AlgebraicKernel_d_2::Isolate_2 Concept Reference

Definition

Computes an isolating box for a given AlgebraicKernel_d_2::Algebraic_real_2.

Refines:

AdaptableFunctor

See also

AlgebraicKernel_d_2::IsolateX_2

AlgebraicKernel_d_2::IsolateY_2

AlgebraicKernel_d_2::ComputePolynomialX_2

AlgebraicKernel_d_2::ComputePolynomialY_2

Types
typedef CGAL::cpp11::array< AlgebraicKernel_d_1::Bound, 4 >	result_type

Operations
result_type	operator() (AlgebraicKernel_d_2::Algebraic_real_2 a, AlgebraicKernel_d_2::Polynomial_2 f)
	The returned CGAL::cpp11::array $[xl,xu,yl,yu]$ represents an open isolating box $B=(xl,xu)\times(yl,yu)$ for $a$ with respect to $f$. More...
result_type	operator() (AlgebraicKernel_d_2::Algebraic_real_2 a, AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g)
	The returned CGAL::cpp11::array $[xl,xu,yl,yu]$ represents an open isolating box $B=(xl,xu)\times(yl,yu)$ for $a$ with respect to the common solutions of $f$ and $g$. More...

Member Function Documentation

operator()() [1/2]

result_type AlgebraicKernel_d_2::Isolate_2::operator()	(	AlgebraicKernel_d_2::Algebraic_real_2	a,
		AlgebraicKernel_d_2::Polynomial_2	f
	)

The returned CGAL::cpp11::array $[xl,xu,yl,yu]$ represents an open isolating box $B=(xl,xu)\times(yl,yu)$ for $a$ with respect to $f$.

Precondition

$f(a)\neq0$

Postcondition

$a \in B$.

$\{ r | f(r)=0 \} \cap\overline{B} = \emptyset$.

operator()() [2/2]

result_type AlgebraicKernel_d_2::Isolate_2::operator()	(	AlgebraicKernel_d_2::Algebraic_real_2	a,
		AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g
	)

The returned CGAL::cpp11::array $[xl,xu,yl,yu]$ represents an open isolating box $B=(xl,xu)\times(yl,yu)$ for $a$ with respect to the common solutions of $f$ and $g$.

It is not necessary that $a$ is a common solution of $f$ and $g$.

Postcondition

$a \in B$.

$\{ r | f(r)=g(r)=0 \} \cap\overline{B} \in\{\{a\},\emptyset\}$.