absolutly value of x.

Definition at line 827 of file big_int.hpp.

big_int Arageli::pow	(	const big_int &	x,
		int	p
	)			[inline]

Raise x in to a power p.

Just uses Arageli::power.

Definition at line 835 of file big_int.hpp.

big_int Arageli::pow	(	const big_int &	x,
		const big_int &	p
	)			[inline]

Raise x in to a power p.

Just uses Arageli::power.

Definition at line 840 of file big_int.hpp.

big_int Arageli::log2

(

const big_int &

x

)

[inline]

Returns the base-2 logarithm of abs(x). If x == 0, returns -1.

Definition at line 844 of file big_int.hpp.

template<typename T1, typename T2>

int Arageli::cmp	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Performs Arageli like comparision.

There is specialization of this function (or an overloaded version) for each main Arageli object. Returns

• 0 if a == b,
• -1 if a < b,
• 1 if a > b.

Definition at line 35 of file cmp.hpp.

template<typename T>

int Arageli::sign

(

const T &

x

)

[inline]

Sign of element.

Returns +1, 0 or -1.

Definition at line 50 of file cmp.hpp.

template<typename T>

bool Arageli::is_even

(

const T &

x

)

[inline]

Returns true if x is even.

Definition at line 56 of file cmp.hpp.

template<typename T>

bool Arageli::is_odd

(

const T &

x

)

[inline]

Returns true if x is odd.

Definition at line 62 of file cmp.hpp.

template<typename T1, typename T2>

bool Arageli::is_divisible	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Returns true if a is divisible by b.

Definition at line 68 of file cmp.hpp.

template<typename T>

bool Arageli::is_positive

(

const T &

x

)

[inline]

Returns true if x is greater then null.

Definition at line 74 of file cmp.hpp.

template<typename T>

bool Arageli::is_negative

(

const T &

x

)

[inline]

Returns true if x is less then null.

Definition at line 79 of file cmp.hpp.

template<typename T>

bool Arageli::is_integer

(

const T &

x

)

[inline]

Returns true if x is integer.

Definition at line 85 of file cmp.hpp.

template<typename Out, typename T, typename M, typename CFG>

void Arageli::output_list	(	Out &	out,
		const cone< T, M, CFG > &	x
	)

template<typename Out, typename T, typename M, typename CFG>

Out& Arageli::operator<<	(	Out &	out,
		const cone< T, M, CFG > &	x
	)			[inline]

Definition at line 739 of file cone.hpp.

template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>

cone<T1, M1, CFG1> Arageli::intersection	(	cone< T1, M1, CFG1 >	a,
		const cone< T2, M2, CFG2 > &	b
	)			[inline]

Definition at line 750 of file cone.hpp.

template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>

cone<T1, M1, CFG1> Arageli::cone_union	(	cone< T1, M1, CFG1 >	a,
		const cone< T2, M2, CFG2 > &	b
	)			[inline]

Definition at line 763 of file cone.hpp.

template<typename T1, typename M1, typename CFG1, typename T2, typename M2, typename CFG2>

int Arageli::cmp	(	const cone< T1, M1, CFG1 > &	a,
		const cone< T2, M2, CFG2 > &	b
	)

Definition at line 776 of file cone.hpp.

std::ostream& Arageli::operator<<	(	std::ostream &	out,
		const exception &	e
	)			[inline]

Definition at line 83 of file exception.hpp.

template<typename T>

const T& Arageli::unit

(

)

[inline]

åäèíè÷íûé ýëåìåíò

Definition at line 85 of file factory.hpp.

template<typename T>

T Arageli::unit

(

const T &

x

)

[inline]

åäèíè÷íûé ýëåìåíò

Definition at line 90 of file factory.hpp.

template<typename T>

bool Arageli::is_unit

(

const T &

x

)

[inline]

ïðîâåðêà íà ðàâåíñòâî åäèíè÷íîìó ýëåìåíòó

Definition at line 95 of file factory.hpp.

template<typename T>

const T& Arageli::opposite_unit

(

)

[inline]

ïðîòèâîïîëîæíûé ê åäèíè÷íîìó ýëåìåíòó (-1)

Definition at line 100 of file factory.hpp.

template<typename T>

T Arageli::opposite_unit

(

const T &

x

)

[inline]

ïðîòèâîïîëîæíûé ê åäèíè÷íîìó ýëåìåíòó (-1)

Definition at line 105 of file factory.hpp.

template<typename T>

bool Arageli::is_opposite_unit

(

const T &

x

)

[inline]

ïðîâåðêà íà ðàâåíñòâî -1

Definition at line 110 of file factory.hpp.

template<typename T>

const T& Arageli::null

(

)

[inline]

íóëåâîé ýëåìåíò

Definition at line 115 of file factory.hpp.

template<typename T>

T Arageli::null

(

const T &

)

[inline]

íóëåâîé ýëåìåíò

Definition at line 120 of file factory.hpp.

template<typename T>

bool Arageli::is_null

(

const T &

x

)

[inline]

ïðîâåðêà íà ðàâåíñòâî íóëåâîìó ýëåìåíòó

Definition at line 125 of file factory.hpp.

template<typename T>

T Arageli::opposite

(

const T &

x

)

[inline]

ïðîòèâîïîëîæíûé ýëåìåíò

Definition at line 130 of file factory.hpp.

