CGAL 5.4.4 - Algebraic Kernel
AlgebraicKernel_d_1::ConstructAlgebraicReal_1 Concept Reference

## Definition

Constructs AlgebraicKernel_d_1::Algebraic_real_1.

Refines:
AdaptableFunctor
AlgebraicKernel_d_2::ConstructAlgebraicReal_2

## Types

typedef AlgebraicKernel_d_1::Algebraic_real_1 result_type

## Operations

result_type operator() (int a)
introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to $$a$$.

result_type operator() (AlgebraicKernel_d_1::Bound a)
introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to $$a$$.

result_type operator() (AlgebraicKernel_d_1::Coefficient a)
introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to $$a$$.

result_type operator() (AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::size_type i)
introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the $$i$$-th real root of $$p$$. More...

result_type operator() (AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::Bound l, AlgebraicKernel_d_1::Bound u)
introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the only real root of $$p$$ in the open interval $$I = (l,u)$$. More...

## ◆ operator()() [1/2]

 result_type AlgebraicKernel_d_1::ConstructAlgebraicReal_1::operator() ( AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::size_type i )

introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the $$i$$-th real root of $$p$$.

The index starts at $$0$$, that is, $$p$$ must have at least $$i+1$$ real roots.

Precondition
$$p$$ is square free.
$$p$$ has at least $$i+1$$ real roots.

## ◆ operator()() [2/2]

 result_type AlgebraicKernel_d_1::ConstructAlgebraicReal_1::operator() ( AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::Bound l, AlgebraicKernel_d_1::Bound u )

introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the only real root of $$p$$ in the open interval $$I = (l,u)$$.

Precondition
$$l < u$$
$$p$$ is square free.
$$p$$ has exactly one real root in $$I$$
$$p$$ has no real root on $$\partial I$$