commit 405fa6cbf3aee8a83be0de6fe7c950072d713e35
author Austin Schuh <austin@peloton-tech.com> Sun Sep 06 18:13:55 2015 -0700
committer Austin Schuh <austin@peloton-tech.com> Sun Sep 06 18:16:15 2015 -0700
tree 6fe708f268e614da9baec77a4dfc4e2a276f8ffc
parent d7786b2a25d9f0e66f568d9da23472795532d4c4

Added cddlib-094h from http://www.inf.ethz.ch/personal/fukudak/cdd_home/

Change-Id: I64519509269e434b1b9ea87c3fe0805e711c0ac9

third_party/cddlib/doc/cddlibman.aux

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+\newlabel{EXAMPLES}{{6}{16}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Numerical Accuracy}{16}}
+\newlabel{accuracy}{{7}{16}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Other Useful Codes}{16}}
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+\citation{w-ldpo-93b}
+\citation{b-pplhome}
+\citation{m-pdcip-97}
+\citation{bfm-pdmvf-97}
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+\citation{e-cgp}
+\citation{fg-lpfaq}
+\citation{f-pcfaq-98}
+\citation{dhhhty-latte-05}
+\citation{w-msv-05}
+\citation{f-fzctmacp-04}
+\citation{j-gvum-05}
+\citation{fjt-cgf-05}
+\citation{r-topcom-05}
+\bibstyle{plain}
+\bibdata{fukuda1,fukuda2}
+\bibcite{a-dcg}{1}
+\@writefile{toc}{\contentsline {section}{\numberline {9}Codes Using Cddlib}{17}}
+\newlabel{USERCODES}{{9}{17}}
+\bibcite{a-lrshome-01}{2}
+\bibcite{abs-hgach-97}{3}
+\bibcite{af-pachv-92}{4}
+\bibcite{b-pplhome}{5}
+\bibcite{bdh-qach-03}{6}
+\bibcite{bfm-pdmvf-97}{7}
+\bibcite{cl-porta-97}{8}
+\bibcite{dhhhty-latte-05}{9}
+\bibcite{e-acg-87}{10}
+\bibcite{e-cgp}{11}
+\bibcite{fg-lpfaq}{12}
+\bibcite{f-pcfaq-98}{13}
+\bibcite{f-fzctmacp-04}{14}
+\bibcite{fjt-cgf-05}{15}
+\bibcite{fp-ddmr-96}{16}
+\bibcite{j-gvum-05}{17}
+\bibcite{m-pdcip-97}{18}
+\bibcite{mrtt-ddm-53}{19}
+\bibcite{m-cg-94}{20}
+\bibcite{r-topcom-05}{21}
+\bibcite{w-msv-05}{22}
+\bibcite{w-ldpo-93b}{23}

third_party/cddlib/doc/cddlibman.bbl

diff --git a/third_party/cddlib/doc/cddlibman.bbl b/third_party/cddlib/doc/cddlibman.bbl
new file mode 100644
index 0000000..937abb9
--- /dev/null
+++ b/third_party/cddlib/doc/cddlibman.bbl
@@ -0,0 +1,169 @@
+\begin{thebibliography}{10}
+
+\bibitem{a-dcg}
+N.~Amenta.
+\newblock Directory of computational geometry.
+\newblock
+  \htmladdnormallink{http://www.geom.uiuc.edu/software/cglist/}{http://www.geo%
+m.uiuc.edu/software/cglist/}.
+
+\bibitem{a-lrshome-01}
+D.~Avis.
+\newblock {\em lrs Homepage}.
+\newblock
+  \htmladdnormallink{http://cgm.cs.mcgill.ca/\~{}avis/C/lrs.html}{http://cgm.c%
+s.mcgill.ca/\~{}avis/C/lrs.html}.
+
+\bibitem{abs-hgach-97}
+D.~Avis, D.~Bremner, and R.~Seidel.
+\newblock How good are convex hull algorithms.
+\newblock {\em Computational Geometry: Theory and Applications}, 7:265--302,
+  1997.
+
+\bibitem{af-pachv-92}
+D.~Avis and K.~Fukuda.
+\newblock A pivoting algorithm for convex hulls and vertex enumeration of
+  arrangements and polyhedra.
+\newblock {\em Discrete Comput. Geom.}, 8:295--313, 1992.
+
+\bibitem{b-pplhome}
+R.~Bagnara.
+\newblock Parma polyhedra library homepage, 2004.
+\newblock \htmladdnormallink{http://www.cs.unipr.it/ppl/}
+  {http://www.cs.unipr.it/ppl/}.
+
+\bibitem{bdh-qach-03}
+C.B. Barber, D.P. Dobkin, and H.~Huhdanpaa.
+\newblock {\em qhull, Version 2003.1}, 2003.
+\newblock program and report available from
+  \htmladdnormallink{http://www.qhull.org/} {http://www.qhull.org/}.
+
+\bibitem{bfm-pdmvf-97}
+D.~Bremner, K.~Fukuda, and A.~Marzetta.
+\newblock Primal-dual methods for vertex and facet enumeration.
+\newblock In {\em Proc. 13th Annu. ACM Sympos. Comput. Geom.}, pages 49--56,
+  1997.
+
+\bibitem{cl-porta-97}
+T.~Christof and A.~L{\"o}bel.
+\newblock {PORTA}: Polyhedron representation transformation algorithm (ver.
+  1.3.1), 1997.
+\newblock \htmladdnormallink{http://www.zib.de/Optimization/Software/Porta/}
+  {http://www.zib.de/Optimization/Software/Porta/}.
