\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Polynomial

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PolynomialTraits_d::TotalDegree Concept Reference
Concepts

## Definition

This `AdaptableUnaryFunction` computes the total degree of a `PolynomialTraits_d::Polynomial_d`.

Given a (multivariate) monomial the sum of all appearing exponents is the total degree of this monomial. The total degree of a polynomial \( p\) is the maximum of the total degrees of all appearing (multivariate) monomials in \( p\).

For instance the total degree of \( p = x_0^2x_1^3+x_1^4\) is \( 5\).

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

Refines:

  `AdaptableUnaryFunction`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::Degree`
  `PolynomialTraits_d::DegreeVector`

## Types
typedef int | result_type
typedef PolynomialTraits_d::Polynomial_d | argument_type

## Operations
result_type | operator() (argument_type p)
| Computes the total degree of \( p\).