\begin{ccRefConcept}{PolynomialTraits_d::Degree}

\ccDefinition

This \ccc{AdaptableUnaryFunction} computes the degree 
of a \ccc{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. 

 

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


\ccTypes

\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}

\ccCreationVariable{fo}
\ccTypedef{typedef int result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}

\ccOperations
\ccMethod{result_type operator()(argument_type p);}
         {Computes the degree of $p$ with respect to the outermost variable $x_{d-1}$.}
\ccMethod{result_type operator()(argument_type p, int i);}
         {Computes the degree of $p$ with respect to variable $x_i$.
         \ccPrecond $0 \leq i  < d$
         }

%\ccHasModels

\ccSeeAlso

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

\end{ccRefConcept}