
concept  AlgebraicStructureTraits_::Div 
 AdaptableBinaryFunction computes the integral quotient of division with remainder. More...


concept  AlgebraicStructureTraits_::Divides 
 AdaptableBinaryFunction , returns true if the first argument divides the second argument. More...


concept  AlgebraicStructureTraits_::DivMod 
 AdaptableFunctor computes both integral quotient and remainder of division with remainder. The quotient \( q\) and remainder \( r\) are computed such that \( x = q*y + r\) and \( r < y\) with respect to the proper integer norm of the represented ring. In particular, \( r\) is chosen to be \( 0\) if possible. Moreover, we require \( q\) to be minimized with respect to the proper integer norm. More...


concept  AlgebraicStructureTraits_::Gcd 
 AdaptableBinaryFunction providing the gcd. More...


concept  AlgebraicStructureTraits_::IntegralDivision 
 AdaptableBinaryFunction providing an integral division. More...


concept  AlgebraicStructureTraits_::Inverse 
 AdaptableUnaryFunction providing the inverse element with respect to multiplication of a Field . More...


concept  AlgebraicStructureTraits_::IsOne 
 AdaptableUnaryFunction , returns true in case the argument is the one of the ring. More...


concept  AlgebraicStructureTraits_::IsSquare 
 AdaptableBinaryFunction that computes whether the first argument is a square. If the first argument is a square the second argument, which is taken by reference, contains the square root. Otherwise, the content of the second argument is undefined. More...


concept  AlgebraicStructureTraits_::IsZero 
 AdaptableUnaryFunction , returns true in case the argument is the zero element of the ring. More...


concept  AlgebraicStructureTraits_::KthRoot 
 AdaptableBinaryFunction providing the kth root. More...


concept  AlgebraicStructureTraits_::Mod 
 AdaptableBinaryFunction computes the remainder of division with remainder. More...


concept  AlgebraicStructureTraits_::RootOf 
 AdaptableFunctor computes a real root of a squarefree univariate polynomial. More...


concept  AlgebraicStructureTraits_::Simplify 
 This AdaptableUnaryFunction may simplify a given object. More...


concept  AlgebraicStructureTraits_::Sqrt 
 AdaptableUnaryFunction providing the square root. More...


concept  AlgebraicStructureTraits_::Square 
 AdaptableUnaryFunction , computing the square of the argument. More...


concept  AlgebraicStructureTraits_::UnitPart 
 This AdaptableUnaryFunction computes the unit part of a given ring element. More...


concept  AlgebraicStructureTraits 
 A model of AlgebraicStructureTraits reflects the algebraic structure of an associated type Type . More...


concept  EuclideanRing 
 A model of EuclideanRing represents an euclidean ring (or Euclidean domain). It is an UniqueFactorizationDomain that affords a suitable notion of minimality of remainders such that given \( x\) and \( y \neq 0\) we obtain an (almost) unique solution to \( x = qy + r \) by demanding that a solution \( (q,r)\) is chosen to minimize \( r\). In particular, \( r\) is chosen to be \( 0\) if possible. More...


concept  Field 
 A model of Field is an IntegralDomain in which every nonzero element has a multiplicative inverse. Thus, one can divide by any nonzero element. Hence division is defined for any divisor != 0. For a Field, we require this division operation to be available through operators / and /=. More...


concept  FieldNumberType 
 The concept FieldNumberType combines the requirements of the concepts Field and RealEmbeddable . A model of FieldNumberType can be used as a template parameter for Cartesian kernels. More...


concept  FieldWithKthRoot 
 A model of FieldWithKthRoot is a FieldWithSqrt that has operations to take kth roots. More...


concept  FieldWithRootOf 
 A model of FieldWithRootOf is a FieldWithKthRoot with the possibility to construct it as the root of a univariate polynomial. More...


concept  FieldWithSqrt 
 A model of FieldWithSqrt is a Field that has operations to take square roots. More...


concept  FractionTraits 
 A model of FractionTraits is associated with a type Type . More...


concept  FractionTraits_::Decompose 
 Functor decomposing a Fraction into its numerator and denominator. More...


concept  FractionTraits_::Compose 
 AdaptableBinaryFunction , returns the fraction of its arguments. More...


concept  FractionTraits_::CommonFactor 
 AdaptableBinaryFunction , finds great common factor of denominators. More...


concept  IntegralDomain 
 IntegralDomain refines IntegralDomainWithoutDivision by providing an integral division. More...


concept  IntegralDomainWithoutDivision 
 This is the most basic concept for algebraic structures considered within CGAL. More...


concept  RealEmbeddable 
 A model of this concepts represents numbers that are embeddable on the real axis. The type obeys the algebraic structure and compares two values according to the total order of the real numbers. More...


concept  RealEmbeddableTraits_::Abs 
 AdaptableUnaryFunction computes the absolute value of a number. More...


concept  RealEmbeddableTraits_::Compare 
 AdaptableBinaryFunction compares two real embeddable numbers. More...


concept  RealEmbeddableTraits_::IsNegative 
 AdaptableUnaryFunction , returns true in case the argument is negative. More...


concept  RealEmbeddableTraits_::IsPositive 
 AdaptableUnaryFunction , returns true in case the argument is positive. More...


concept  RealEmbeddableTraits_::IsZero 
 AdaptableUnaryFunction , returns true in case the argument is 0. More...


concept  RealEmbeddableTraits_::Sgn 
 This AdaptableUnaryFunction computes the sign of a real embeddable number. More...


concept  RealEmbeddableTraits_::ToDouble 
 AdaptableUnaryFunction computes a double approximation of a real embeddable number. More...


concept  RealEmbeddableTraits_::ToInterval 
 AdaptableUnaryFunction computes for a given real embeddable number \( x\) a double interval containing \( x\). This interval is represented by std::pair<double,double> . More...


concept  RealEmbeddableTraits 
 A model of RealEmbeddableTraits is associated to a number type Type and reflects the properties of this type with respect to the concept RealEmbeddable . More...


concept  RingNumberType 
 The concept RingNumberType combines the requirements of the concepts IntegralDomainWithoutDivision and RealEmbeddable . A model of RingNumberType can be used as a template parameter for Homogeneous kernels. More...


concept  UniqueFactorizationDomain 
 A model of UniqueFactorizationDomain is an IntegralDomain with the additional property that the ring it represents is a unique factorization domain (a.k.a. UFD or factorial ring), meaning that every nonzero nonunit element has a factorization into irreducible elements that is unique up to order and up to multiplication by invertible elements (units). (An irreducible element is a nonunit ring element that cannot be factored further into two nonunit elements. In a UFD, the irreducible elements are precisely the prime elements.) More...