template<typename T>

T& Arageli::opposite	(	const T &	x,
		T *	y
	)			[inline]

ïðîòèâîïîëîæíûé ýëåìåíò

Definition at line 135 of file factory.hpp.

template<typename T>

T& Arageli::opposite

(

T *

x

)

[inline]

ïðîòèâîïîëîæíûé ýëåìåíò

Definition at line 140 of file factory.hpp.

template<typename T>

T Arageli::inverse

(

const T &

x

)

[inline]

îáðàòíûé ýëåìåíò ê äàííîìó

Definition at line 145 of file factory.hpp.

template<typename T>

T& Arageli::inverse	(	const T &	x,
		T *	y
	)			[inline]

îáðàòíûé ýëåìåíò ê äàííîìó

Definition at line 150 of file factory.hpp.

template<typename T>

T& Arageli::inverse

(

T *

x

)

[inline]

îáðàòíûé ýëåìåíò ê äàííîìó

Definition at line 155 of file factory.hpp.

Arageli::ARAGELI_UNARY_FUNCTION_TRAITS	(	indirection	,
		typename omit_asterisk< Arg >::type	,
		false	,
		false
	)

Arageli::ARAGELI_UNARY_FUNCTION_TRAITS	(	postfix_increment	,
		typename omit_ref< Arg >::type	,
		true	,
		false
	)

Arageli::ARAGELI_UNARY_FUNCTION_TRAITS	(	postfix_decrement	,
		typename omit_ref< Arg >::type	,
		true	,
		false
	)

Arageli::ARAGELI_BINARY_FUNCTION_TRAITS	(	subscript	,
		typename omit_asterisk< Arg1 >::type	,
		false	,
		false	,
		false
	)

template<typename T>

bool Arageli::is_prime

(

const T &

x

)

[inline]

Determines if x is prime via appropriate algorithm for T.

Definition at line 86 of file prime.hpp.

template<typename M>

void Arageli::gauss_field_row_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col
	)

Gauss elimination of column col with row manipulation.

Eliminates nonzeros in column col exclude the element (row, col) by row manipulation. Pivot element (row, col) becomes 1.

template<typename M>

void Arageli::gauss_field_col_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col
	)

Gauss elimination of row with column manipulation.

Eliminates nonzeros in row exclude the element (row, col) by column manipulation. Pivot element (row, col) becomes 1.

template<typename M, typename T>

void Arageli::gauss_bareiss_row_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col,
		T &	det,
		T &	det_denom
	)

Gauss-Bareiss elimination of column col with row manipulation.

Eliminates nonzeros in column col exclude the element (row, col) by row manipulation.

template<typename M, typename T>

void Arageli::gauss_bareiss_col_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col,
		T &	det,
		T &	det_denom
	)

Gauss-Bareiss elimination of row with column manipulation.

Eliminates nonzeros in row exclude the element (row, col) by column manipulation.

template<typename M>

void Arageli::gauss_bareiss_row_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col
	)

Gauss-Bareiss elimination of column col with row manipulation.

Eliminates nonzeros in column col exclude the element (row, col) by row manipulation.

Definition at line 102 of file gauss.hpp.

template<typename M>

void Arageli::gauss_bareiss_col_iter	(	M &	a,
		typename M::size_type	row,
		typename M::size_type	col
	)

Gauss-Bareiss elimination of row with column manipulation.

Eliminates nonzeros in row exclude the element (row, col) by column manipulation.

Definition at line 118 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		const T_factory &	tfctr,
		Ctrler	ctrler
	)

Produces the reduced row echelon form B of the matrix a over a field.

Elementary row operations are performed on a, a matrix over a field, to reduce it to reduced row echelon (Gauss-Jordan) form. Returns b, q, basis, det:

• q is such that b = q * a;
• r = basis.size() is the rank of A;
• B.sumbatrix(mesh_grid(1,r), basis) is the r-by-r identity matrix; (?)
• det is the value of the max size left upper corner minor of A.

template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 270 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det
	)			[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 276 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis
	)			[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 282 of file gauss.hpp.

template<typename A, typename B, typename Q>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b,
		Q &	q
	)			[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 292 of file gauss.hpp.

template<typename A, typename B>

void Arageli::rref_gauss_field	(	const A &	a,
		B &	b
	)			[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 303 of file gauss.hpp.

template<typename A>

A Arageli::rref_gauss_field

(

const A &

a

)

[inline]

Produces the reduced row echelon form B of a matrix A.

Definition at line 315 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>

void Arageli::rref_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		const T_factory &	tfctr,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

It's the same that rref_gauss_field funtion.

Definition at line 336 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>

void Arageli::rref_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 352 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T>

void Arageli::rref_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 358 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis>

void Arageli::rref_field	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 364 of file gauss.hpp.

template<typename A, typename B, typename Q>

void Arageli::rref_field	(	const A &	a,
		B &	b,
		Q &	q
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 374 of file gauss.hpp.

template<typename A, typename B>

void Arageli::rref_field	(	const A &	a,
		B &	b
	)			[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 385 of file gauss.hpp.

template<typename A>

A Arageli::rref_field

(

const A &

a

)

[inline]

Produces the reduced row echelon form B of the matrix a over a field.

