doc/omega.tex

   1 \section{\texorpdfstring{\protect\Omegalib/ interface}
   2 {Omega interface}}
   3
   4 The \ai[\tt]{barvinok} distribution includes an interface
   5 to \Omegalib/ \shortcite{Omega_lib} \ai[\tt]{occ}, an extension
   6 of \ai[\tt]{oc} \shortcite{Omega_calc}.
   7 The extension adds the operations shown in Figure~\ref{f:unary}.
   8 Here are some examples:
   9 \begin{verbatim}
  10 symbolic n, m;
  11 P := { [i,j] : 0 <= i <= n and i <= j <= m };
  12 card P;
  13
  14 P := {[i,j] : 0 <= i < 4*n-1 and 0 <= j < n and
  15               n-1 <= i+j <= 3*n-2 };
  16 C1 := {[i,j] : 0 <= i < 4*n-1 and 0 <= j < n and
  17                2*n-1 <= i+j <= 4*n-2 and i <= 2*n-1 };
  18
  19 count_lexsmaller P within C1;
  20
  21 vertices C1;
  22
  23 bmax { [i] -> 2*n*i - n*n + 3*n - 1/2*i*i - 3/2*i-1 :
  24         (exists j : 0 <= i < 4*n-1 and 0 <= j < n and
  25                     2*n-1 <= i+j <= 4*n-2 and i <= 2*n-1 ) };
  26
  27 sum { [i,j] -> i*j + n*i*i*j : i,j >= 0 and 5i + 27j <= n+m };
  28 \end{verbatim}
  29
  30 \begin{figure}
  31 \begin{tabular}{lp{0.25\textwidth}p{0.5\textwidth}}
  32 Name & Syntax & Explanation
  33 \\
  34 \hline
  35 Card & \ai[\tt]{card} $r$ & Computes the number of integer points in $r$ and
  36 prints the result to standard output
  37 \\
  38 Card & \ai[\tt]{card} $r$ {\tt using} \ai[\tt]{parker} &
  39 Computes the number of integer points in $r$ and
  40 prints the result to standard output
  41 using the method of \shortciteN{Parker2004}
  42 \\
  43 Ranking & \ai[\tt]{ranking} $r$ & Computes the rank function of $r$ and
  44 prints the result to standard output
  45 \shortcite{Loechner2002,Turjan2002}
  46 \\
  47 Predecessors & \ai[\tt]{count\_lexsmaller} $r$ \ai[\tt]{within} $d$ &
  48 Computes a function from the elements of $d$ to
  49 the number of elements of $r$ that are lexicographically
  50 smaller than that element and
  51 prints the result to standard output.
  52 \\
  53 Vertices & \ai[\tt]{vertices} $r$ &
  54 Computes the parametric vertices of $r$ using \PolyLib/ \shortcite{Loechner1999}.
  55 \\
  56 Bernstein & \ai[\tt]{bmax} $f$ &
  57 Computes the \ai{Bernstein coefficient}s of the function $f$ over its domain
  58 and removes the redundant coefficients by calling
  59 \ai[\tt]{piecewise\_lst::maximize}.  The results are printed to standard
  60 output.  See the example for how to specify the function $f$.
  61 \\
  62 Sum & \ai[\tt]{sum} $f$ &
  63 Computes the sum of the given polynomial $f$ over its domain
  64 using \ai[\tt]{barvinok\_summate}.
  65 \end{tabular}
  66 \caption{Extra relational operations of {\tt occ}}
  67 \label{f:unary}
  68 \end{figure}