+
+\bibitem{dhhhty-latte-05}
+J.~de~Loera, D.~Haws, R.~Hemmecke, Peter Huggins, J.~Tauzer, and R.~Yoshida.
+\newblock {\em Latt{E}}.
+\newblock University of California, Davis, 2005.
+\newblock available from
+  \htmladdnormallink{http://www.math.ucdavis.edu/~latte/}{http://www.math.ucda%
+vis.edu/~latte/}.
+
+\bibitem{e-acg-87}
+H.~Edelsbrunner.
+\newblock {\em Algorithms in {C}ombinatorial {G}eometry}.
+\newblock Springer-Verlag, 1987.
+
+\bibitem{e-cgp}
+J.~Erickson.
+\newblock Computational geometry pages, list of software libraries and codes.
+\newblock
+  \htmladdnormallink{http://compgeom.cs.uiuc.edu/\~{}jeffe/compgeom/}{http://c%
+ompgeom.cs.uiuc.edu/\~{}jeffe/compgeom/}.
+
+\bibitem{fg-lpfaq}
+R.~Fourer and J.W. Gregory.
+\newblock Linear programming frequently asked questions ({LP-FAQ}).
+\newblock
+  \htmladdnormallink{http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programm%
+ing-faq.html}
+  {http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html}.
+
+\bibitem{f-pcfaq-98}
+K.~Fukuda.
+\newblock Polyhedral computation {FAQ}, 1998.
+\newblock Both html and ps versions available from
+  \htmladdnormallink{http://www.ifor.math.ethz.ch/\~{}fukuda/fukuda.html}
+  {http://www.ifor.math.ethz.ch/\~{}fukuda/fukuda.html}.
+
+\bibitem{f-fzctmacp-04}
+K.~Fukuda.
+\newblock From the zonotope construction to the {M}inkowski addition of convex
+  polytopes.
+\newblock {\em Journal of Symbolic Computation}, 38(4):1261--1272, 2004.
+\newblock pdf file available from
+  \htmladdnormallink{http://www.cs.mcgill.ca/\~{}fukuda/download/paper/minksum%
+031007jsc.pdf}{http://www.cs.mcgill.ca/\~{}fukuda/download/paper/minksum031007%
+jsc.pdf}.
+
+\bibitem{fjt-cgf-05}
+K.~Fukuda, A.~Jensen, and R.~Thomas.
+\newblock Computing {G}r{\"o}bner fans.
+\newblock Technical report.
+\newblock In preparation.
+
+\bibitem{fp-ddmr-96}
+K.~Fukuda and A.~Prodon.
+\newblock Double description method revisited.
+\newblock In M.~Deza, R.~Euler, and I.~Manoussakis, editors, {\em Combinatorics
+  and Computer Science}, volume 1120 of {\em Lecture Notes in Computer
+  Science}, pages 91--111. Springer-Verlag, 1996.
+\newblock ps file available from
+  \htmladdnormallink{ftp://ftp.ifor.math.ethz.ch/pub/fukuda/reports/ddrev96031%
+5.ps.gz}{ftp://ftp.ifor.math.ethz.ch/pub/fukuda/reports/ddrev960315.ps.gz}.
+
+\bibitem{j-gvum-05}
+A.N. Jensen.
+\newblock {\em Gfan version 0.1: A User's Manual}.
+\newblock Department of Mathematical Sciences, University of Aarhus and
+  Institute for Operations Research, ETH Zurich, 2005.
+\newblock available from
+  \htmladdnormallink{http://home.imf.au.dk/ajensen/software/gfan/gfan.html}{ht%
+tp://home.imf.au.dk/ajensen/software/gfan/gfan.html}.
+
+\bibitem{m-pdcip-97}
+A.~Marzetta.
+\newblock {\em pd -- {C}-implementation of the primal-dual algoirithm}, 1997.
+\newblock code available from
+  \htmladdnormallink{http://www.cs.unb.ca/profs/bremner/pd/}
+  {http://www.cs.unb.ca/profs/bremner/pd/}.
+
+\bibitem{mrtt-ddm-53}
+T.S. Motzkin, H.~Raiffa, GL. Thompson, and R.M. Thrall.
+\newblock The double description method.
+\newblock In H.W. Kuhn and A.W.Tucker, editors, {\em Contributions to theory of
+  games, Vol. 2}. Princeton University Press, Princeton, RI, 1953.
+
+\bibitem{m-cg-94}
+K.~Mulmuley.
+\newblock {\em Computational {G}eometry, {A}n {I}ntroduction {T}hrough
+  {R}andamized {A}lgorithms}.
+\newblock Prentice-Hall, 1994.
+
+\bibitem{r-topcom-05}
+J.~Rambau.
+\newblock {\em TOPCOM, a package for computing Triangulations Of Point
+  Configurations and Oriented Matroids}.
+\newblock University of Bayreuth, 2005.
+\newblock available from
+  \htmladdnormallink{http://www.uni-bayreuth.de/departments/wirtschaftsmathema%
+tik/rambau/TOPCOM/}{http://www.uni-bayreuth.de/departments/wirtschaftsmathemat%
+ik/rambau/TOPCOMl}.
+
+\bibitem{w-msv-05}
+C.~Weibel.
+\newblock {\em Minksum version 1.1}.
+\newblock Mathematics Institute, EPF Lausanne, 2005.
+\newblock available from
+  \htmladdnormallink{http://roso.epfl.ch/cw/poly/public.php}{http://roso.epfl.%
+ch/cw/poly/public.php}.
+
+\bibitem{w-ldpo-93b}
+D.K. Wilde.