Definition at line 397 of file gauss.hpp.

template<typename A1, typename A2, typename I>

void Arageli::mat_col_copy_order	(	const A1 &	a1,
		A2 &	a2,
		const I &	idx
	)

Copies columns from a1 to a2 in order indexes in idx then tails the rest.

template<typename A1, typename A2, typename I>

void Arageli::vec_copy_order	(	const A1 &	a1,
		A2 &	a2,
		const I &	idx
	)

Copies elements from a1 to a2 in order indexes in idx then tails the rest.

template<typename A, typename B>

void Arageli::vec_inverse_permutation	(	const A &	a,
		B &	b
	)

Inverses permutation vector.

template<typename A, typename B, typename Q, typename Basis_in, typename Basis_out, typename Det>

void Arageli::rref_order	(	const A &	a,
		B &	b,
		Q &	q,
		const Basis_in &	basis_in,
		Basis_out &	basis_out,
		Det &	det
	)

Produces the reduced row echelon from B of the matrix A with a specific column order.

Makes RREF(A) with permutated columns according to basis_in. basis_in contains indexes of columns, basis_out indicates additional permutaitaon of columns.

template<typename T, bool REFCNT>

matrix<T, REFCNT> Arageli::inverse

(

const matrix< T, REFCNT > &

A

)

Matrix inversion.

Returns inversion of matrix A Requirement: A must be square.

template<typename T, bool REFCNT>

T Arageli::det

(

const matrix< T, REFCNT > &

A

)

Returns determinant of A.

Returns determinant of A. Precondition: A must be square

template<typename T, bool REFCNT>

matrix<T, REFCNT>::size_type Arageli::rank

(

const matrix< T, REFCNT > &

A

)

Returns a rank of a matrix.

template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		const T_factory &	tfctr,
		Ctrler	ctrler
	)

Produces the reduced row echelon form B of the matrix a over an integer domain.

Produces the reduced row echelon form B of the integer matrix a by Gauss-Bareiss algorithm. Returns b, q, basis, det:

• q is such that b = q * a;
• r = basis.size() is the rank of A;
• B.sumbatrix(mesh_grid(1,r), basis) is the r-by-r non-singular diagonal matrix; (?)
• det is a determinant of a. (?)

template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 503 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 509 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 515 of file gauss.hpp.

template<typename A, typename B, typename Q>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b,
		Q &	q
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 525 of file gauss.hpp.

template<typename A, typename B>

void Arageli::rref_gauss_bareiss	(	const A &	a,
		B &	b
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 536 of file gauss.hpp.

template<typename A>

A Arageli::rref_gauss_bareiss

(

const A &

a

)

[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 548 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>

void Arageli::rref_int	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		const T_factory &	tfctr,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

It's the same that rref_gauss_bareiss funtion.

Definition at line 570 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>

void Arageli::rref_int	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 586 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T>

void Arageli::rref_int	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 592 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis>

void Arageli::rref_int	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 598 of file gauss.hpp.

template<typename A, typename B, typename Q>

void Arageli::rref_int	(	const A &	a,
		B &	b,
		Q &	q
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 608 of file gauss.hpp.

template<typename A, typename B>

void Arageli::rref_int	(	const A &	a,
		B &	b
	)			[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 619 of file gauss.hpp.

template<typename A>

A Arageli::rref_int

(

const A &

a

)

[inline]

Produces the reduced row echelon form B of the matrix a over an integer domain.

Definition at line 631 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename T_factory, typename Ctrler>

void Arageli::rref	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		const T_factory &	tfctr,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a.

Exact meaning of RREF depends on type of result (integer domain or field); see rref_field and rref_int respectively.

Definition at line 694 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T, typename Ctrler>

void Arageli::rref	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det,
		Ctrler	ctrler
	)			[inline]

Produces the reduced row echelon form B of the matrix a.

Definition at line 716 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis, typename T>

void Arageli::rref	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis,
		T &	det
	)			[inline]

Produces the reduced row echelon form B of the matrix a.

Definition at line 722 of file gauss.hpp.

template<typename A, typename B, typename Q, typename Basis>

void Arageli::rref	(	const A &	a,
		B &	b,
		Q &	q,
		Basis &	basis
	)

Produces the reduced row echelon form B of the matrix a.

Definition at line 728 of file gauss.hpp.

template<typename A, typename B, typename Q>

void Arageli::rref	(	const A &	a,
		B &	b,
		Q &	q
	)			[inline]

Produces the reduced row echelon form B of the matrix a.

Definition at line 738 of file gauss.hpp.

template<typename A, typename B>

void Arageli::rref	(	const A &	a,
		B &	b
	)			[inline]

Produces the reduced row echelon form B of the matrix a.

Definition at line 749 of file gauss.hpp.

template<typename A>

A Arageli::rref

(

const A &

a

)

[inline]

Produces the reduced row echelon form B of the matrix a.

Definition at line 761 of file gauss.hpp.

template<typename T, bool REFCNT>

T Arageli::det_int

(

const matrix< T, REFCNT > &

A

)

Returns determinant of integer matrix A.

template<typename T, bool REFCNT>

matrix<T, REFCNT>::size_type Arageli::rank_int

(

const matrix< T, REFCNT > &

A

)

Returns a rank of integer matrix.

template<typename T, typename T_factory>

T Arageli::euclid	(	T	a,
		T	b,
		const T_factory &	tfctr
	)

Processes the Euclidean algorithm on a and b.

If is_null(a) and is_null(b) then the function returns tfctr.unit(a).

template<typename T>

T Arageli::euclid	(	const T &	a,
		const T &	b
	)			[inline]

Processes the Euclidean algorithm on a and b.

