CGAL 6.1.2 - Polynomial: PolynomialTraits_d::PseudoDivision Concept Reference

CGAL 6.1.2 - Polynomial

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PolynomialTraits_d::PseudoDivision Concept Reference
Reference Manual » Concepts

## Definition

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

Given \( f\) and \( g \neq 0\) this functor computes 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 is useful if the regular division is not available, which is the case if `PolynomialTraits_d::Coefficient_type` is not a `Field`. Hence in general it is not possible to invert the leading coefficient of \( g\). Instead \( f\) is extended by \( D\) allowing integral divisions in the internal computation.

Refines
  `AdaptableFunctor`
  `CopyConstructible`
  `DefaultConstructible`

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

## Types
typedef void | result_type

## Operations
result_type | operator() (PolynomialTraits_d::Polynomial_d f, PolynomialTraits_d::Polynomial_d g, PolynomialTraits_d::Polynomial_d &q, PolynomialTraits_d::Polynomial_d &r, PolynomialTraits_d::Coefficient_type &D)
| Computes the pseudo division with respect to the outermost variable \( x_{d-1}\).