+\newblock A library for doing polyhedral operations.
+\newblock Master's thesis, Oregon State University, Corvallis, Oregon, Dec
+  1993.
+\newblock Also published in IRISA technical report PI 785, Rennes, France; Dec,
+  1993.
+
+\end{thebibliography}

third_party/cddlib/doc/cddlibman.blg

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third_party/cddlib/doc/cddlibman.dvi

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+Overfull \hbox (2.6514pt too wide) in paragraph at lines 4--9
+[]\OT1/cmr/m/n/10.95 N. Amenta.  Di-rec-tory of com-pu-ta-tional ge-om-e-try.  
+http://www.geom.uiuc.edu/software/cglist/. 
+ []
+
+[17]
+Underfull \hbox (badness 2302) in paragraph at lines 68--73
+[]\OT1/cmr/m/n/10.95 J. Er-ick-son.  Com-pu-ta-tional ge-om-e-try pages, list o
+f soft-ware li-braries and codes.
+ []
+
+[18]) [19] (./cddlibman.aux) ) 
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+Output written on cddlibman.dvi (19 pages, 73224 bytes).

third_party/cddlib/doc/cddlibman.pdf

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+%!PS-AdobeFont-1.1: CMBX12 1.0
+%%CreationDate: 1991 Aug 20 16:34:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMBX12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Bold) readonly def
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+/isFixedPitch false def
+end readonly def
+/FontName /CMBX12 def
+/PaintType 0 def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+dup 40 /parenleft put
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+dup 45 /hyphen put
+dup 46 /period put
+dup 47 /slash put
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+%%CreationDate: 1996 Jul 23 07:53:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+/Weight (Medium) readonly def
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+dup 106 /j put
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+readonly def
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+currentdict end
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%!PS-AdobeFont-1.1: CMTT10 1.00B
+%%CreationDate: 1992 Apr 26 10:42:42
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMTT10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch true def
+end readonly def
+/FontName /CMTT10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+0 1 255 {1 index exch /.notdef put} for
+dup 35 /numbersign put
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+dup 40 /parenleft put
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+readonly def
+/FontBBox{-4 -235 731 800}readonly def
+currentdict end
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+%%CreationDate: 1992 Feb 19 19:54:52
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
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+%%EndFont 
+%%BeginFont: CMBX10
+%!PS-AdobeFont-1.1: CMBX10 1.00B
+%%CreationDate: 1992 Feb 19 19:54:06
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMBX10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Bold) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMBX10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 12 /fi put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 45 /hyphen put
+dup 46 /period put
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+readonly def
+/FontBBox{-301 -250 1164 946}readonly def
+currentdict end
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+%%EndFont 
+%%BeginFont: CMR12
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR12 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 46 /period put
+dup 48 /zero put
+dup 50 /two put
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+readonly def
+/FontBBox{-34 -251 988 750}readonly def
+currentdict end
+currentfile eexec
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third_party/cddlib/doc/cddlibman.tex

diff --git a/third_party/cddlib/doc/cddlibman.tex b/third_party/cddlib/doc/cddlibman.tex
new file mode 100644
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--- /dev/null
+++ b/third_party/cddlib/doc/cddlibman.tex
@@ -0,0 +1,1180 @@
+% The name of this file: cddlibman.tex
+% written by by Komei Fukuda
+% created March 15, 1999
+% modified February 7, 2008
+%
+\documentclass[11pt]{article}
+\usepackage{html,amsmath,amssymb}
+\renewcommand{\baselinestretch}{1}
+\renewcommand{\arraystretch}{1}
+\setlength{\oddsidemargin}{0mm}
+\setlength{\textwidth}{165mm}
+\setlength{\topmargin}{-15mm}
+\setlength{\textheight}{232mm}
+%\setlength{\headsep}{0in}
+%\setlength{\headheight}{0pt}
+\pagestyle{plain}
+
+\newcommand {\0} {{\bf 0}}
+\newcommand{\R}{{\Bbb R}}
+
+\begin{document}
+\title{cddlib Reference Manual}
+\author{Komei Fukuda\\
+Institute for Operations Research\\
+and Institute of Theoretical Computer Science\\
+ETH Zentrum, CH-8092 Zurich, Switzerland\\
+}
+\date{ (cddlib ver. 0.94, manual ver. February 7, 2008)}
+
+\maketitle
+
+\tableofcontents
+
+\begin{abstract}
+This is a reference manual for cddlib-094.  
+The manual describes the library functions and data types implemented 
+in the cddlib C-library which is to perform fundamental polyhedral 
+computations such as representation conversions and linear programming
+in both floating-point and GMP rational exact arithmetic.
+Please read the accompanying README file and test programs to 
+complement the manual.
+
+The new functions added in this version include {\tt dd\_MatrixCanonicalize}
+to find a non-redundant proper H- or V-representation,
+{\tt dd\_FindRelativeInterior} to find a relative interior point
+of an H-polyhedron, and  {\tt dd\_ExistsRestrictedFace} (Farkas-type 
+alternative theorem verifier)
+to check the existence of a point satisfying a specified system
+of linear inequalities possibly including multiple strict inequalities.
