\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 5.0 - Polynomial
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PolynomialTraits_d::TranslateHomogeneous Concept Reference
Polynomial 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

◆ 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
\( 0 \leq i < d\).