CGAL 5.0 - Algebraic Kernel
AlgebraicKernel_d_2::ConstructAlgebraicReal_2 Concept Reference

## Definition

Constructs an AlgebraicKernel_d_2::Algebraic_real_2.

Refines:
AdaptableFunctor
AlgebraicKernel_d_1::ConstructAlgebraicReal_1

## Types

typedef AlgebraicKernel_d_2::Algebraic_real_2 result_type

## Operations

result_type operator() (int x, int y)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to $$(x,y)$$.

result_type operator() (AlgebraicKernel_d_2::Bound x, AlgebraicKernel_d_2::Bound y)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to $$(x,y)$$.

result_type operator() (AlgebraicKernel_d_2::Coefficient x, AlgebraicKernel_d_2::Coefficient y)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to $$(x,y)$$.

result_type operator() (AlgebraicKernel_d_2::Algebraic_real_1 x, AlgebraicKernel_d_2::Algebraic_real_1 y)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to $$(x,y)$$.

result_type operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::size_type i)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the $$i$$-th real common solution of $$f$$ and $$g$$, with respect to xy-lexicographic order. More...

result_type operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::Bound x_l, AlgebraicKernel_d_2::Bound x_u, AlgebraicKernel_d_2::Bound y_l, AlgebraicKernel_d_2::Bound y_u)
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the only real intersection of $$f$$ and $$g$$ in the open box $$B = (x_l,x_u)\times(y_l,y_u)$$. More...

## ◆ operator()() [1/2]

 result_type AlgebraicKernel_d_2::ConstructAlgebraicReal_2::operator() ( AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::size_type i )

introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the $$i$$-th real common solution of $$f$$ and $$g$$, with respect to xy-lexicographic order.

The index starts at $$0$$, that is, the system must have at least $$i+1$$ real solutions.

Precondition
$$f$$ is square free.
$$g$$ is square free.
$$f$$ and $$g$$ are coprime.

## ◆ operator()() [2/2]

 result_type AlgebraicKernel_d_2::ConstructAlgebraicReal_2::operator() ( AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::Bound x_l, AlgebraicKernel_d_2::Bound x_u, AlgebraicKernel_d_2::Bound y_l, AlgebraicKernel_d_2::Bound y_u )

introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the only real intersection of $$f$$ and $$g$$ in the open box $$B = (x_l,x_u)\times(y_l,y_u)$$.

Precondition
$$x_l < x_u$$
$$y_l < y_u$$
$$f$$ is square free.
$$g$$ is square free.
$$f$$ and $$g$$ are coprime.
$$f$$ and $$g$$ have exactly one common solution in $$B$$
$$f$$ and $$g$$ have no common solution on $$\partial B$$