CGAL 6.2 - Algebraic Kernel: Class and Concept List

CGAL 6.2 - 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]

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