CGAL 6.1.2 - 2D Circular Geometry Kernel: AlgebraicKernelForCircles Concept Reference

CGAL 6.1.2 - 2D Circular Geometry Kernel

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AlgebraicKernelForCircles Concept Reference
Reference Manual » Algebraic Concepts

## Definition

The `AlgebraicKernelForCircles` concept is meant to provide the curved kernel with all the algebraic functionalities required for the manipulation of circular arcs.

Has models
  `CGAL::Algebraic_kernel_for_circles_2_2`

See also
  `CircularKernel`
  `CGAL::Circular_kernel_2<Kernel,AlgebraicKernelForCircles>`

## Concepts
concept | CompareX
concept | CompareXY
concept | CompareY
concept | ConstructPolynomial_1_2
concept | ConstructPolynomialForCircles_2_2
concept | Polynomial_1_2
| Concept to represent bivariate polynomials of degree 1 whose coefficients are of a type that is a model of the concept `RingNumberType`. More...
concept | PolynomialForCircles_2_2
| Concept to represent bivariate polynomials of degree up to 2 capable of storing equations of circles, whose center's coordinates, as well as the square of the radius, are of a type that is a model of the concept `FieldNumberType`. More...
concept | RootForCircles_2_2
| Concept to represent the roots of a system of two equations of degree 2 in two variables `x` and `y` that are models of concept `AlgebraicKernelForCircles::PolynomialForCircles_2_2` More...
concept | SignAt
concept | Solve
concept | XCriticalPoints
concept | YCriticalPoints

## Types
A model of `AlgebraicKernelForCircles` is supposed to provide
typedef unspecified_type | RT
| A model of `RingNumberType`.
typedef unspecified_type | FT
| A model of `FieldNumberType<RT>`.
typedef unspecified_type | Polynomial_1_2
| A model of `AlgebraicKernelForCircles::Polynomial_1_2`, for bivariate polynomials of degree up to 1.
typedef unspecified_type | Polynomial_for_circles_2_2
| A model of `AlgebraicKernelForCircles::PolynomialForCircles_2_2`, for bivariate polynomials of degree up to 2 that can store equations of circles.
typedef unspecified_type | Root_of_2
| A model of `RootOf_2`, for algebraic numbers of degree up to 2.
typedef unspecified_type | Root_for_circles_2_2
| A model of `AlgebraicKernelForCircles::RootForCircles_2_2`, for solutions of systems of two models of `AlgebraicKernelForCircles::PolynomialForCircles_2_2`.
typedef unspecified_type | Construct_polynomial_1_2
| A model of `AlgebraicKernelForCircles::ConstructPolynomial_1_2`.
typedef unspecified_type | Construct_polynomial_for_circles_2_2
| A model of `AlgebraicKernelForCircles::ConstructPolynomialForCircles_2_2`.
typedef unspecified_type | Compare_x
| A model of the concept `AlgebraicKernelForCircles::CompareX`.
typedef unspecified_type | Compare_y
| A model of the concept `AlgebraicKernelForCircles::CompareY`.
typedef unspecified_type | Compare_xy
| A model of the concept `AlgebraicKernelForCircles::CompareXY`.
typedef unspecified_type | Sign_at
| A model of the concept `AlgebraicKernelForCircles::SignAt`.
typedef unspecified_type | X_critical_points
| A model of the concept `AlgebraicKernelForCircles::XCriticalPoints`.
typedef unspecified_type | Y_critical_points
| A model of the concept `AlgebraicKernelForCircles::YCriticalPoints`.
typedef unspecified_type | Solve
| A model of the concept `AlgebraicKernelForCircles::Solve`.