 CGAL 5.3 - Polynomial
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

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...

## ◆ operator()()

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

Computes the degree of $$p$$ with respect to variable $$x_i$$.

Precondition
$$0 \leq i < d$$.