+
+The new functions are particularly important for the development of
+related software packages MinkSum (by Ch. Weibel) and Gfan
+(by Anders Jensen),
+
+\end{abstract}
+
+\section{Introduction} \label{INTRODUCTION}
+
+The program  cddlib  is an efficient implementation \cite{fp-ddmr-96}  of 
+the double description Method~\cite{mrtt-ddm-53}
+for generating  all vertices (i.e. extreme points)
+and extreme rays of a general 
+convex polyhedron given by 
+a system of linear inequalities:
+\[
+   P = \{ x=(x_1, x_2, \ldots, x_d)^T \in R^{d}:  b - A  x  \ge 0 \}
+\]
+where $A$ is a given $m \times d$ real matrix and 
+$b$ is a given real $m$-vector.   In the mathematical
+language, the computation is the transformation
+of an {\em H-representation\/} of a convex polytope
+to an {\em V-representation}.  
+
+cddlib is a C-library version of the previously released C-code cdd/cdd+.
+In order to make this library version, a large part of the cdd source
+(Version 0.61) has been rewritten.
+This library version is more flexible since it can be called from other programs in C/C++.
+Unlike cdd/cdd+, cddlib can handle any general input and is more general.
+Furtthermore,  additional functions have been written to extend its functionality.
+
+One useful feature of  cddlib/cdd/cdd+ is its capability
+of handling the dual (reverse)  problem without any transformation
+of data.  The dual transformation problem of a V-representation
+to a minimal H-representation and is often called the 
+{\em (convex) hull problem\/}.  More explicitly,
+is to obtain a linear inequality representation
+of a convex polyhedron given as the Minkowski sum of 
+the convex hull of a finite set of points and the nonnegative
+hull of a finite set of points in $R^{d}$: 
+\[
+P = conv(v_1,\ldots,v_n) +  nonneg(r_{n+1},\ldots,r_{n+s}), 
+\]
+where
+ the {\em Minkowski sum of two subsets $S$ and $T$} of $R^{d}$ is defined
+as 
+\[
+S + T = \{ s + t \; |  s \in S \mbox{ and } t \in T \}.
+\]
+As we see in this manual, the computation can be done
+in straightforward manner.  Unlike the earlier versions of
+cdd/cdd+ that assume certain regularity conditions for input, 
+cddlib is designed to do a correct transformation for any general input.
+The user must be aware of the fact that in certain cases the
+transformation is not unique and there are polyhedra with
+infinitely many representations.  For example, a line
+segment (1-dimensional polytope) in $R^3$ has infinitely
+many minimal H-representations, and a halfspace in the same space
+has infinitely many minimal V-representations.  cddlib generates
+merely one minimal representation.
+
+cddlib comes with an LP code to solve the general
+linear programming (LP) problem to maximize (or minimize) a linear
+function over polyhedron $P$.   It is useful mainly for solving 
+dense LP's with large $m$ (say, up to few hundred thousands) and small $d$ 
+(say, up to 100).  It implements a revised dual simplex method that
+updates $(d+1)\times (d+1)$ matrix for a pivot operation.
+
+The program cddlib has an I/O routines that read and write files in 
+{\em Polyhedra format\/} which was defined by David Avis and
+the author in 1993, and has been updated in 1997 and 1999.  
+The program called lrs and lrslib \cite{a-lrshome-01} developed by David Avis is
+a C-implementation of the reverse search algorithm~\cite{af-pachv-92} 
+for the same enumeration purpose, and it conforms to Polyhedra format as well.
+Hopefully, this compatibility of the two programs
+enables users to use both programs for the same input files
+and to choose whichever is useful for their purposes.
+From our experiences with relatively large problems,
+the two methods are both useful and perhaps complementary
+to each other.  In general, the program cddlib tends to be
+efficient for highly degenerate inputs and the program rs
+tends to be efficient for nondegenerate or slightly
+degenerate problems.
+
+Although the program can be used for nondegenerate inputs,
+it might not be very efficient.  For nondegenerate inputs, 
+other available programs, such as the reverse search code lrs or
+qhull (developed by the Geometry Center),
+might be more efficient.  See Section~\ref{CODES} 
+for pointers to these codes.  
+The paper \cite{abs-hgach-97} contains many interesting results on polyhedral
+computation and experimental results on cdd+, lrs, qhull and porta.
+
+This program can be distributed freely under the GNU GENERAL PUBLIC LICENSE.
+Please read the file COPYING carefully before using.
+
+I will not take any responsibility of any problems you might have
+with this program.  But I will be glad to receive bug reports or suggestions
+at the e-mail addresses above. If cddlib turns out to be useful, 
+please kindly inform  me of  what purposes cdd has been used for. 
+I will be happy to include a list of applications in future
+distribution  if I receive  enough replies.
+The most powerful support for free software development
+is user's appreciation and collaboration.
+
+\section{Polyhedra H- and V-Formats (Version 1999)} \label{FORMAT}
+\bigskip
+Every convex polyhedron has two representations, one as
+the intersection of finite halfspaces and the other
+as Minkowski sum of the convex hull of finite points
+and the nonnegative hull of finite directions.  These are
+called H-representation and V-representation, respectively.
+
+Naturally there are two basic Polyhedra formats, 
+H-format for  H-representation and V-format for
+V-representation.    These two formats are designed
+to be almost indistinguishable, and in fact, one can
+almost pretend one for the other.   There is some asymmetry
+arising from the asymmetry of two representations.
+
+First we start with the H-representation.
+Let $A$ be an $m \times d$ matrix, and let $b$ be a column $m$-vector.
