CGAL::Algebraic_kernel_d_1< Coeff > Class Template Reference

#include <CGAL/Algebraic_kernel_d_1.h>

Definition

The class represents an algebraic real root by a square free polynomial and an isolating interval that uniquely defines the root.

The template argument Coeff determines the coefficient type of the kernel, which is also the coefficient type of the supported polynomials.

Currently, the following coefficient types are supported:

• Gmpz, Gmpq, (requires configuration with external libraries GMP, MPFR and MPFI)
• CORE::BigInt, CORE::BigRat, (requires configuration with external library GMP)
• leda_integer, leda_rational. (requires configuration with external library LEDA)

Advanced

The template argument type can also be set to Sqrt_extension<NT,ROOT>, where NT is one of the types listed above. ROOT should be one of the integer types. See also the documentation of Sqrt_extension<NT,ROOT>.

The current method to isolate roots is the bitstream Descartes method presented in [6]. The used method to refine the approximation of an algebraic real root is a slightly modified (filtered) version of the one presented in [1]. The method has quadratic convergence.

Is Model Of:

AlgebraicKernel_d_1

See also

AlgebraicKernel_d_1

Polynomial_d

CGAL::Algebraic_kernel_d_2<Coeff>

Examples:

Algebraic_kernel_d/Compare_1.cpp, Algebraic_kernel_d/Construct_algebraic_real_1.cpp, Algebraic_kernel_d/Isolate_1.cpp, Algebraic_kernel_d/Sign_at_1.cpp, and Algebraic_kernel_d/Solve_1.cpp.

Types
typedef unspecified_type	Coefficient
	Same type as the template argument Coeff.
typedef unspecified_type	Polynomial_1
	A model of AlgebraicKernel_d_1::Polynomial_1.
typedef unspecified_type	Algebraic_real_1
	A model of AlgebraicKernel_d_1::Algebraic_real_1.
typedef unspecified_type	Bound
	The choice of Coeff also determines the provided bound type. More...
typedef unspecified_type	Multiplicity_type
	The multiplicity type is int.

Member Typedef Documentation

Bound

template<typename Coeff >

typedef unspecified_type CGAL::Algebraic_kernel_d_1< Coeff >::Bound

The choice of Coeff also determines the provided bound type.

In case of Coeff is:

• Gmpz or Gmpq, this is Gmpq,
• CORE::BigInt or CORE::BigRat, this is CORE::BigRat,
• leda_integer or leda_rational, this is leda_rational.