CGAL 6.1.2 - Polynomial

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PolynomialTraits_d::TranslateHomogeneous Concept Reference
Reference Manual » 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 \( x_i\).

## Member Function Documentation

## ◆ operator()()

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
  \( 0 \leq i < d\).