CGAL 4.12 - Algebraic Kernel
Bivariate Algebraic Kernel

## Concepts

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_d_2::CompareX_2
Compares the first coordinates of AlgebraicKernel_d_2::Algebraic_real_2s. More...

conceptAlgebraicKernel_d_2::CompareXY_2
Compares AlgebraicKernel_d_2::Algebraic_real_2s lexicographically. More...

conceptAlgebraicKernel_d_2::CompareY_2
Compares the second coordinated of AlgebraicKernel_d_2::Algebraic_real_2s. More...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_d_2::ComputeX_2
Computes the first coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2. More...

conceptAlgebraicKernel_d_2::ComputeY_2
Computes the second coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2. More...

conceptAlgebraicKernel_d_2::ConstructAlgebraicReal_2
Constructs an AlgebraicKernel_d_2::Algebraic_real_2. More...

conceptAlgebraicKernel_d_2::IsCoprime_2
Computes whether a given pair of bivariate polynomials is coprime. More...

conceptAlgebraicKernel_d_2::Isolate_2
Computes an isolating box for a given AlgebraicKernel_d_2::Algebraic_real_2. More...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_d_2::IsSquareFree_2
Computes whether the given bivariate polynomial is square free. More...

conceptAlgebraicKernel_d_2::IsZeroAt_2
Computes whether an AlgebraicKernel_d_2::Polynomial_2 is zero at a given AlgebraicKernel_d_2::Algebraic_real_2. More...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_d_2::MakeSquareFree_2
Returns a square free part of a bivariate polynomial. More...

conceptAlgebraicKernel_d_2::NumberOfSolutions_2
Computes the number of real solutions of the given bivariate polynomial system. More...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_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...

conceptAlgebraicKernel_d_2::SquareFreeFactorize_2
Computes a square free factorization of an AlgebraicKernel_d_2::Polynomial_2. More...

conceptAlgebraicKernel_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...