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CGAL 5.1.4 - Algebraic Kernel
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AlgebraicKernel_d_2::Isolate_2 Concept Reference

Definition

Types

typedef std::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 std::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 std::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 std::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]

The returned std::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\}.