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\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 5.0.1 - Polynomial
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PolynomialTraits_d::Degree Concept Reference

Definition

This AdaptableUnaryFunction computes the degree of a PolynomialTraits_d::Polynomial_d with respect to a certain variable.

The degree of p with respect to a certain variable x_i, is the highest power e of x_i such that the coefficient of x_i^{e} in p is not zero.

For instance the degree of p = x_0^2x_1^3+x_1^4 with respect to x_1 is 4.

The degree of the zero polynomial is set to 0. From the mathematical point of view this should be -infinity, but this would imply an inconvenient return type.

Refines:

AdaptableUnaryFunction

CopyConstructible

DefaultConstructible

See also
Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::TotalDegree
PolynomialTraits_d::DegreeVector

Types

typedef int result_type
 
typedef PolynomialTraits_d::Polynomial_d argument_type
 

Operations

result_type operator() (argument_type p)
 Computes the degree of p with respect to the outermost variable x_{d-1}.
 
result_type operator() (argument_type p, int i)
 Computes the degree of p with respect to variable x_i. More...
 

Member Function Documentation

◆ operator()()

result_type PolynomialTraits_d::Degree::operator() ( argument_type  p,
int  i 
)

Computes the degree of p with respect to variable x_i.

Precondition
0 \leq i < d.