\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.2 - Polynomial
PolynomialTraits_d::Permute Concept Reference

Definition

This AdaptableFunctor permutes the variables of the given polynomial with respect to a permutation \( \sigma\), that is, each monomial \( \prod x_i^{e_i}\) will be mapped to the monomial \( \prod x_{\sigma(i)}^{e_i}\). The permutation \( \sigma\) is given by the iterator range of length PolynomialTraits_d::d, which is supposed to contain the second row of the permutation.

For instance, let \( p\) be a polynomial in 4 variables and it is intended to change the order of the variables such that \( x_0 \mapsto x_2\), \( x_1 \mapsto x_0\), \( x_2 \mapsto x_1\) and \( x_3 \mapsto x_3\). In this case the iterator range should contain the sequence \( [2,0,1,3]\).

Refines:

AdaptableFunctor

CopyConstructible

DefaultConstructible

See also
Polynomial_d
PolynomialTraits_d

Types

typedef PolynomialTraits_d::Polynomial_d result_type
 

Operations

template<class Input_iterator >
result_type operator() (PolynomialTraits_d::Polynomial_d p, Input_iterator begin, Input_iterator end)
 Returns \( p\) with interchanged variables as defined by the iterator range. More...
 

Member Function Documentation

◆ operator()()

template<class Input_iterator >
result_type PolynomialTraits_d::Permute::operator() ( PolynomialTraits_d::Polynomial_d  p,
Input_iterator  begin,
Input_iterator  end 
)

Returns \( p\) with interchanged variables as defined by the iterator range.

Precondition
(end-begin == PolynomialTraits_d::d)
std::iterator_traits< InputIterator >::value_type is convertible to int.
The iterator range contains each value in \( \{0,\dots,d-1\}\) exactly once.