\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 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]
oNCGAL
|oCAlgebraic_kernel_d_1The class represents an algebraic real root by a square free polynomial and an isolating interval that uniquely defines the root
|oCAlgebraic_kernel_d_2This class gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\)
|oCAlgebraic_kernel_rs_gmpq_d_1
|\CAlgebraic_kernel_rs_gmpz_d_1
oCAlgebraicKernel_d_1A model of the AlgebraicKernel_d_1 concept is meant to provide the algebraic functionalities on univariate polynomials of general degree \( d\)
|oCApproximateAbsolute_1A 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
|oCApproximateRelative_1A 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
|oCBoundBetween_1Computes a number of type AlgebraicKernel_d_1::Bound in-between two AlgebraicKernel_d_1::Algebraic_real_1 values
|oCCompare_1Compares AlgebraicKernel_d_1::Algebraic_real_1 values
|oCComputePolynomial_1Computes a square free univariate polynomial \( p\), such that the given AlgebraicKernel_d_1::Algebraic_real_1 is a root of \( p\)
|oCConstructAlgebraicReal_1Constructs AlgebraicKernel_d_1::Algebraic_real_1
|oCIsCoprime_1Determines whether a given pair of univariate polynomials \( p_1, p_2\) is coprime, namely if \( \deg({\rm gcd}(p_1 ,p_2)) = 0\)
|oCIsolate_1Computes an open isolating interval for an AlgebraicKernel_d_1::Algebraic_real_1 with respect to the real roots of a given univariate polynomial
|oCIsSquareFree_1Computes whether the given univariate polynomial is square free
|oCIsZeroAt_1Computes whether an AlgebraicKernel_d_1::Polynomial_1 is zero at a given AlgebraicKernel_d_1::Algebraic_real_1
|oCMakeCoprime_1Computes 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
|oCMakeSquareFree_1Returns a square free part of a univariate polynomial
|oCNumberOfSolutions_1Computes the number of real solutions of the given univariate polynomial
|oCSignAt_1Computes the sign of a univariate polynomial AlgebraicKernel_d_1::Polynomial_1 at a real value of type AlgebraicKernel_d_1::Algebraic_real_1
|oCSolve_1Computes the real roots of a univariate polynomial
|\CSquareFreeFactorize_1Computes a square free factorization of an AlgebraicKernel_d_1::Polynomial_1
\CAlgebraicKernel_d_2A model of the AlgebraicKernel_d_2 concept gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\)
 oCApproximateAbsoluteX_2A 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
 oCApproximateAbsoluteY_2A 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
 oCApproximateRelativeX_2A 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
 oCApproximateRelativeY_2A 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
 oCBoundBetweenX_2Computes a number of type AlgebraicKernel_d_1::Bound in-between the first coordinates of two AlgebraicKernel_d_2::AlgebraicReal_2
 oCBoundBetweenY_2Computes a number of type AlgebraicKernel_d_1::Bound in-between the second coordinates of two AlgebraicKernel_d_2::AlgebraicReal_2
 oCCompareX_2Compares the first coordinates of AlgebraicKernel_d_2::Algebraic_real_2s
 oCCompareXY_2Compares AlgebraicKernel_d_2::Algebraic_real_2s lexicographically
 oCCompareY_2Compares the second coordinated of AlgebraicKernel_d_2::Algebraic_real_2s
 oCComputePolynomialX_2Computes 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 \( p\)
 oCComputePolynomialY_2Computes 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 \( p\)
 oCComputeX_2Computes the first coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2
 oCComputeY_2Computes the second coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2
 oCConstructAlgebraicReal_2Constructs an AlgebraicKernel_d_2::Algebraic_real_2
 oCIsCoprime_2Computes whether a given pair of bivariate polynomials is coprime
 oCIsolate_2Computes an isolating box for a given AlgebraicKernel_d_2::Algebraic_real_2
 oCIsolateX_2Computes 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
 oCIsolateY_2Computes 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
 oCIsSquareFree_2Computes whether the given bivariate polynomial is square free
 oCIsZeroAt_2Computes whether an AlgebraicKernel_d_2::Polynomial_2 is zero at a given AlgebraicKernel_d_2::Algebraic_real_2
 oCMakeCoprime_2Computes for a given pair of bivariate polynomials \( p_1\), \( p_2\) their common part \( g\) and coprime parts \( q_1\), \( q_2\) respectively
 oCMakeSquareFree_2Returns a square free part of a bivariate polynomial
 oCNumberOfSolutions_2Computes the number of real solutions of the given bivariate polynomial system
 oCSignAt_2Computes the sign of a bivariate polynomial AlgebraicKernel_d_2::Polynomial_2 at a value of type AlgebraicKernel_d_2::Algebraic_real_2
 oCSolve_2Computes the real zero-dimensional solutions of a bivariate polynomial system. The multiplicity stored in the output iterator is the multiplicity in the system
 \CSquareFreeFactorize_2Computes a square free factorization of an AlgebraicKernel_d_2::Polynomial_2