Definition at line 45 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::euclid_binary	(	T	a,
		T	b,
		const T_factory &	tfctr
	)

Processes the Euclidean algorithm on a and b.

If is_null(a) and is_null(b) then the function returns tfctr.unit(a).

template<typename T>

T Arageli::euclid_binary	(	const T &	a,
		const T &	b
	)			[inline]

Processes the Euclidean algorithm on a and b.

Definition at line 57 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::euclid	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b,
		const T_factory &	tfctr
	)

Computes Euclidean algorithm for each corresponding pair of a and b.

The factory of tfctr of type T_factory is a factory for type compatible with T or T1.

template<typename T, bool REFCNT, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::euclid	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b
	)			[inline]

Computes Euclidean algorithm for each corresponding pair of a and b.

Definition at line 76 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::euclid_bezout	(	const T &	a,
		const T &	b,
		T &	u,
		T &	v,
		const T_factory &	tfctr
	)

The greatest common divisor and Bezout's coefficients.

template<typename T>

T Arageli::euclid_bezout	(	const T &	a,
		const T &	b,
		T &	u,
		T &	v
	)			[inline]

The greatest common divisor and Bezout's coefficients.

Definition at line 100 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::gcd	(	const T &	a,
		const T &	b,
		const T_factory &	tfctr,
		const type_category::type &
	)			[inline]

Definition at line 112 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::gcd	(	const T &	a,
		const T &	b,
		const T_factory &	tfctr,
		const type_category::integer &
	)			[inline]

Definition at line 116 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::gcd	(	const T &	a,
		const T &	b,
		const T_factory &	tfctr
	)			[inline]

Computes GCD for a and b.

Definition at line 121 of file gcd.hpp.

template<typename T>

T Arageli::gcd	(	const T &	a,
		const T &	b
	)			[inline]

Computes GCD for a and b.

Definition at line 126 of file gcd.hpp.

template<typename T1, typename T2>

T1 Arageli::gcd	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Computes GCD for a and b.

Definition at line 131 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory>

T Arageli::gcd	(	const vector< T, REFCNT > &	x,
		const T_factory &	tfctr
	)

Computes GCD for all items of vector 'x'.

template<typename T, bool REFCNT>

T Arageli::gcd

(

const vector< T, REFCNT > &

x

)

[inline]

Computes GCD for all items of vector 'x'.

Definition at line 140 of file gcd.hpp.

template<typename T>

T Arageli::gcd3	(	const T &	a,
		const T &	b,
		const T &	c
	)			[inline]

Compute GCD(a, b, c).

Definition at line 146 of file gcd.hpp.

template<typename T>

T Arageli::gcdex	(	const T &	a,
		const T &	b,
		T &	u,
		T &	v,
		T &	w,
		T &	z
	)

Extended GCD; abs(u*z - w*v) == 1; a*w + b*z == 0.

template<typename T>

T Arageli::gcdex	(	const T &	a,
		const T &	b,
		const T &	N,
		T &	u,
		T &	v,
		T &	w,
		T &	z
	)

template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::gcd_vec	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b,
		const T_factory &	tfctr
	)

Computes GCD for each corresponding pair of a and b.

template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::gcd	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b,
		const T_factory &	tfctr
	)			[inline]

Computes GCD for each corresponding pair of a and b.

Definition at line 181 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory>

vector<T, REFCNT> Arageli::gcd	(	const vector< T, REFCNT > &	a,
		const vector< T, REFCNT > &	b,
		const T_factory &	tfctr
	)			[inline]

Computes GCD for each corresponding pair of a and b.

Definition at line 192 of file gcd.hpp.

template<typename T, bool REFCNT, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::gcd	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b
	)			[inline]

Computes GCD for each corresponding pair of a and b.

Definition at line 203 of file gcd.hpp.

template<typename T, bool REFCNT>

vector<T, REFCNT> Arageli::gcd	(	const vector< T, REFCNT > &	a,
		const vector< T, REFCNT > &	b
	)			[inline]

Computes GCD for each corresponding pair of a and b.

Definition at line 213 of file gcd.hpp.

template<typename T, typename T_factory>

T Arageli::lcm	(	const T &	a,
		const T &	b,
		const T_factory &	tfctr
	)			[inline]

Computes LCM for a and b.

Definition at line 222 of file gcd.hpp.

template<typename T>

T Arageli::lcm	(	const T &	a,
		const T &	b
	)			[inline]

Computes LCM for a and b.

Definition at line 227 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory>

T Arageli::lcm	(	const vector< T, REFCNT > &	x,
		const T_factory &	tfctr
	)

Computes LCM for all items of vector 'x'.

template<typename T, bool REFCNT>

T Arageli::lcm

(

const vector< T, REFCNT > &

x

)

[inline]

Computes LCM for all items of vector 'x'.

Definition at line 236 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::lcm_vec	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b,
		const T_factory &	tfctr
	)

Computes LCM for each corresponding pair of a and b.

template<typename T, bool REFCNT, typename T_factory, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::lcm	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b,
		const T_factory &	tfctr
	)			[inline]

Computes LCM for each corresponding pair of a and b.

Definition at line 261 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory>

vector<T, REFCNT> Arageli::lcm	(	const vector< T, REFCNT > &	a,
		const vector< T, REFCNT > &	b,
		const T_factory &	tfctr
	)			[inline]

Computes LCM for each corresponding pair of a and b.

