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.

Member Function Documentation

operator()()

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.