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

CGAL 4.8 - Polynomial

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PolynomialTraits_d::Invert Concept Reference
Concepts

## Definition

This `AdaptableUnaryFunction` inverts one variable in a given `PolynomialTraits_d::Polynomial_d`, that is, for a given polynomial \( p\) it computes \( x^{degree(p)}p(1/x)\).

Note that this functor operates on the polynomial in the univariate view, that is, the polynomial is considered as a univariate polynomial in one specific variable.

This functor is provided for efficiency reasons, since this operation just inverts the order of the coefficients with respect to the specified variable.

Refines:

  `AdaptableUnaryFunction`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`

## Types
typedef PolynomialTraits_d::Polynomial_d | result_type
typedef PolynomialTraits_d::Polynomial_d | argument_type

## Operations
result_type | operator() (argument_type p)
| Returns \( x^{degree(p)}p(1/x)\), where x refers to the outermost variable \( x_{d-1}\).
result_type | operator() (argument_type p, int i)
| Return \( x^{degree(p,i)}p(1/x)\), where x refers to the variable \( x_{i}\). More...

## Member Function Documentation

result_type PolynomialTraits_d::Invert::operator() | ( | argument_type | p,
|  | int | i
| ) |  |

Return \( x^{degree(p,i)}p(1/x)\), where x refers to the variable \( x_{i}\).

Precondition
  \( 0 \leq i < d\).