\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Algebraic Kernel

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Algebraic Kernel Reference

##

Eric Berberich, Michael Hemmer, Michael Kerber, Sylvain Lazard, Luis Peñaranda, and Monique Teillaud
Real solving of polynomials is a fundamental problem with a wide application range. This package is targeted to provide black-box implementations of state-of-the-art algorithms to determine, compare and approximate real roots of univariate polynomials and bivariate polynomial systems. Such a black-box is called an Algebraic Kernel. So far the package only provides models for the univariate kernel. Nevertheless, it already defines concepts for the bivariate kernel, since this settles the interface for upcoming implementations.

Introduced in: CGAL 3.6
Depends on: Some models depend on RS and RS3.
BibTeX: cgal:bht-ak-16a
License: LGPL

## Classified Reference Pages

## Concepts

### Univariate Algebraic Kernel

- `AlgebraicKernel_d_1`
- `AlgebraicKernel_d_1::ConstructAlgebraicReal_1`
- `AlgebraicKernel_d_1::ComputePolynomial_1`
- `AlgebraicKernel_d_1::Isolate_1`
- `AlgebraicKernel_d_1::IsSquareFree_1`
- `AlgebraicKernel_d_1::MakeSquareFree_1`
- `AlgebraicKernel_d_1::SquareFreeFactorize_1`
- `AlgebraicKernel_d_1::IsCoprime_1`
- `AlgebraicKernel_d_1::MakeCoprime_1`
- `AlgebraicKernel_d_1::Solve_1`
- `AlgebraicKernel_d_1::NumberOfSolutions_1`
- `AlgebraicKernel_d_1::SignAt_1`
- `AlgebraicKernel_d_1::IsZeroAt_1`
- `AlgebraicKernel_d_1::Compare_1`
- `AlgebraicKernel_d_1::BoundBetween_1`
- `AlgebraicKernel_d_1::ApproximateAbsolute_1`
- `AlgebraicKernel_d_1::ApproximateRelative_1`

### Bivariate Algebraic Kernel

- `AlgebraicKernel_d_2`
- `AlgebraicKernel_d_2::ConstructAlgebraicReal_2`
- `AlgebraicKernel_d_2::ComputePolynomialX_2`
- `AlgebraicKernel_d_2::ComputePolynomialY_2`
- `AlgebraicKernel_d_2::Isolate_2`
- `AlgebraicKernel_d_2::IsolateX_2`
- `AlgebraicKernel_d_2::IsolateY_2`
- `AlgebraicKernel_d_2::IsSquareFree_2`
- `AlgebraicKernel_d_2::MakeSquareFree_2`
- `AlgebraicKernel_d_2::SquareFreeFactorize_2`
- `AlgebraicKernel_d_2::IsCoprime_2`
- `AlgebraicKernel_d_2::MakeCoprime_2`
- `AlgebraicKernel_d_2::Solve_2`
- `AlgebraicKernel_d_2::NumberOfSolutions_2`
- `AlgebraicKernel_d_2::SignAt_2`
- `AlgebraicKernel_d_2::IsZeroAt_2`
- `AlgebraicKernel_d_2::ComputeX_2`
- `AlgebraicKernel_d_2::ComputeY_2`
- `AlgebraicKernel_d_2::CompareX_2`
- `AlgebraicKernel_d_2::CompareY_2`
- `AlgebraicKernel_d_2::CompareXY_2`
- `AlgebraicKernel_d_2::ApproximateAbsoluteX_2`
- `AlgebraicKernel_d_2::ApproximateRelativeX_2`
- `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
- `AlgebraicKernel_d_2::ApproximateRelativeY_2`
- `AlgebraicKernel_d_2::BoundBetweenX_2`
- `AlgebraicKernel_d_2::BoundBetweenY_2`

## Models

- `CGAL::Algebraic_kernel_d_1<Coeff>`
- `CGAL::Algebraic_kernel_d_2<Coeff>`
- `CGAL::Algebraic_kernel_rs_gmpz_d_1`
- `CGAL::Algebraic_kernel_rs_gmpq_d_1`

## Modules
| Concepts
| Models