+The Polyhedra format  ({\em  H-format} )  of 
+the system  $\; b - A x \ge \0\;$ of $m$ inequalities in $d$ variables
+$x =(x_1, x_2, \ldots, x_d)^T$ is
+
+\begin{tabular}{ccl}
+\\ \hline
+\multicolumn{3}{l} {various comments}\\
+\multicolumn{3}{l} {{\bf H-representation}}\\
+\multicolumn{3}{l} {{\bf (linearity $t\;$ $i_1\;$  $i_2\;$  $\ldots$ $\;i_t$)}}\\
+\multicolumn{3}{l} {{\bf begin}}\\
+ $m$ & $d+1$ & numbertype\\
+ $b$ & $-A$ \\
+\multicolumn{3}{l} {{\bf end}}\\
+\multicolumn{3}{l} {various options} \\ \hline
+\end{tabular}
+
+\bigskip
+\noindent
+where numbertype can be one of integer, rational or real.
+When rational type is selected, each component
+of $b$ and $A$ can be specified by the usual integer expression 
+or by the rational expression ``$p / q$''  or  ``$-p / q$'' where
+$p$ and $q$ are arbitrary long positive integers (see the example
+input file rational.ine).  In the 1997 format,
+we introduced ``H-representation'' which must appear
+before ``begin''. 
+There was one restriction in the old polyhedra format 
+(before 1997):  the last $d$ rows must determine
+a vertex of $P$.  This is obsolete now.
+
+In the new 1999 format, we added the possibility of specifying {\bf linearity\/}.
+This means that
+for H-representation, some of the input rows can be specified as  {\bf equalities}:  
+$b_{i_j} - A_{i_j} x = 0 \;$ for all $j=1,2, \ldots, t$.
+The linearity line may be omitted if there are no equalities.
+
+Option lines can be used to control computation of a specific program.
+In particular both cdd and lrs use the option lines to represent
+a linear objective function.  See the attached LP files, samplelp*.ine.
+
+\bigskip
+Next we define Polyhedra  {\em V-format}.  Let $P$ be 
+represented by $n$ gerating points and $s$ generating directions (rays) as 
+$P = conv(v_1,\ldots,v_n) +  nonneg(r_{n+1},\ldots,r_{n+s})$.
+Then the Polyhedra V-format for $P$ is 
+
+\begin{tabular}{cll}
+\\ \hline
+\multicolumn{3}{l} {various comments}\\
+\multicolumn{3}{l} {{\bf V-representation}}\\
+\multicolumn{3}{l} {({\bf linearity $t\;$ $i_1\;$  $i_2\;$  $\ldots$ $\;i_t$ })}\\
+\multicolumn{3}{l} {{\bf begin}}\\
+ $n+s$ & $d+1$ & numbertype\\
+ $1$ & $v_1$  & \\
+ $\vdots$ & $\vdots$  & \\
+ $1$ & $v_n$  & \\
+ $0$ & $r_{n+1}$  & \\
+ $\vdots$ & $\vdots$  & \\
+ $0$ & $r_{n+s}$  & \\
+\multicolumn{3}{l} {{\bf end}}\\
+\multicolumn{3}{l} {various options} \\ \hline
+\end{tabular}
+
+\bigskip
+\noindent
+Here we do not require that
+vertices and rays are listed
+separately; they can appear mixed in arbitrary
+order.
+
+Linearity for V-representation specifies a subset of generators
+whose coefficients are relaxed
+to be {\bf free}:  for all $j=1,2, \ldots, t$, the $k=i_j$th generator ($v_{k}$ or $r_k$ whichever is the $i_j$th generator) is a free generator. 
+This means for each such a ray $r_k$, 
+the line generated by $r_k$ is in the polyhedron,
+and for each such a vertex $v_k$, its coefficient is no longer nonnegative
+but still the coefficients for all $v_i$'s must sum up to one. 
+It is highly unlikely that one needs to
+use linearity for vertex generators, and it is defined mostly
+for formality.
+
+When the representation statement, either ``H-representation''
+or ``V-representation'', is omitted, the former
+``H-representation'' is assumed.
+
+It is strongly suggested to use the following rule for naming
+H-format files and V-format files:   
+\begin{description}
+\item[(a)] use the filename  extension ``.ine'' for H-files (where ine stands for inequalities), and 
+\item[(b)]  use the filename  extension ``.ext'' for V-files (where ext stands for extreme points/rays). 
+\end{description}
+
+
+\section{Basic Object Types (Structures) in cddlib}  \label{DATASTR}
+
+Here are the types (defined in cddtypes.h) that are 
+important for the cddlib user.  The most important one, 
+{\tt dd\_MatrixType},
+is to store a Polyhedra data in a straightforward manner.
+Once the user sets up a (pointer to)  {\tt dd\_MatrixType} data,
+he/she can load the data to an internal data type ({\tt dd\_PolyhedraType})
+by using functions described in the next section, and apply
+the double descrition method to get another representation.
+As an option  {\tt dd\_MatrixType} can save a linear objective function
+to be used by a linear programming solver.
+
+The two dimensional array data in the structure {\tt dd\_MatrixType} is
+{\tt dd\_Amatrix} whose components are of type {\tt mytype\/}.
+The type mytype is set to be either the rational type {\tt mpq\_t} of 
+the GNU MP Library or the C double array of size $1$.
+This abstract type allows us to write a single program that can
+be compiled with the two or more different arithmetics, see example
+programs such as simplecdd.c, testlp*.c and testcdd*.c
+in the {\tt src} and {\tt src-gmp} subdirectories of the source
+distribution.
+
+There is another data type that is used very often, {\tt dd\_SetFamilyType}.
+This is to store a family of subsets of a finite set.  Such a family
+can represent the incidence relations between the set of extreme
+points and the set of facets of a polyhedron.  Also, it can represent a
+graph structure by listing the set of vertices adjacent to each vertex (i.e.