Definition at line 272 of file gcd.hpp.

template<typename T, bool REFCNT, typename T1, bool REFCNT1>

vector<T, REFCNT> Arageli::lcm	(	const vector< T, REFCNT > &	a,
		const vector< T1, REFCNT1 > &	b
	)			[inline]

Computes LCM for each corresponding pair of a and b.

Definition at line 283 of file gcd.hpp.

template<typename T, bool REFCNT>

vector<T, REFCNT> Arageli::lcm	(	const vector< T, REFCNT > &	a,
		const vector< T, REFCNT > &	b
	)			[inline]

Definition at line 292 of file gcd.hpp.

template<typename T, typename T_factory>

bool Arageli::is_coprime	(	const T &	a,
		const T &	b,
		const T_factory &	tfctr
	)			[inline]

Returns true if two objects are coprime.

Definition at line 308 of file gcd.hpp.

template<typename T>

bool Arageli::is_coprime	(	const T &	a,
		const T &	b
	)			[inline]

Returns true if two objects are coprime.

Definition at line 313 of file gcd.hpp.

template<typename T, bool REFCNT, typename T_factory>

bool Arageli::is_coprime	(	const vector< T, REFCNT > &	x,
		const T_factory &	tfctr
	)			[inline]

Returns true if all objects in the vector are coprime.

Definition at line 318 of file gcd.hpp.

template<typename T, bool REFCNT>

bool Arageli::is_coprime

(

const vector< T, REFCNT > &

x

)

[inline]

Returns true if all objects in the vector are coprime.

Definition at line 323 of file gcd.hpp.

template<class T>

matrix<T> Arageli::hermite_old

(

const matrix< T > &

m_

)

The old original function for producing Hermite form.

template<typename MA, typename MH, typename MU>

void Arageli::hermite_upper	(	const MA &	A,
		MH &	H,
		MU &	U
	)			[inline]

Produces the upper Hermite form H of an integer matrix A.

Returns H, U: U is unimodular princpal left transform such that H = U * A;

Definition at line 57 of file hermite.hpp.

template<typename MA, typename MH, typename MU>

void Arageli::hermite_lower	(	const MA &	A,
		MH &	H,
		MU &	U
	)			[inline]

Produces the lower Hermite form H of an integer matrix A.

Returns H, U: U is unimodular princpal rigth transform such that H = A * U;

Definition at line 86 of file hermite.hpp.

template<typename M>

M Arageli::hermite

(

const M &

A

)

[inline]

Produces the upper Hermite form H of an integer matrix A.

Definition at line 106 of file hermite.hpp.

template<typename M>

M Arageli::hermite_transform_matrix

(

const M &

A

)

[inline]

Produces the unimodular princpal left transform U such that U*A is a Hermite form of an integer matrix A.

Definition at line 123 of file hermite.hpp.

template<typename T, typename T_factory>

T Arageli::inverse_mod	(	const T &	a,
		const T &	m,
		const T_factory &	tfctr
	)			[inline]

Returns inversion of a modulo n.

Requirement: n must be prime.

Definition at line 43 of file intalg.hpp.

template<typename T>

T Arageli::inverse_mod	(	const T &	a,
		const T &	n
	)			[inline]

Returns inversion of a modulo n.

Requirement: n must be prime.

Definition at line 58 of file intalg.hpp.

template<typename T, typename I, typename T_factory>

T Arageli::power_mod	(	T	a,
		I	n,
		const T &	m,
		const T_factory &	tfctr
	)

Exponentiates a in to power n modulo m via squaring and adding.

Requirements: n and m must be a positive.

template<typename T, typename I>

T Arageli::power_mod	(	const T &	a,
		const I &	n,
		const T &	m
	)			[inline]

Exponentiates a in to power n modulo m via squaring and adding.

Requirements: n and m must be a positive.

Definition at line 70 of file intalg.hpp.

template<typename T1, typename T2, typename T3>

T3 Arageli::mod	(	const T1 &	a,
		const T2 &	b,
		const T3 &	d
	)

Definition at line 99 of file intalg.hpp.

template<typename T1, typename T2>

T2 Arageli::mod	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Compute a modulo b.

Definition at line 105 of file intalg.hpp.

template<typename T1, typename T2, typename T3>

T3 Arageli::div_mod	(	const T1 &	a,
		const T2 &	b,
		const T3 &	d
	)

Compute a/b modulo d.

template<typename T1, typename T2, typename T3>

T3 Arageli::rem_mod	(	const T1 &	a,
		const T2 &	b,
		const T3 &	d
	)			[inline]

Compute residue of division a by b modulo d.

If d is a prime, the function returns 0.

Definition at line 117 of file intalg.hpp.

template<typename T1, typename T2>

T2 Arageli::ann	(	const T1 &	a,
		const T2 &	n
	)			[inline]

Compute n/gcd(a, n).

