\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Polynomial

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
PolynomialTraits_d::Permute Concept Reference
Concepts

## 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

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.