CGAL 4.7 - Algebraic Kernel: Bivariate Algebraic Kernel

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

CGAL 4.7 - Algebraic Kernel

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Classes
Bivariate Algebraic Kernel
Concepts

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## Concepts

concept | AlgebraicKernel_d_2::ApproximateAbsoluteX_2

A model of `AlgebraicKernel_d_2::ApproximateAbsoluteX_2` is an `AdaptableBinaryFunction` that computes an approximation of the \( x\)-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value with respect to a given absolute precision. More...

concept | AlgebraicKernel_d_2::ApproximateAbsoluteY_2

A model of `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` is an `AdaptableBinaryFunction` that computes an approximation of the \( y\)-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value with respect to a given absolute precision. More...

concept | AlgebraicKernel_d_2::ApproximateRelativeX_2

A model of `AlgebraicKernel_d_2::ApproximateRelativeX_2` is an `AdaptableBinaryFunction` that computes an approximation of the \( x\)-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value with respect to a given relative precision. More...

concept | AlgebraicKernel_d_2::ApproximateRelativeY_2

A model of `AlgebraicKernel_d_2::ApproximateRelativeY_2` is an `AdaptableBinaryFunction` that computes an approximation of the \( y\)-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value with respect to a given relative precision. More...

concept | AlgebraicKernel_d_2::BoundBetweenX_2
| Computes a number of type `AlgebraicKernel_d_1::Bound` in-between the first coordinates of two `AlgebraicKernel_d_2::AlgebraicReal_2`. More...
concept | AlgebraicKernel_d_2::BoundBetweenY_2
| Computes a number of type `AlgebraicKernel_d_1::Bound` in-between the second coordinates of two `AlgebraicKernel_d_2::AlgebraicReal_2`. More...
concept | AlgebraicKernel_d_2::CompareX_2
| Compares the first coordinates of `AlgebraicKernel_d_2::Algebraic_real_2`s. More...
concept | AlgebraicKernel_d_2::CompareXY_2
| Compares `AlgebraicKernel_d_2::Algebraic_real_2`s lexicographically. More...
concept | AlgebraicKernel_d_2::CompareY_2
| Compares the second coordinated of `AlgebraicKernel_d_2::Algebraic_real_2`s. More...
concept | AlgebraicKernel_d_2::ComputePolynomialX_2
| Computes a univariate square free polynomial \( p\), such that the first coordinate of a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \( p\). More...
concept | AlgebraicKernel_d_2::ComputePolynomialY_2
| Computes a univariate square free polynomial \( p\), such that the second coordinate of a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \( p\). More...
concept | AlgebraicKernel_d_2::ComputeX_2
| Computes the first coordinate of an `AlgebraicKernel_d_2::AlgebraicReal_2`. More...
concept | AlgebraicKernel_d_2::ComputeY_2
| Computes the second coordinate of an `AlgebraicKernel_d_2::AlgebraicReal_2`. More...
concept | AlgebraicKernel_d_2::ConstructAlgebraicReal_2
| Constructs an `AlgebraicKernel_d_2::Algebraic_real_2`. More...
concept | AlgebraicKernel_d_2::IsCoprime_2
| Computes whether a given pair of bivariate polynomials is coprime. More...
concept | AlgebraicKernel_d_2::Isolate_2
| Computes an isolating box for a given `AlgebraicKernel_d_2::Algebraic_real_2`. More...
concept | AlgebraicKernel_d_2::IsolateX_2
| Computes an isolating interval for the first coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` with respect to the real roots of a univariate polynomial. More...
concept | AlgebraicKernel_d_2::IsolateY_2
| Computes an isolating interval for the second coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` with respect to the real roots of a univariate polynomial. More...
concept | AlgebraicKernel_d_2::IsSquareFree_2
| Computes whether the given bivariate polynomial is square free. More...
concept | AlgebraicKernel_d_2::IsZeroAt_2
| Computes whether an `AlgebraicKernel_d_2::Polynomial_2` is zero at a given `AlgebraicKernel_d_2::Algebraic_real_2`. More...
concept | AlgebraicKernel_d_2::MakeCoprime_2
| Computes for a given pair of bivariate polynomials \( p_1\), \( p_2\) their common part \( g\) and coprime parts \( q_1\), \( q_2\) respectively. More...
concept | AlgebraicKernel_d_2::MakeSquareFree_2
| Returns a square free part of a bivariate polynomial. More...
concept | AlgebraicKernel_d_2::NumberOfSolutions_2
| Computes the number of real solutions of the given bivariate polynomial system. More...
concept | AlgebraicKernel_d_2::SignAt_2
| Computes the sign of a bivariate polynomial `AlgebraicKernel_d_2::Polynomial_2` at a value of type `AlgebraicKernel_d_2::Algebraic_real_2`. More...
concept | AlgebraicKernel_d_2::Solve_2
| Computes the real zero-dimensional solutions of a bivariate polynomial system. The multiplicity stored in the output iterator is the multiplicity in the system. More...
concept | AlgebraicKernel_d_2::SquareFreeFactorize_2
| Computes a square free factorization of an `AlgebraicKernel_d_2::Polynomial_2`. More...
concept | AlgebraicKernel_d_2
| A model of the `AlgebraicKernel_d_2` concept gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\). More...