+the adjacency list).   To implement  {\tt dd\_SetFamilyType},
+we use  a separate set library called {\tt setoper}, that
+handles the basic set operations,   This library is briefly introduced in
+Section~\ref{SetFunctions}.
+
+
+\begin{verbatim}
+
+#define dd_FALSE 0
+#define dd_TRUE 1
+
+typedef long dd_rowrange;
+typedef long dd_colrange;
+typedef long dd_bigrange;
+
+typedef set_type dd_rowset;   /* set_type defined in setoper.h */
+typedef set_type dd_colset;
+typedef long *dd_rowindex;   
+typedef int *dd_rowflag;   
+typedef long *dd_colindex;
+typedef mytype **dd_Amatrix;  /* mytype is either GMP mpq_t or 1-dim double array. */
+typedef mytype *dd_Arow;
+typedef set_type *dd_SetVector;
+
+typedef enum {
+  dd_Real, dd_Rational, dd_Integer, dd_Unknown
+} dd_NumberType;
+
+typedef enum {
+  dd_Inequality, dd_Generator, dd_Unspecified
+} dd_RepresentationType;
+
+typedef enum {
+  dd_MaxIndex, dd_MinIndex, dd_MinCutoff, dd_MaxCutoff, dd_MixCutoff,
+   dd_LexMin, dd_LexMax, dd_RandomRow
+} dd_RowOrderType;
+
+typedef enum {
+  dd_InProgress, dd_AllFound, dd_RegionEmpty
+} dd_CompStatusType;
+
+typedef enum {
+  dd_DimensionTooLarge, dd_ImproperInputFormat, 
+  dd_NegativeMatrixSize, dd_EmptyVrepresentation,
+  dd_IFileNotFound, dd_OFileNotOpen, dd_NoLPObjective, 
+  dd_NoRealNumberSupport, dd_NoError
+} dd_ErrorType;
+
+typedef enum {
+  dd_LPnone=0, dd_LPmax, dd_LPmin
+} dd_LPObjectiveType;
+
+typedef enum {
+  dd_LPSundecided, dd_Optimal, dd_Inconsistent, dd_DualInconsistent,
+  dd_StrucInconsistent, dd_StrucDualInconsistent,
+  dd_Unbounded, dd_DualUnbounded
+} dd_LPStatusType;
+
+typedef struct matrixdata *dd_MatrixPtr;
+typedef struct matrixdata {
+  dd_rowrange rowsize;
+  dd_rowset linset; 
+    /*  a subset of rows of linearity (ie, generators of
+        linearity space for V-representation, and equations
+        for H-representation. */
+  dd_colrange colsize;
+  dd_RepresentationType representation;
+  dd_NumberType numbtype;
+  dd_Amatrix matrix;
+  dd_LPObjectiveType objective;
+  dd_Arow rowvec;
+}  dd_MatrixType;
+
+typedef struct setfamily *dd_SetFamilyPtr;
+typedef struct setfamily {
+  dd_bigrange famsize;
+  dd_bigrange setsize;
+  dd_SetVector set;  
+} dd_SetFamilyType;
+
+typedef struct lpsolution *dd_LPSolutionPtr;
+typedef struct lpsolution {
+  dd_DataFileType filename;
+  dd_LPObjectiveType objective;
+  dd_LPSolverType solver; 
+  dd_rowrange m;
+  dd_colrange d;
+  dd_NumberType numbtype;
+
+  dd_LPStatusType LPS;  /* the current solution status */
+  mytype optvalue;  /* optimal value */
+  dd_Arow sol;   /* primal solution */
+  dd_Arow dsol;  /* dual solution */
+  dd_colindex nbindex;  /* current basis represented by nonbasic indices */
+  dd_rowrange re;  /* row index as a certificate in the case of inconsistency */
+  dd_colrange se;  /* col index as a certificate in the case of dual inconsistency */
+  long pivots[5]; 
+   /* pivots[0]=setup (to find a basis), pivots[1]=PhaseI or Criss-Cross,
+      pivots[2]=Phase II, pivots[3]=Anticycling, pivots[4]=GMP postopt  */
+  long total_pivots;
+} dd_LPSolutionType;
+
+\end{verbatim}
+
+\section{Library Functions}  \label{LIBRARY}
+
+Here we list some of the most important library functions/procedures. 
+We use the following convention: 
+{\tt poly} is of type {\tt dd\_PolyhedraPtr},
+{\tt matrix}, {\tt matrix1} and {\tt matrix2} are of type {\tt dd\_MatrixPtr},
+{\tt matrixP}, of type {\tt dd\_MatrixPtr*},
+{\tt err} is of type {\tt dd\_ErrorType*}, 
+{\tt ifile} and {\tt ofile} are of type {\tt char*},
+{\tt A} is of type {\tt dd\_Amatrix},
+{\tt point} and {\tt vector} are of type {\tt dd\_Arow},
+{\tt d} is of type {\tt dd\_colrange}, 
+{\tt m} and {\tt i} are of type {\tt dd\_rowrange},
+{\tt x} is of type {\tt mytype}, 
+{\tt a} is of type {\tt signed long integer},
+{\tt b} is of type {\tt double},
+{\tt set} is of type {\tt set\_type}.
+  Also,
+{\tt setfam} is of type {\tt dd\_SetFamilyPtr},
+{\tt lp} is of type {\tt dd\_LPPtr},
+{\tt lps} is of type {\tt dd\_LPSolutionPtr},
+{\tt solver} is of type {\tt dd\_LPSolverType},
+{\tt roworder} is of type {\tt dd\_RowOrderType}.
