1 \section{\texorpdfstring{\protect\Omegalib/ interface
}
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:
11 P :=
{ [i,j
] :
0 <= i <= n and i <= j <= m
};
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 };
19 count_lexsmaller P within C1;
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 )
};
27 sum
{ [i,j
] -> i*j + n*i*i*j : i,j >=
0 and
5i +
27j <= n+m
};
31 \begin{tabular
}{lp
{0.25\textwidth}p
{0.5\textwidth}}
32 Name & Syntax & Explanation
35 Card &
\ai[\tt]{card
} $r$ & Computes the number of integer points in $r$ and
36 prints the result to standard output
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
}
43 Ranking &
\ai[\tt]{ranking
} $r$ & Computes the rank function of $r$ and
44 prints the result to standard output
45 \shortcite{Loechner2002,Turjan2002
}
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.
53 Vertices &
\ai[\tt]{vertices
} $r$ &
54 Computes the parametric vertices of $r$ using
\PolyLib/
\shortcite{Loechner1999
}.
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 $f$.
62 Sum &
\ai[\tt]{sum
} $f$ &
63 Computes the sum of the given polynomial $f$ over its domain
64 using
\ai[\tt]{barvinok
\_summate}.
66 \caption{Extra relational operations of
{\tt occ
}}