\begin{ccRefConcept}{PolynomialTraits_d::ScaleHomogeneous}
\ccDefinition

Given a numerator $a$ and a denominator $b$ this \ccc{AdaptableFunctor} 
scales a \ccc{PolynomialTraits_d::Polynomial_d} $p$ with respect to one variable, 
that is, it computes $b^{degree(p)}\cdot p(a/b\cdot x)$.

Note that this functor operates on the polynomial in the univariate view, that is, 
the polynomial is considered as a univariate homogeneous polynomial in one specific variable. 

\ccRefines 
\ccc{AdaptableFunctor}\\
\ccc{CopyConstructible}\\
\ccc{DefaultConstructible}\\

\ccTypes

\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d   result_type;}{}

\ccOperations
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d  p,
                                 PolynomialTraits_d::Innermost_coefficient_type   a,
                                 PolynomialTraits_d::Innermost_coefficient_type   b);}
         { Returns $b^{degree}\cdot p(a/b\cdot x)$, 
        with respect to the outermost variable. }
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d  p,
                                 PolynomialTraits_d::Innermost_coefficient_type   a,
                                 PolynomialTraits_d::Innermost_coefficient_type   b,
                                 int i);}
         { Same as first operator but for variable $x_i$. 
          \ccPrecond{$0 \leq i  < d$.}
         }

%\ccHasModels

\ccSeeAlso

\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}\\

\end{ccRefConcept}