\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.1 - Algebraic Foundations
CGAL Namespace Reference

Namespaces

 cpp11
 
 cpp98
 

Classes

class  Algebraic_structure_traits
 An instance of Algebraic_structure_traits is a model of AlgebraicStructureTraits, where T is the associated type. More...
 
struct  binary_function
 
struct  Boolean_tag
 
struct  Cast_function_object
 
class  CC_safe_handle
 
struct  Coercion_traits
 An instance of Coercion_traits reflects the type coercion of the types A and B, it is symmetric in the two template arguments. More...
 
struct  Compact
 
class  Compact_container
 
class  Compact_container_base
 
struct  Compact_container_traits
 
class  Compare_to_less
 
class  Concurrent_compact_container
 
struct  Concurrent_compact_container_traits
 
class  Const_oneset_iterator
 
struct  Construct_array
 
class  Counting_iterator
 
class  Creator_1
 
class  Creator_2
 
class  Creator_3
 
class  Creator_4
 
class  Creator_5
 
class  Creator_uniform_2
 
class  Creator_uniform_3
 
class  Creator_uniform_4
 
class  Creator_uniform_5
 
class  Creator_uniform_6
 
class  Creator_uniform_7
 
class  Creator_uniform_8
 
class  Creator_uniform_9
 
class  Creator_uniform_d
 
struct  Default
 
struct  Dereference
 
class  Dispatch_or_drop_output_iterator
 
class  Dispatch_output_iterator
 
struct  Emptyset_iterator
 
struct  Euclidean_ring_tag
 Tag indicating that a type is a model of the EuclideanRing concept. More...
 
struct  Fast
 
struct  Field_tag
 Tag indicating that a type is a model of the Field concept. More...
 
struct  Field_with_kth_root_tag
 Tag indicating that a type is a model of the FieldWithKthRoot concept. More...
 
struct  Field_with_root_of_tag
 Tag indicating that a type is a model of the FieldWithRootOf concept. More...
 
struct  Field_with_sqrt_tag
 Tag indicating that a type is a model of the FieldWithSqrt concept. More...
 
struct  Filter_iterator
 
class  Fourtuple
 
class  Fraction_traits
 An instance of Fraction_traits is a model of FractionTraits, where T is the associated type. More...
 
struct  Get_address
 
class  Gmpfi
 
class  Gmpfr
 
class  Gmpq
 
class  Gmpz
 
class  Gmpzf
 
struct  Identity
 
class  In_place_list
 
class  In_place_list_base
 
class  Insert_iterator
 
struct  Integral_domain_tag
 Tag indicating that a type is a model of the IntegralDomain concept. More...
 
struct  Integral_domain_without_division_tag
 Tag indicating that a type is a model of the IntegralDomainWithoutDivision concept. More...
 
class  Interval_nt
 
class  Inverse_index
 
class  Is_valid
 
class  Iterator_range
 
class  Join_input_iterator_1
 
class  Join_input_iterator_2
 
class  Join_input_iterator_3
 
class  Lazy_exact_nt
 
struct  Location_policy
 
struct  Max
 
struct  Min
 
class  MP_Float
 
struct  Mpzf
 
class  Multiset
 
class  N_step_adaptor
 
struct  NT_converter
 
struct  Null_functor
 
struct  Null_tag
 
class  Number_type_checker
 
class  Object
 
class  Oneset_iterator
 
struct  Parallel_tag
 
struct  Project_facet
 
struct  Project_next
 
struct  Project_next_opposite
 
struct  Project_normal
 
struct  Project_opposite_prev
 
struct  Project_plane
 
struct  Project_point
 
struct  Project_prev
 
struct  Project_vertex
 
struct  Protect_FPU_rounding
 
class  Quadruple
 
class  Quotient
 
class  Random_access_adaptor
 
class  Random_access_value_adaptor
 
class  Rational_traits
 
class  Real_embeddable_traits
 An instance of Real_embeddable_traits is a model of RealEmbeddableTraits, where T is the associated type. More...
 
struct  Root_of_traits
 
struct  Sequential_tag
 
class  Set_ieee_double_precision
 
class  Sixtuple
 
class  Spatial_lock_grid_3
 
class  Sqrt_extension
 
class  Threetuple
 
class  Triple
 
class  Twotuple
 
struct  unary_function
 
class  Uncertain
 
struct  Unique_factorization_domain_tag
 Tag indicating that a type is a model of the UniqueFactorizationDomain concept. More...
 
struct  value_type_traits
 
struct  value_type_traits< std::back_insert_iterator< Container > >
 
struct  value_type_traits< std::front_insert_iterator< Container > >
 
struct  value_type_traits< std::insert_iterator< Container > >
 

Typedefs

typedef Location_policy< CompactCompact_location
 
typedef Location_policy< FastFast_location
 
typedef CGAL::Boolean_tag< false > Tag_false
 
typedef CGAL::Boolean_tag< true > Tag_true
 
typedef void(* Failure_function) (const char *type, const char *expression, const char *file, int line, const char *explanation)
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef unspecified_type Exact_integer
 
typedef unspecified_type Exact_rational
 

Enumerations

enum  Failure_behaviour
 

Functions

OutputIterator copy_n (InputIterator first, Size n, OutputIterator result)
 
std::pair< ForwardIterator, ForwardIteratormin_max_element (ForwardIterator first, ForwardIterator last)
 
std::pair< ForwardIterator, ForwardIteratormin_max_element (ForwardIterator first, ForwardIterator last, CompareMin comp_min, CompareMax comp_max)
 
