\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 5.0 - Algebraic Kernel
List of all members
AlgebraicKernel_d_1::ConstructAlgebraicReal_1 Concept Reference
Algebraic Kernel Reference » Concepts » Univariate Algebraic Kernel

Definition

Constructs AlgebraicKernel_d_1::Algebraic_real_1.

Refines:
AdaptableFunctor
See also
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...
 

Member Function Documentation

◆ 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 \( \partial I\)