CGAL 4.7 - Polynomial: PolynomialTraits_d::PseudoDivisionQuotient 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::PseudoDivisionQuotient Concept Reference
Concepts

## Definition

This `AdaptableBinaryFunction` computes the quotient of the pseudo division of two polynomials \( f\) and \( g\).

Given \( f\) and \( g \neq 0\) one can compute quotient \( q\) and remainder \( r\) such that \( D \cdot f = g \cdot q + r\) and \( degree(r) < degree(g)\), where \( D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}\)

This functor computes \( q\).

Refines:

  `AdaptableBinaryFunction`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::PseudoDivision`
  `PolynomialTraits_d::PseudoDivisionRemainder`
  `PolynomialTraits_d::PseudoDivisionQuotient`

## Types

typedef PolynomialTraits_d::Polynomial_d | result_type
typedef PolynomialTraits_d::Polynomial_d | first_argument_type
typedef PolynomialTraits_d::Polynomial_d | second_argument_type

## Operations

result_type | operator() (first_argument_type f, second_argument_type g)
| Returns the quotient \( q\) of the pseudo division of \( f\) and \( g\) with respect to the outermost variable \( x_{d-1}\).