\begin{ccRefConcept}{PolynomialTraits_d::TotalDegree}

\ccDefinition

This \ccc{AdaptableUnaryFunction} computes the total degree 
of a \ccc{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 $-inf$, but this would imply an inconvenient return type. 

 

\ccRefines 
\ccc{AdaptableUnaryFunction}\\
\ccc{CopyConstructible}\\
\ccc{DefaultConstructible}\\


\ccTypes

\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef int result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}

\ccOperations
\ccCreationVariable{fo}
\ccMethod{result_type operator()(argument_type p);}
         {Computes the total degree of $p$.}


%\ccHasModels

\ccSeeAlso

\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}\\
\ccRefIdfierPage{PolynomialTraits_d::Degree}\\
\ccRefIdfierPage{PolynomialTraits_d::DegreeVector}

\end{ccRefConcept}