Definition at line 123 of file intalg.hpp.

template<typename T1, typename T2, typename T3>

T3 Arageli::quo_mod	(	const T1 &	a,
		const T2 &	b,
		const T3 &	d
	)

template<typename T>

T Arageli::split	(	const T &	a,
		const T &	d
	)

template<typename T>

T Arageli::stab	(	const T &	a,
		const T &	b,
		const T &	N
	)

template<typename T>

T Arageli::split_stab	(	const T &	a,
		const T &	b,
		const T &	N
	)

template<typename T>

T Arageli::unit	(	const T &	a,
		const T &	N
	)

template<typename T>

T Arageli::stab	(	const T &	a,
		const T &	b,
		const T &	N,
		const T &	d
	)			[inline]

Definition at line 154 of file intalg.hpp.

template<typename T>

T Arageli::split_stab	(	const T &	a,
		const T &	b,
		const T &	N,
		const T &	d
	)			[inline]

Definition at line 160 of file intalg.hpp.

template<typename T>

T Arageli::split_mod	(	const T &	a,
		const T &	d
	)

template<typename T>

T Arageli::stab_mod	(	const T &	a,
		const T &	b,
		const T &	N
	)

template<typename T>

T Arageli::stab_mod	(	const T &	a,
		const T &	b,
		const T &	N,
		const T &	d
	)			[inline]

Definition at line 176 of file intalg.hpp.

template<typename T>

bool Arageli::is_invertible_mod	(	const T &	a,
		const T &	N
	)

Returns true iff a is invertible element modulo N.

template<typename T>

std::size_t Arageli::nbits

(

const T &

a

)

[inline]

Compute number of bit in binary notation of a.

Definition at line 187 of file intalg.hpp.

template<typename T, typename T_factory>

std::size_t Arageli::nbits	(	T	a,
		const T_factory &	tfctr
	)

Compute number of bit in binary notation of a.

template<typename T, typename T_factory>

T Arageli::factorial_successive_multiplication	(	T	a,
		const T_factory &	tfctr
	)

Computes factorial via just successive multiplication (by definition).

Computes a*(a-1)*(a-2)* ... *3*2.

template<typename T>

T Arageli::factorial_successive_multiplication

(

const T &

a

)

[inline]

Computes factorial via just successive multiplication (by definition).

Definition at line 203 of file intalg.hpp.

template<typename T, typename T_factory>

T Arageli::factorial_even_odd_multiplication	(	T	a,
		const T_factory &	tfctr
	)

Computes factorial via even and odd multiplier separation.

template<typename T>

T Arageli::factorial_even_odd_multiplication

(

const T &

a

)

[inline]

Computes factorial via even and odd multiplier separation.

Definition at line 213 of file intalg.hpp.

template<typename T, typename T_factory>

T Arageli::factorial	(	const T &	a,
		const T_factory &	tfctr
	)			[inline]

Computes factorial of a via apropriate algorithm.

Definition at line 219 of file intalg.hpp.

template<typename T>

T Arageli::factorial

(

const T &

a

)

[inline]

Computes factorial of a via apropriate algorithm.

Definition at line 224 of file intalg.hpp.

template<typename T, typename T_factory>

int Arageli::jacobi	(	T	a,
		T	n,
		const T_factory &	tfctr
	)

Computes the Jacobi symbol (a/n).

Requirements: m > 1, m is odd.

template<typename T>

int Arageli::jacobi	(	const T &	a,
		const T &	n
	)			[inline]

Computes the Jacobi symbol (a/n).

Requirements: m > 1, m is odd.

Definition at line 242 of file intalg.hpp.

template<typename T, typename TT>

T Arageli::sqrt_mod_shenks	(	const T &	a,
		const T &	n,
		const TT &	tt
	)

The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).

Returns x such that x^2 = a (mod n). Requirement: 0 <= a < n, n is prime and n = 1 (mod 4).

template<typename T>

T Arageli::sqrt_mod_shenks	(	const T &	a,
		const T &	n
	)			[inline]

The Shenks algorithm (square root of a modulo n, for n = 1 (mod 4)).

Returns x such that x^2 = a (mod n). Requirement: 0 <= a < n, n is prime and n = 1 (mod 4).

Definition at line 265 of file intalg.hpp.

template<typename Gen, typename IntGen>

void Arageli::intconvex_simple	(	const Gen &	gen,
		IntGen &	intgen
	)

A convex hull of integer points of a polyhedron.

This function takes a set of generatrices of the base cone of a polyhedron. And it returns a set of generatrices of the base cone of convex hull of integer pointes of that polyhedron. This function implements a primitive algorithm and finds the convex hull very slow. It's deathly algorithm! Source of the idea: Emelichev V.A., Kovalev M.M., Kravcov M.K. Mnogogranniki, grafy, optimizacija (Nauka, 1981)(Russian), pp. 107--110. System of generatrices in gen is not necessarily minimal; and retrieved system intgen is not necessarily minimal (actually it's very big). WARINING! Type of elements of gen should be integer.

template<typename A, typename T, typename Ctrler>

void Arageli::intcount_barvinok	(	const A &	a,
		T &	res,
		Ctrler	ctrler
	)

Counts all integer points in bodily polytope.

template<typename A, typename T>

void Arageli::intcount_barvinok	(	const A &	a,
		T &	res
	)			[inline]

Counts all integer points in bodily polytope.

Definition at line 56 of file intcount_barvinok.hpp.

template<typename A>

A::element_type Arageli::intcount_barvinok

(

const A &

a

)

[inline]

Counts all integer points in bodily polytope.

