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 Typedef Documentation

typedef CGAL::Sign PolynomialTraits_d::SignAtHomogeneous::result_type

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.