\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.8.1 - Polynomial
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PolynomialTraits_d::SignAtHomogeneous Concept Reference

Definition

This AdaptableFunctor returns the sign of a PolynomialTraits_d::Polynomial_d \( p\) at a given homogeneous point, which is given by an iterator range.

The polynomial is interpreted as a homogeneous polynomial in all variables.

For instance the polynomial \( p(x_0,x_1) = x_0^2x_1^3+x_1^4\) is interpreted as the homogeneous polynomial \( p(x_0,x_1,w) = x_0^2x_1^3+x_1^4w^1\).

This functor is well defined if PolynomialTraits_d::Innermost_coefficient_type is RealEmbeddable.

Refines:

AdaptableFunctor

CopyConstructible

DefaultConstructible

See Also
Polynomial_d
PolynomialTraits_d

Types

typedef CGAL::Sign result_type
 

Operations

template<class InputIterator >
result_type operator() (PolynomialTraits_d::Polynomial_d p, InputIterator begin, InputIterator end)
 Returns the sign of \( p\) at the given homogeneous point, where begin is referring to the innermost variable. More...
 

Member Function Documentation

template<class InputIterator >
result_type PolynomialTraits_d::SignAtHomogeneous::operator() ( PolynomialTraits_d::Polynomial_d  p,
InputIterator  begin,
InputIterator  end 
)

Returns the sign of \( p\) at the given homogeneous point, where begin is referring to the innermost variable.

Precondition
(end-begin==PolynomialTraits_d::d+1)
std::iterator_traits< InputIterator >::value_type is ExplicitInteroperable with PolynomialTraits_d::Innermost_coefficient_type.