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CGAL 4.5 - Algebraic Kernel
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CGAL 4.5 - Algebraic Kernel
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A model of the AlgebraicKernel_d_2 concept gathers necessary tools for solving and handling bivariate polynomial systems of general degree \( d\).
AlgebraicKernel_d_1 Concepts | |
| concept | 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 | 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 | 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 | 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 | 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 | 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 | CompareX_2 |
Compares the first coordinates of AlgebraicKernel_d_2::Algebraic_real_2s. More... | |
| concept | CompareXY_2 |
Compares AlgebraicKernel_d_2::Algebraic_real_2s lexicographically. More... | |
| concept | CompareY_2 |
Compares the second coordinated of AlgebraicKernel_d_2::Algebraic_real_2s. More... | |
| concept | 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 | 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 | ComputeX_2 |
Computes the first coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2. More... | |
| concept | ComputeY_2 |
Computes the second coordinate of an AlgebraicKernel_d_2::AlgebraicReal_2. More... | |
| concept | ConstructAlgebraicReal_2 |
Constructs an AlgebraicKernel_d_2::Algebraic_real_2. More... | |
| concept | IsCoprime_2 |
| Computes whether a given pair of bivariate polynomials is coprime. More... | |
| concept | Isolate_2 |
Computes an isolating box for a given AlgebraicKernel_d_2::Algebraic_real_2. More... | |
| concept | 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 | 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 | IsSquareFree_2 |
| Computes whether the given bivariate polynomial is square free. More... | |
| concept | IsZeroAt_2 |
Computes whether an AlgebraicKernel_d_2::Polynomial_2 is zero at a given AlgebraicKernel_d_2::Algebraic_real_2. More... | |
| concept | 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 | MakeSquareFree_2 |
| Returns a square free part of a bivariate polynomial. More... | |
| concept | NumberOfSolutions_2 |
| Computes the number of real solutions of the given bivariate polynomial system. More... | |
| concept | 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 | 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 | SquareFreeFactorize_2 |
Computes a square free factorization of an AlgebraicKernel_d_2::Polynomial_2. More... | |
Types | |
| typedef unspecified_type | Polynomial_2 |
A bivariate polynomial that is a model of Polynomial_d, where CGAL::Polynomial_traits_d<Polynomial_2>::Innermost_coefficient_type is AlgebraicKernel_d_1::Coefficient. | |
| typedef unspecified_type | Algebraic_real_2 |
| A type that is used to represent real solutions of bivariate zero dimensional polynomial systems. More... | |
Operations | |
For each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix | |
| AlgebraicKernel_d_2::Bound_between_x_2 | bound_between_x_2_object () const |
A type that is used to represent real solutions of bivariate zero dimensional polynomial systems.
A model of DefaultConstructible, CopyConstructible and Assignable.
1.8.4