Definition at line 62 of file intcount_barvinok.hpp.

template<typename T>

interval<T> Arageli::operator+	(	const interval< T > &	a,
		const interval< T > &	b
	)

Definition at line 193 of file interval.hpp.

template<typename T>

interval<T> Arageli::operator-	(	const interval< T > &	a,
		const interval< T > &	b
	)

Definition at line 210 of file interval.hpp.

template<typename T>

interval<T> Arageli::operator *	(	const interval< T > &	a,
		const interval< T > &	b
	)

Definition at line 227 of file interval.hpp.

template<typename T>

interval<T> Arageli::operator/	(	const interval< T > &	a,
		const interval< T > &	b
	)

Definition at line 244 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::are_overlap_intervals_oooo	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Definition at line 263 of file interval.hpp.

template<typename Seg1, typename Seg2>

bool Arageli::is_overlap_segs	(	const Seg1 &	a,
		const Seg2 &	b
	)			[inline]

Definition at line 281 of file interval.hpp.

template<typename Out, typename T>

Out& Arageli::operator<<	(	Out &	out,
		const interval< T > &	x
	)

Definition at line 288 of file interval.hpp.

template<typename In, typename T>

In& Arageli::operator>>	(	In &	in,
		interval< T > &	x
	)

Definition at line 295 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::are_comparable_oooo	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Determines if a and b are exactly comparable as two open intervals.

Definition at line 322 of file interval.hpp.

template<typename T1, typename T2>

int Arageli::cmp	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Semi-lexicographical comparision between two intervals.

An empty interval less than all others.

Definition at line 329 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator<	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Definition at line 347 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator>	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Definition at line 355 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator<=	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Definition at line 363 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator>=	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Definition at line 371 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator==	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)

Definition at line 379 of file interval.hpp.

template<typename T1, typename T2>

bool Arageli::operator!=	(	const interval< T1 > &	a,
		const interval< T2 > &	b
	)			[inline]

Definition at line 387 of file interval.hpp.

template<typename T>

interval<T> Arageli::abs

(

const interval< T > &

x

)

Definition at line 392 of file interval.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_polynom_first_default	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)			[inline]

Default ouputting method for subexpression as the first coefficient in a polynomial.

Definition at line 29 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_polynom_internal_default	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)

Default ouputting method for subexpression as an internal coefficient in a polynomial.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_pow_default	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)

Default ouputting method for subexpression as a degree of variable in a polynomial.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_polynom_first_default	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)

Default inputting method for subexpression as the first coefficient in a polynomial.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_polynom_internal_default	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)

Default inputting method for subexpression as an internal coefficient in a polynomial.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_pow_default	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)			[inline]

Default inutting method for subexpression as a degree of variable in a polynomial.

Definition at line 55 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_polynom_first	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)			[inline]

Definition at line 61 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_polynom_internal	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)			[inline]

Definition at line 66 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_ostream<Ch, ChT>& Arageli::output_pow	(	std::basic_ostream< Ch, ChT > &	out,
		const T &	x
	)			[inline]

Definition at line 71 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_polynom_first	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)			[inline]

Definition at line 76 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_polynom_internal	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)			[inline]

Definition at line 81 of file io.hpp.

template<typename T, typename Ch, typename ChT>

std::basic_istream<Ch, ChT>& Arageli::input_pow	(	std::basic_istream< Ch, ChT > &	in,
		T &	x
	)			[inline]

Definition at line 86 of file io.hpp.

template<typename T, typename TB, typename F>

apply_iterator<T, TB, F> Arageli::operator+	(	apply_iterator< T, TB, F >	x,
		typename apply_iterator< T, TB, F >::difference_type	n
	)

Definition at line 104 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

apply_iterator<T, TB, F> Arageli::operator-	(	apply_iterator< T, TB, F >	x,
		typename apply_iterator< T, TB, F >::difference_type	n
	)

Definition at line 110 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

std::iterator_traits<TB>::difference_type Arageli::operator-	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 116 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator==	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 130 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator!=	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 131 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator<	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 132 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator>	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 133 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator<=	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 134 of file iteradapt.hpp.

template<typename T, typename TB, typename F>

bool Arageli::operator>=	(	const apply_iterator< T, TB, F > &	a,
		const apply_iterator< T, TB, F > &	b
	)			[inline]

Definition at line 135 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

std::iterator_traits<TB1>::difference_type Arageli::operator-	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 226 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator==	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 231 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator!=	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 235 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator<	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 239 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator>	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 243 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator<=	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 247 of file iteradapt.hpp.

template<typename T, typename TB1, typename TB2, typename F>

bool Arageli::operator>=	(	const Iterpair< T, TB1, TB2, F > &	a,
		const Iterpair< T, TB1, TB2, F > &	b
	)			[inline]

Definition at line 251 of file iteradapt.hpp.

template<typename B_type, typename H_type>

bool Arageli::lll_reduction	(	B_type &	B,
		H_type &	H
	)

LLL basis reduction.

Parameters:

	B	should be a matrix
	H	should be a matrix

big_int Arageli::entier

(

const big_int &

de

)

Definition at line 33 of file logarithm.cpp.

big_int Arageli::frac	(	const big_int &	de,
		std::size_t	kbits
	)

Definition at line 71 of file logarithm.cpp.

std::size_t Arageli::lg10

(

const big_int &

b

)

Returns lg (b).

Definition at line 110 of file logarithm.cpp.

std::size_t Arageli::lg10

(

std::size_t

b

)

Returns lg (b).

