CGAL 4.7 - Polynomial: PolynomialTraits_d::TranslateHomogeneous Concept Reference

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

CGAL 4.7 - Polynomial

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PolynomialTraits_d::TranslateHomogeneous Concept Reference
Concepts

## Definition

Given numerator \( a\) and denominator \( b\) this `AdaptableFunctor` translates a `PolynomialTraits_d::Polynomial_d` \( p\) with respect to one variable by \( a/b\), that is, it computes \( b^{degree(p)}\cdot p(x+a/b)\).

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

Refines:

  `AdaptableFunctor`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`

## Types

typedef PolynomialTraits_d::Polynomial_d | result_type

## Operations

result_type | operator() (PolynomialTraits_d::Polynomial_d p, PolynomialTraits_d::Innermost_coefficient_type a, PolynomialTraits_d::Innermost_coefficient_type b)
| Returns \( b^{degree(p)}\cdot p(x+a/b)\), with respect to the outermost variable.
result_type | operator() (PolynomialTraits_d::Polynomial_d p, PolynomialTraits_d::Innermost_coefficient_type a, PolynomialTraits_d::Innermost_coefficient_type b, int i)
| Same as first operator but for variable \( x_i\). More...

## Member Function Documentation

result_type PolynomialTraits_d::TranslateHomogeneous::operator() | ( | PolynomialTraits_d::Polynomial_d | p,
|  | PolynomialTraits_d::Innermost_coefficient_type | a,
|  | PolynomialTraits_d::Innermost_coefficient_type | b,
|  | int | i
| ) |  |

Same as first operator but for variable \( x_i\).

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