\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.1 - Algebraic Kernel
List of all members
AlgebraicKernel_d_2::ConstructAlgebraicReal_2 Concept Reference
Algebraic Kernel Reference » Concepts » Bivariate Algebraic Kernel

Definition

Constructs an AlgebraicKernel_d_2::Algebraic_real_2.

Refines:
AdaptableFunctor
See also
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...
 

Member Function Documentation

◆ 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 \( \partial B\)