PolynomialTraits_d::SubstituteHomogeneous

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PolynomialTraits_d::SubstituteHomogeneous

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(x₀,x₁) = x₀²x₁³+x₁⁴ is interpreted as the homogeneous polynomial p(x₀,x₁,w) = x₀²x₁³+x₁⁴w¹.

Refines

Assignable
CopyConstructible
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.

Operations

template<class Input_iterator>

result_type

fo ( 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 x₀.

Precondition:

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