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\subsection{Sparse Distributive Representation}

\begin{description}
\item[Conversion\footnotemark :] \ \
  \footnotetext{
    See Section \ref{c:PA s:I} for a description of the sparse recursive
    representation.
  }
  \begin{description}
  \item[{\tt B <- DIPFP(r,A) 
}]\index{DIPFP}  Distributive polynomial from polynomial. {\em Computes a
  polynomial in sparse distributive representation from a polynomial in the
  sparse recursive representation.}
  \item[{\tt B <- PFDIP(r,A) 
}]\index{PFDIP}  Polynomial from distributive polynomial. {\em Computes a
  polynomial in the sparse recursive representation from a polynomial in
  the sparse distributive representation.}
  \end{description}

\item[Input/Output:] \ \
  \begin{description}
  \item[{\tt A <- DIIPREAD(V) 
}]\index{DIIPREAD}  Distributive integral polynomial read.
  \item[{\tt  DIIPWRITE(r,A,V) 
}]\index{DIIPWRITE}  Distributive integral polynomial write.
  \item[{\tt A <- DIRPREAD(V) 
}]\index{DIRPREAD}  Distributive rational polynomial read.
  \item[{\tt  DIRPWRITE(r,A,V) 
}]\index{DIRPWRITE}  Distributive rational polynomial write.
  \end{description}

\item[Miscellaneous:] \ \
  \begin{description}
  \item[{\tt n <- DIPDEG(r,A) 
}]\index{DIPDEG}  Distributive polynomial degree.
  \item[{\tt  DIPINS(a,d,A; t,B) 
}]\index{DIPINS}  Distributive polynomial, insert term.
  \end{description}

\end{description}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Dense Recursive Representation}

\begin{description}
\item[Basic arithmetic:] \ \
  \begin{description}
  \item[{\tt C <- DMPPRD(r,m,A,B) 
}]\index{DMPPRD}  Dense modular polynomial product.
  \item[{\tt C <- DMPSUM(r,m,A,B) 
}]\index{DMPSUM}  Dense modular polynomial sum.
  \item[{\tt C <- DMUPNR(p,A,B) 
}]\index{DMUPNR}  Dense modular univariate polynomial natural remainder.
  \end{description}

\item[Conversion\footnotemark :] \ \
  \footnotetext{
    See Section \ref{c:PA s:I} for a description of the sparse recursive
    representation.
  }
  \begin{description}
  \item[{\tt B <- DPFP(r,A) 
}]\index{DPFP}  Dense polynomial from polynomial. {\em Computes a
  polynomial in dense recursive representation from a polynomial in the
  sparse recursive representation.}
  \item[{\tt B <- PFDP(r,A) 
}]\index{PFDP}  Polynomial from dense polynomial. {\em Computes a polynomial
  in the sparse recursive representation from a polynomial in the dense
  recursive representation.}
  \end{description}

\end{description}