Definition at line 121 of file logarithm.cpp.

big_int Arageli::power_of_ten

(

std::size_t

pow

)

Returns 10^pow.

Definition at line 133 of file logarithm.cpp.

big_int Arageli::entier_1

(

const big_int &

be

)

Definition at line 143 of file logarithm.cpp.

big_int Arageli::frac_1	(	const big_int &	de,
		std::size_t	kbits
	)

Returns 10 ^ {de/log2_10} with kbits - 1 precision.

Definition at line 167 of file logarithm.cpp.

void Arageli::do_bin_convert	(	const big_int &	dm,
		const big_int &	de,
		std::size_t	p,
		big_int &	bm,
		big_int &	be
	)

Definition at line 217 of file logarithm.cpp.

std::size_t Arageli::do_dec_convert	(	big_int &	dm,
		big_int &	de,
		std::size_t	p,
		const big_int &	bm,
		const big_int &	be
	)

Definition at line 246 of file logarithm.cpp.

template<typename T, bool REFCNT>

matrix<T, true> Arageli::transpose

(

const matrix< T, REFCNT > &

a

)

Definition at line 2704 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

int Arageli::cmp	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Lexicographical comparision of two matrix.

Each matrix is represented as (rows, cols, elements) and on this form performs lexicographical comparision, where sequences of elements have compared lexicographicaly too. Returns

• 0 if a == b,
• -1 if a < b
• +1 if a > b

Definition at line 2726 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator<=	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2784 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator<=	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2784 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator<=	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2784 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator>=	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2785 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator>=	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2785 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator>=	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2785 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator<	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2786 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator<	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2786 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator<	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2786 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator>	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2787 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator>	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2787 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator>	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2787 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator==	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2788 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator==	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2788 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator==	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2788 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

bool Arageli::operator!=	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2789 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

bool Arageli::operator!=	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 2789 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

bool Arageli::operator!=	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 2789 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_add_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2842 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::add_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2842 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::add_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2842 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_sub_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2843 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::sub_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2843 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::sub_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2843 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_mul_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2844 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mul_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2844 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mul_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2844 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_div_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2845 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::div_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2845 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::div_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2845 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_mod_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2846 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mod_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2846 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mod_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2846 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_bitand_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2847 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitand_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2847 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitand_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2847 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_bitor_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2848 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitor_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2848 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitor_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2848 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_bitxor_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2849 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitxor_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2849 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitxor_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2849 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_shl_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2850 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shl_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2850 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shl_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2850 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::each_shr_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2851 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shr_matrix_scalar	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2851 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shr_scalar_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2851 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mul_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2860 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::div_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2864 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::add_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2868 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::sub_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2869 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::mod_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2870 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitand_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2871 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitor_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2872 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::bitxor_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2873 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shl_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2874 of file matrix.hpp.

template<typename T1, typename T2, typename T3>

T3& Arageli::shr_matrix_matrix	(	const T1 &	a,
		const T2 &	b,
		T3 &	res
	)

Definition at line 2875 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator+	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator+	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator+	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator+	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator+	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator+	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator+	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator+	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator+	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3027 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator-	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator-	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator-	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator-	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator-	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator-	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator-	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator-	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator-	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3028 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator *	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator *	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator *	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator *	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator *	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator *	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator *	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator *	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator *	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3029 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator/	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator/	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator/	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator/	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator/	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator/	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator/	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator/	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator/	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3030 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator%	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator%	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator%	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator%	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator%	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator%	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator%	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator%	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator%	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3031 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator &	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator &	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator &	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator &	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator &	(	const T2 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<rational<T1>, REFCNT1> Arageli::operator &	(	const matrix< rational< T1 >, REFCNT1 > &	a,
		const rational< T1 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T2, bool REFCNT2>

matrix<rational<T2>, REFCNT2> Arageli::operator &	(	const rational< T2 > &	a,
		const matrix< rational< T2 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator &	(	const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	a,
		const sparse_polynom< T1, D1, REFCNT1 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, typename D1, bool REFCNT1, bool REFCNT2>

matrix<sparse_polynom <T1, D1, REFCNT1>, REFCNT2> Arageli::operator &	(	const sparse_polynom< T1, D1, REFCNT1 > &	a,
		const matrix< sparse_polynom< T1, D1, REFCNT1 >, REFCNT2 > &	b
	)			[inline]

Definition at line 3032 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2, bool REFCNT2>

matrix<T1, REFCNT1> Arageli::operator|	(	const matrix< T1, REFCNT1 > &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3033 of file matrix.hpp.

template<typename T1, bool REFCNT1, typename T2>

matrix<T1, REFCNT1> Arageli::operator|	(	const matrix< T1, REFCNT1 > &	a,
		const T2 &	b
	)			[inline]

Definition at line 3033 of file matrix.hpp.

template<typename T1, typename T2, bool REFCNT2>

matrix<T2, REFCNT2> Arageli::operator|	(	const T1 &	a,
		const matrix< T2, REFCNT2 > &	b
	)			[inline]

Definition at line 3033 of file matrix.hpp.

template<typename T1, bool REFCNT1>

matrix<T1, REFCNT1> Arageli::operator|	(	const matrix< T1, REFCNT1 > &	a,
		const T1 &	b
	)