CGAL 4.7 - Algebraic Kernel: Class and Concept List

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

CGAL 4.7 - Algebraic Kernel

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Class and Concept List
Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.
[detail level 12]

CGAL |
Algebraic_kernel_d_1 | The class represents an algebraic real root by a square free polynomial and an isolating interval that uniquely defines the root
Algebraic_kernel_d_2 | This class gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\)
Algebraic_kernel_rs_gmpq_d_1 |
Algebraic_kernel_rs_gmpz_d_1 |
AlgebraicKernel_d_1 | A model of the `AlgebraicKernel_d_1` concept is meant to provide the algebraic functionalities on univariate polynomials of general degree \( d\)
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
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
BoundBetween_1 | Computes a number of type `AlgebraicKernel_d_1::Bound` in-between two `AlgebraicKernel_d_1::Algebraic_real_1` values
Compare_1 | Compares `AlgebraicKernel_d_1::Algebraic_real_1` values
ComputePolynomial_1 | Computes a square free univariate polynomial \( p\), such that the given `AlgebraicKernel_d_1::Algebraic_real_1` is a root of \( p\)
ConstructAlgebraicReal_1 | Constructs `AlgebraicKernel_d_1::Algebraic_real_1`
IsCoprime_1 | Determines whether a given pair of univariate polynomials \( p_1, p_2\) is coprime, namely if \( \deg({\rm gcd}(p_1 ,p_2)) = 0\)
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
IsSquareFree_1 | Computes whether the given univariate polynomial is square free
IsZeroAt_1 | Computes whether an `AlgebraicKernel_d_1::Polynomial_1` is zero at a given `AlgebraicKernel_d_1::Algebraic_real_1`
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
MakeSquareFree_1 | Returns a square free part of a univariate polynomial
NumberOfSolutions_1 | Computes the number of real solutions of the given univariate polynomial
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`
Solve_1 | Computes the real roots of a univariate polynomial
SquareFreeFactorize_1 | Computes a square free factorization of an `AlgebraicKernel_d_1::Polynomial_1`
AlgebraicKernel_d_2 | A model of the `AlgebraicKernel_d_2` concept gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\)
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
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
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
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
BoundBetweenX_2 | Computes a number of type `AlgebraicKernel_d_1::Bound` in-between the first coordinates of two `AlgebraicKernel_d_2::AlgebraicReal_2`
BoundBetweenY_2 | Computes a number of type `AlgebraicKernel_d_1::Bound` in-between the second coordinates of two `AlgebraicKernel_d_2::AlgebraicReal_2`
CompareX_2 | Compares the first coordinates of `AlgebraicKernel_d_2::Algebraic_real_2`s
CompareXY_2 | Compares `AlgebraicKernel_d_2::Algebraic_real_2`s lexicographically
CompareY_2 | Compares the second coordinated of `AlgebraicKernel_d_2::Algebraic_real_2`s
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 \( p\)
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 \( p\)
ComputeX_2 | Computes the first coordinate of an `AlgebraicKernel_d_2::AlgebraicReal_2`
ComputeY_2 | Computes the second coordinate of an `AlgebraicKernel_d_2::AlgebraicReal_2`
ConstructAlgebraicReal_2 | Constructs an `AlgebraicKernel_d_2::Algebraic_real_2`
IsCoprime_2 | Computes whether a given pair of bivariate polynomials is coprime
Isolate_2 | Computes an isolating box for a given `AlgebraicKernel_d_2::Algebraic_real_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
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
IsSquareFree_2 | Computes whether the given bivariate polynomial is square free
IsZeroAt_2 | Computes whether an `AlgebraicKernel_d_2::Polynomial_2` is zero at a given `AlgebraicKernel_d_2::Algebraic_real_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
MakeSquareFree_2 | Returns a square free part of a bivariate polynomial
NumberOfSolutions_2 | Computes the number of real solutions of the given bivariate polynomial system
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`
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
SquareFreeFactorize_2 | Computes a square free factorization of an `AlgebraicKernel_d_2::Polynomial_2`