From 0e766424260f037d19938c040398e6f53691e032 Mon Sep 17 00:00:00 2001
From: Sven Verdoolaege <skimo@kotnet.org>
Date: Tue, 31 Oct 2006 16:23:27 +0100
Subject: [PATCH] doc: document barvinok_enumerate_scarf

---
 doc/Internal.tex | 29 +++++++++++++++++++++++------
 doc/barvinok.bib | 24 ++++++++++++++++++++++++
 2 files changed, 47 insertions(+), 6 deletions(-)

diff --git a/doc/Internal.tex b/doc/Internal.tex
index 006383c..eab318b 100644
--- a/doc/Internal.tex
+++ b/doc/Internal.tex
@@ -805,6 +805,9 @@ evalue* barvinok_enumerate_e_with_options(Polyhedron *P,
           struct barvinok_options *options);
 evalue *barvinok_enumerate_pip(Polyhedron *P,
           unsigned exist, unsigned nparam, unsigned MaxRays);
+evalue *barvinok_enumerate_scarf(Polyhedron *P,
+          unsigned exist, unsigned nparam,
+          struct barvinok_options *options);
 \end{verbatim}
 The first function tries the simplification rules from
 \citeN[Section~4.6.2]{Verdoolaege2005PhD} before resorting to the method
@@ -817,19 +820,33 @@ the argument \verb+nparam+ refers to the number of parameters.
 The order of the dimensions in \verb+P+ is:
 counted variables first, then existential variables and finally
 the parameters.
+The function \ai[\tt]{barvinok\_enumerate\_scarf} performs the same
+computation as the function \ai[\tt]{barvinok\_enumerate\_scarf\_series}
+below, but produces an explicit representation instead of a generating function.
 
-The function 
-\ai[\tt]{barvinok\_series} or
-\ai[\tt]{barvinok\_series\_with\_options} enumerates parametric polytopes
-in the form of a \rgf/.
-The polyhedron \verb+P+ is assumed to have only
-lexico-positive rays.
 \begin{verbatim}
 gen_fun * barvinok_series(Polyhedron *P, Polyhedron* C, 
                           unsigned MaxRays);
 gen_fun * barvinok_series_with_options(Polyhedron *P,
     Polyhedron* C, barvinok_options *options);
+gen_fun *barvinok_enumerate_scarf_series(Polyhedron *P,
+                          unsigned exist, unsigned nparam,
+                          barvinok_options *options);
 \end{verbatim}
+The function 
+\ai[\tt]{barvinok\_series} or
+\ai[\tt]{barvinok\_series\_with\_options} enumerates parametric polytopes
+in the form of a \rgf/.
+The polyhedron \verb+P+ is assumed to have only
+lexico-positive rays.
+\\
+The function \ai[\tt]{barvinok\_enumerate\_scarf\_series} computes a
+generating function for the number of point in the parametric set
+defined by \verb+P+ with \verb+exist+ existentially quantified
+variables, which is assumed to be 2.
+This function implements the technique of
+\shortciteN{Scarf2006Neighborhood} using the \ai{neighborhood complex}
+description of \shortciteN{Scarf1981indivisibilities:II}.
 
 \subsection{Auxiliary Functions}
 
diff --git a/doc/barvinok.bib b/doc/barvinok.bib
index c1ff438..94c1268 100644
--- a/doc/barvinok.bib
+++ b/doc/barvinok.bib
@@ -331,3 +331,27 @@ month = jul,
   month =  mar,
 }
 
+@article{Scarf2006Neighborhood,
+  author    = {Herbert E. Scarf and
+               Kevin M. Woods},
+  title     = {Neighborhood Complexes and Generating Functions for Affine
+               Semigroups.},
+  journal   = {Discrete {\&} Computational Geometry},
+  volume    = {35},
+  number    = {3},
+  year      = {2006},
+  pages     = {385-403},
+  ee        = {http://dx.doi.org/10.1007/s00454-005-1222-y},
+  bibsource = {DBLP, http://dblp.uni-trier.de}
+}
+
+@ARTICLE{Scarf1981indivisibilities:II,
+AUTHOR={Scarf, Herbert E},
+TITLE={Production Sets with Indivisibilities-Part {II}: The Case of Two Activities},
+JOURNAL={Econometrica},
+YEAR=1981,
+VOLUME={49},
+NUMBER={2},
+PAGES={395-423},
+MONTH=Mar,
+}
-- 
2.11.4.GIT