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 \end{verbatim}
  27
  28 \begin{figure}
  29 \begin{tabular}{lp{0.25\textwidth}p{0.5\textwidth}}
  30 Name & Syntax & Explanation
  31 \\
  32 \hline
  33 Card & \ai[\tt]{card} $r$ & Computes the number of integer points in $r$ and
  34 prints the result to standard output
  35 \\
  36 Card & \ai[\tt]{card} $r$ {\tt using} \ai[\tt]{parker} &
  37 Computes the number of integer points in $r$ and
  38 prints the result to standard output
  39 using the method of \shortciteN{Parker2004}
  40 \\
  41 Ranking & \ai[\tt]{ranking} $r$ & Computes the rank function of $r$ and
  42 prints the result to standard output
  43 \shortcite{Loechner2002,Turjan2002}
  44 \\
  45 Predecessors & \ai[\tt]{count\_lexsmaller} $r$ \ai[\tt]{within} $d$ &
  46 Computes a function from the elements of $d$ to
  47 the number of elements of $r$ that are lexicographically
  48 smaller than that element and
  49 prints the result to standard output.
  50 \\
  51 Vertices & \ai[\tt]{vertices} $r$ &
  52 Computes the parametric vertices of $r$ using \PolyLib/ \shortcite{Loechner1999}.
  53 \\
  54 Bernstein & \ai[\tt]{bmax} $f$ &
  55 Computes the \ai{Bernstein coefficient}s of the function $f$ over its domain
  56 and removes the redundant coefficients by calling
  57 \ai[\tt]{piecewise\_lst::maximize}.  The results are printed to standard
  58 output.  See the example for how to specify the function $f$.
  59 \end{tabular}
  60 \caption{Extra relational operations of {\tt occ}}
  61 \label{f:unary}
  62 \end{figure}