\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Polynomial

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
PolynomialTraits_d::SignAtHomogeneous Concept Reference
Concepts

## 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`.