+
+
+\subsection{Library Initialization}  \label{Initialization}
+
+\begin{description}
+
+\item[{\tt void dd\_set\_global\_constants(void)}]:\\
+This is to set the global constants such as {\tt dd\_zero},
+{\tt dd\_purezero} and
+{\tt dd\_one} for sign recognition and basic arithmetic
+operations.  {Every program to use cddlib must call this function}
+before doing any computation.    Just call this once.
+ See Section \ref{constants} for the definitions of
+constants.
+
+\item[{\tt void dd\_free\_global\_constants(void)}]:\\
+This is to free the global constants. This should be called
+when one does not use cddlib functions anymore.
+\end{description}
+
+\subsection{Core Functions}  \label{CoreLibrary}
+
+There are two types of core functions in cddlib.  The first type
+runs the double description (DD) algorithm and does a representation
+conversion of a specified polyhedron.  The standard header
+for this type is {\tt dd\_DD*}.  The second type solves
+one or more linear programs with no special headers.   
+Both types of computations are nontrivial
+and the users (especially for the DD algorithm) must
+know that there is a serous limit in the sizes of problems
+that can be practically solved. 
+Please check *.ext and *.ine files that come with cddlib to get
+ideas of tractable problems. 
+
+In addition to previously defined objects, the symbol  {\tt roworder} is
+of {\tt dd\_RowOrderType}. The symbol {\tt matrixP} is 
+a pointer to {\bf dd\_MatrixType}.
+the arguments {\tt impl\_lin} and {\tt redset} are both a pointer 
+to {\tt dd\_rowset} type, and {\tt newpos} is a pointer to 
+{\tt dd\_rowindex} type. 
+
+
+\begin{description}
+\item[{\tt dd\_PolyhedraPtr dd\_DDMatrix2Poly(matrix, err)}]:\\
+Store the representation given by {\tt matrix} in a polyhedra data, and
+generate the second representation of {\tt *poly}.  It returns
+a pointer to the data. {\tt *err}
+returns {\tt dd\_NoError} if the computation terminates normally.  Otherwise,
+it returns a value according to the error occured.
+
+\item[{\tt dd\_PolyhedraPtr dd\_DDMatrix2Poly2(matrix, roworder, err)}]:\\
+This is the same function as  {\tt dd\_DDMatrix2Poly} except that the insertion
+order is specified by the user.  The argument {\tt roworder} is of {\tt dd\_RowOrderType}
+and takes one of the values:
+  {\tt dd\_MaxIndex}, {\tt dd\_MinIndex}, {\tt dd\_MinCutoff}, {\tt dd\_MaxCutoff}, {\tt dd\_MixCutoff},
+   {\tt dd\_LexMin}, {\tt dd\_LexMax}, {\tt dd\_RandomRow}.   In general, {\tt dd\_LexMin} is
+the best choice which is in fact chosen in {\tt dd\_DDMatrix2Poly}.  If you know that 
+the input is already sorted in the order you like, use  {\tt dd\_MinIndex} or  {\tt dd\_MaxIndex}.
+If the input contains many redundant rows (say more than $80\%$ redundant),
+you might want to try {\tt dd\_MaxCutoff} which might result in much faster termination,
+see \cite{abs-hgach-97,fp-ddmr-96}
+
+\item[{\tt boolean dd\_DDInputAppend(poly, matrix, err)}]:\\
+Modify the input representation in {\tt *poly}
+by appending the matrix of {\tt *matrix}, and compute
+the second representation.  The number of columns in
+{\tt *matrix} must be equal to the input representation.
+
+\item[{\tt boolean dd\_LPSolve(lp, solver, err)}]:\\
+Solve {\tt lp} by the algorithm {\tt solver} and save
+the solututions in {\tt *lp}.  Unlike the earlier versions
+(dplex, cdd+), it can deal with equations and totally zero right
+hand sides.   It is recommended that {\tt solver} is
+{\tt dd\_DualSimplex}, the revised dual simplex method
+that updates a $d\times d$ dual basis matrix in each pivot (where
+$d$ is the column size of lp).
+
+The revised dual simplex method is ideal for dense LPs in small number of variables 
+(i.e. small column size, typically less than $100$)
+and many inequality constraints (i.e. large row size, can be a few ten thousands).  
+If your LP has many variables but only few constraints, solve the dual LP by
+this function.
+
+When it is compiled for GMP rational
+arithmetic, it first tries to solve an LP with C  double
+floating-point arithmetic and verifies whether the output
+basis is correct with GMP.  If so, the correct solution is
+computed with GMP.  Otherwise, it (re)solves the LP
+from scratch with GMP.   This is newly implemented
+in the version 093.  The original (non-crossover) version of 
+the same function is still  available as {\tt boolean dd\_LPSolve0}.
+
+\item[{\tt dd\_boolean dd\_Redundant(matrix, i, point, err)}]:\\
+Check whether $i$th data in {\tt matrix} is redundant for the representation.
+If it is nonredundant, it returns a certificate.  For H-representation,
+it is a {\tt point} in $R^d$ which satisfies
+all inequalities except for the $i$th inequality.  If $i$ is a linearity,
+it does nothing and always returns {\tt dd\_FALSE}.
+
+\item[{\tt dd\_rowset dd\_RedundantRows(matrix, err)}]:\\
+Returns a maximal set of row indices such that the associated rows
+can be eliminated without changing the polyhedron.  
+The function works for both V- and H-representations.
+
+\item[{\tt dd\_boolean dd\_SRedundant(matrix, i, point, err)}]:\\
+Check whether $i$th data in {\tt matrix} is strongly redundant for the representation.
