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CGAL 4.4 - Algebraic Kernel
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CGAL 4.4 - Algebraic Kernel
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A model of the AlgebraicKernel_d_1 concept is meant to provide the algebraic functionalities on univariate polynomials of general degree \( d\).
AlgebraicKernel_d_2A model of AlgebraicKernel_d_1 must provide:
Concepts | |
| concept | ApproximateAbsolute_1 |
A model of AlgebraicKernel_d_1::ApproximateAbsolute_1 is an AdaptableBinaryFunction that computes an approximation of an AlgebraicKernel_d_1::Algebraic_real_1 value with respect to a given absolute precision. More... | |
| concept | ApproximateRelative_1 |
A model of AlgebraicKernel_d_1::ApproximateRelative_1 is an AdaptableBinaryFunction that computes an approximation of an AlgebraicKernel_d_1::Algebraic_real_1 value with respect to a given relative precision. More... | |
| concept | BoundBetween_1 |
Computes a number of type AlgebraicKernel_d_1::Bound in-between two AlgebraicKernel_d_1::Algebraic_real_1 values. More... | |
| concept | Compare_1 |
Compares AlgebraicKernel_d_1::Algebraic_real_1 values. More... | |
| concept | ComputePolynomial_1 |
Computes a square free univariate polynomial \( p\), such that the given AlgebraicKernel_d_1::Algebraic_real_1 is a root of \( p\). More... | |
| concept | ConstructAlgebraicReal_1 |
Constructs AlgebraicKernel_d_1::Algebraic_real_1. More... | |
| concept | IsCoprime_1 |
| Determines whether a given pair of univariate polynomials \( p_1, p_2\) is coprime, namely if \( \deg({\rm gcd}(p_1 ,p_2)) = 0\). More... | |
| concept | Isolate_1 |
Computes an open isolating interval for an AlgebraicKernel_d_1::Algebraic_real_1 with respect to the real roots of a given univariate polynomial. More... | |
| concept | IsSquareFree_1 |
| Computes whether the given univariate polynomial is square free. More... | |
| concept | IsZeroAt_1 |
Computes whether an AlgebraicKernel_d_1::Polynomial_1 is zero at a given AlgebraicKernel_d_1::Algebraic_real_1. More... | |
| concept | MakeCoprime_1 |
| Computes for a given pair of univariate polynomials \( p_1\), \( p_2\) their common part \( g\) up to a constant factor and coprime parts \( q_1\), \( q_2\) respectively. More... | |
| concept | MakeSquareFree_1 |
| Returns a square free part of a univariate polynomial. More... | |
| concept | NumberOfSolutions_1 |
| Computes the number of real solutions of the given univariate polynomial. More... | |
| concept | SignAt_1 |
Computes the sign of a univariate polynomial AlgebraicKernel_d_1::Polynomial_1 at a real value of type AlgebraicKernel_d_1::Algebraic_real_1. More... | |
| concept | Solve_1 |
| Computes the real roots of a univariate polynomial. More... | |
| concept | SquareFreeFactorize_1 |
Computes a square free factorization of an AlgebraicKernel_d_1::Polynomial_1. More... | |
Types | |
| typedef unspecified_type | Coefficient |
A model of IntegralDomain and RealEmbeddable. More... | |
| typedef unspecified_type | Polynomial_1 |
A univariate polynomial that is a model of Polynomial_d, where CGAL::Polynomial_traits_d<Polynomial_1>::Innermost_coefficient_type is AlgebraicKernel_d_1::Coefficient. More... | |
| typedef unspecified_type | Algebraic_real_1 |
| A type that is used to represent real roots of univariate polynomials. More... | |
| typedef unspecified_type | Bound |
A type to represent upper and lower bounds of AlgebraicKernel_d_1::Algebraic_real_1. More... | |
| typedef unspecified_type | size_type |
| Size type (unsigned integral type). More... | |
| typedef unspecified_type | Multiplicity_type |
| Multiplicity type (unsigned integral type). More... | |
Operations | |
For each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix | |
| AlgebraicKernel_d_1::Bound_between_1 | bound_between_1_object () const |
A type that is used to represent real roots of univariate polynomials.
The type must be a model of DefaultConstructible, CopyConstructible, Assignable and RealEmbeddable.
A model of AlgebraicKernel_d_1::ApproximateAbsolute_1.
A model of AlgebraicKernel_d_1::ApproximateRelative_1.
A type to represent upper and lower bounds of AlgebraicKernel_d_1::Algebraic_real_1.
The type is ExplicitInteroperable with AlgebraicKernel_d_1::Coefficient and must be a model IntegralDomain, RealEmbeddable and dense in \( \mathbb{R}\).
A model of AlgebraicKernel_d_1::BoundBetween_1.
A model of IntegralDomain and RealEmbeddable.
A model of AlgebraicKernel_d_1::Compare_1.
A model of AlgebraicKernel_d_1::ComputePolynomial_1.
A model of AlgebraicKernel_d_1::ConstructAlgebraicReal_1.
A model of AlgebraicKernel_d_1::IsCoprime_1.
A model of AlgebraicKernel_d_1::IsSquareFree_1.
A model of AlgebraicKernel_d_1::Isolate_1.
A model of AlgebraicKernel_d_1::MakeCoprime_1.
A model of AlgebraicKernel_d_1::MakeSquareFree_1.
Multiplicity type (unsigned integral type).
A model of AlgebraicKernel_d_1::NumberOfSolutions_1.
A univariate polynomial that is a model of Polynomial_d, where CGAL::Polynomial_traits_d<Polynomial_1>::Innermost_coefficient_type is AlgebraicKernel_d_1::Coefficient.
A model of AlgebraicKernel_d_1::SignAt_1.
Size type (unsigned integral type).
A model of AlgebraicKernel_d_1::Solve_1.
A model of AlgebraicKernel_d_1::SquareFreeFactorize_1.
| AlgebraicKernel_d_1::Bound_between_1 AlgebraicKernel_d_1::bound_between_1_object | ( | ) | const |
1.8.5