BidirectionalIterator predecessor (BidirectionalIterator it)
 
ForwardIterator successor (ForwardIterator it)
 
CC_safe_handle< CC_iterator > make_cc_safe_handle (CC_iterator iterator)
 
Compare_to_less< F > compare_to_less (const F &f)
 
Iterator_range< T > make_range (const T &b, const T &e)
 
range_begin (Iterator_range< T > &x)
 
range_end (Iterator_range< T > &x)
 
range_begin (const Iterator_range< T > &x)
 
range_end (const Iterator_range< T > &x)
 
Failure_function set_error_handler (Failure_function handler)
 
Failure_function set_warning_handler (Failure_function handler)
 
Failure_behaviour set_error_behaviour (Failure_behaviour eb)
 
Failure_behaviour set_warning_behaviour (Failure_behaviour eb)
 
bool is_finite (double x)
 
bool is_finite (float x)
 
bool is_finite (long double x)
 
OutputIterator compute_roots_of_2 (const RT &a, const RT &b, const RT &c, OutputIterator oit)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (const RT &a, const RT &b, const RT &c, bool s)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (RT alpha, RT beta, RT gamma)
 
Root_of_traits< RT >::Root_of_2 make_sqrt (const RT &x)
 
Rational simplest_rational_in_interval (double d1, double d2)
 
Rational to_rational (double d)
 
bool is_valid (const T &x)
 
max (const T &x, const T &y)
 
min (const T &x, const T &y)
 
template<class NT >
NT abs (const NT &x)
 The template function abs() returns the absolute value of a number. More...
 
template<class NT1 , class NT2 >
result_type compare (const NT &x, const NT &y)
 The template function compare() compares the first argument with respect to the second, i.e. it returns CGAL::LARGER if \( x\) is larger then \( y\). More...
 
template<class NT1 , class NT2 >
result_type div (const NT1 &x, const NT2 &y)
 The function div() computes the integral quotient of division with remainder. More...
 
template<class NT1 , class NT2 >
void div_mod (const NT1 &x, const NT2 &y, result_type &q, result_type &r)
 computes the quotient \( q\) and remainder \( r\), such that \( x = q*y + r\) and \( r\) minimal with respect to the Euclidean Norm of the result_type. More...
 
template<class NT1 , class NT2 >
result_type gcd (const NT1 &x, const NT2 &y)
 The function gcd() computes the greatest common divisor of two values. More...
 
template<class NT1 , class NT2 >
result_type integral_division (const NT1 &x, const NT2 &y)
 The function integral_division() (a.k.a. exact division or division without remainder) maps ring elements \( (x,y)\) to ring element \( z\) such that \( x = yz\) if such a \( z\) exists (i.e. if \( x\) is divisible by \( y\)). More...
 
template<class NT >
NT inverse (const NT &x)
 The function inverse() returns the inverse element with respect to multiplication. More...
 
result_type is_negative (const NT &x)
 The template function is_negative() determines if a value is negative or not. More...
 
template<class NT >
result_type is_one (const NT &x)
 The function is_one() determines if a value is equal to 1 or not. More...
 
result_type is_positive (const NT &x)
 The template function is_positive() determines if a value is positive or not. More...
 
template<class NT >
result_type is_square (const NT &x)
 An ring element \( x\) is said to be a square iff there exists a ring element \( y\) such that \( x= y*y\). More...
 
template<class NT >
result_type is_square (const NT &x, NT &y)
 An ring element \( x\) is said to be a square iff there exists a ring element \( y\) such that \( x= y*y\). More...
 
template<class NT >
result_type is_zero (const NT &x)
 The function is_zero() determines if a value is equal to 0 or not. More...
 
template<class NT >
NT kth_root (int k, const NT &x)
 The function kth_root() returns the k-th root of a value. More...
 
template<class NT1 , class NT2 >
result_type mod (const NT1 &x, const NT2 &y)
 The function mod() computes the remainder of division with remainder. More...
 
template<class InputIterator >
NT root_of (int k, InputIterator begin, InputIterator end)
 returns the k-th real root of the univariate polynomial, which is defined by the iterator range, where begin refers to the constant term. More...
 
template<class NT >
result_type sign (const NT &x)
 The template function sign() returns the sign of its argument. More...
 
template<class NT >
void simplify (const NT &x)
 The function simplify() may simplify a given object. More...
 
template<class NT >
NT sqrt (const NT &x)
 The function sqrt() returns the square root of a value. More...
 
template<class NT >
NT square (const NT &x)
 The function square() returns the square of a number. More...
 
template<class NT >
double to_double (const NT &x)
 The template function to_double() returns a double approximation of a number. More...
 
template<class NT >
std::pair< double, double > to_interval (const NT &x)
 The template function to_interval() computes for a given real embeddable number \( x\) a double interval containing \( x\). More...
 
template<class NT >
NT unit_part (const NT &x)
 The function unit_part() computes the unit part of a given ring element. More...
 

Variables

 ABORT
 
 EXIT
 
 EXIT_WITH_SUCCESS
 
 CONTINUE
 
 THROW_EXCEPTION