PolynomialTraits_d::SubstituteHomogeneous Concept Reference

Definition

This Functor substitutes all variables of a given multivariate PolynomialTraits_d::Polynomial_d \( p\) by the values given in the iterator range, where begin refers the value for the innermost variable. In contrast to PolynomialTraits_d::Substitute the given polynomial \( p\) is interpreted as a homogeneous polynomial. Hence the iterator range is required to be of length PolynomialTraits_d::d+1.

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

Refines

CopyConstructible

Assignable

DefaultConstructible

Types

Note that the result_type is the coercion type of the value type of the given iterator range and PolynomialTraits_d::Innermost_coefficient_type. In particular std::iterator_traits<Input_iterator>::value_type must be ExplicitInteroperable with PolynomialTraits_d::Innermost_coefficient_type. Hence, it can not be provided as a public type in advance.

See also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::Substitute

CGAL::Coercion_traits

Operations
template<class Input_iterator >
result_type	operator() (PolynomialTraits_d::Polynomial_d p, Input_iterator begin, Input_iterator end)
	Substitutes each variable of \( p\) by the values given in the iterator range, where \( p\) is interpreted as a homogeneous polynomial in all variables.

Member Function Documentation

operator()()

template<class Input_iterator >

result_type PolynomialTraits_d::SubstituteHomogeneous::operator()	(	PolynomialTraits_d::Polynomial_d	p,
		Input_iterator	begin,
		Input_iterator	end
	)

Substitutes each variable of \( p\) by the values given in the iterator range, where \( p\) is interpreted as a homogeneous polynomial in all variables.

The begin iterator refers to the innermost variable \( x_0\).

Precondition

(end-begin == PolynomialTraits_d::d)+1