+If $i$ is a linearity, it does nothing and always returns {\tt dd\_FALSE}.
+Here,  $i$th inequality in H-representation is {\em strongly redundant\/} if it is redundant 
+and there is no point in the polyhedron satisfying the inequality with equality.
+In V-representation,  $i$th point is {\em strongly redundant\/} if it is redundant 
+and it is in the relative interior of the polyhedron. If it is not strongly redundant, it returns a certificate.
+ 
+\item[{\tt dd\_boolean dd\_ImplicitLinearity(matrix, i, err)}]:\\
+Check whether $i$th row
+in the input is forced to be linearity (equality 
+for H-representation).
+If $i$ is linearity itself, 
+it does nothing and always returns {\tt dd\_FALSE}.
+
+\item[{\tt dd\_rowset dd\_ImplicitLinearityRows(matrix, err)}]:\\
+Returns the set of indices of rows that are 
+implicitly linearity.  It simply calls the library function
+{\tt dd\_ImplicitLinearity} for each inequality and collects
+the row indices for which the answer is {\tt dd\_TRUE}.
+
+\item[{\tt dd\_boolean dd\_MatrixCanonicalize(matrixP, impl\_lin, redset, newpos, err)}]:\\
+ The input is a pointer {\tt matrixP} to a matrix and the function
+modifies the matrix by putting a maximally linear independent linearities (basis)
+at the top of the matrix, and removing all redundant data.
+All implicit linearities and all (removed) redundant rows
+in the original matrix will be returned in the corresponding row sets.
+The new positions of the original rows are returned by 
+the array {\tt newpos}.
+
+The cardinality of the new linearity set {\tt  (*matrixP)->linset} is the codimension
+of the polyhedron if it is H-polyhedron, and is the dimension of linearity space
+if it is V-polyhedron.
+
+Note that the present version should not be called a canonicalization
+because it may generate two different representations of the same
+polyhedron.  In the future, this function is expected to be correctly
+implemented. 
+
+\item[{\tt dd\_boolean dd\_MatrixCanonicalizeLinearity(matrixP, impl\_linset, newpos. err)}]:\\
+It does only the first half of {\tt dd\_boolean dd\_MatrixCanonicalize}, namely, it detects all
+implicit linearities and puts a maximally independent linearities
+at the top of the matrix.  For example, this function can be 
+used to detect the dimension of an H-polyhedron.
+
+\item[{\tt dd\_boolean dd\_MatrixRedundancyRemove(matrixP, redset, newpos, err)}]:\\
+It does essentially the second half of {\tt dd\_boolean dd\_MatrixCanonicalize}, 
+namely, it detects all
+redundancies.  This function should be used after {\tt dd\_MatrixCanonicalizeLinearity}
+has been called.
+
+
+\item[{\tt dd\_boolean dd\_FindRelativeInterior(matrix, impl\_lin, lin\_basis, lps, err)}]:\\
+Computes a point in the relative interior of an H-polyhedron given by matrix, by solving
+an LP. The point will be returned by {\tt lps}.
+See the sample program allfaces.c that generates all nonempty faces of an H-polyhedron and
+a relative interior point for each face.   The former returns all implicit linearity rows (implicit equations)
+and the latter returns a basis of the union of linearity rows and implicit linearity rows.
+This means that the cardinality of {\tt *lin\_basis} is the codimension of the polyhedron.
+
+
+\item[{\tt dd\_boolean dd\_ExistsRestrictedFace(matrix, R, S, err)}]:\\
+Returns the answer to the Farkas' type decision problem as to whether there is a point
+in the polyhedron given by matrix satisfying all constraints in {\tt R} with
+equality and all constraints in {\tt S} with strict inequality.  More precisely,
+it is the linear feasibility problem:
+\[
+\begin{array}{llllll}
+\exists\mbox{?} &x  &\mbox{ satisfying } & b_r - A_r x  &= 0, \; \forall r \in R\cup L \\
+                &   &                    & b_s - A_s x  &> 0, \; \forall s \in S \\
+                &   &                    & b_t - A_t x  &\ge 0, \; \forall t \in T,
+\end{array}
+\]
+where $L$ is the set of linearity rows of {\tt matrix}, and $T$ represents
+the set of rows that are not in $R\cup L \cup S$.
+Both {\tt R} and {\tt S} are of {\tt dd\_rowset} type.  The set $S$ is
+supposed to be disjoint from both $R$ and $L$.
+If it is not the case, the set $S$ will be considered as $S \setminus (R \cup L)$.
+
+This function ignores {\tt matrix->representation}, and thus even if it is
+set to {\tt dd\_Generator} or {\tt dd\_Unspecified}, it treats the matrix
+as if it were inequality representation.
+
+\item[{\tt dd\_boolean dd\_ExistsRestrictedFace2(matrix, R, S, lps, err)}]:\\
+It is the same as the function {\tt dd\_ExistsRestrictedFace} except that
+it returns also a certificate for the answer.  The certificate is a solution
+to the bounded LP: 
+\[
+\begin{array}{lllllll}
+\mbox{(P)} &\max  z  &\mbox{ subject to } & b_r - A_r x  &   & = 0, \; \forall r \in R\cup L \\
+           &         &                    & b_s - A_s x  &-z &\ge 0, \;  \forall s \in S \\
+          &         &                    & b_t - A_t x   &   &\ge 0, \; \forall t \in T \\
+         &         &                    & 1              & -z&\ge 0,
+\end{array}
+\]
+where $L$ is the set of linearity rows of {\tt matrix}, and $T$ represents
+the set of rows that are not in $R\cup L \cup S$.
+The answer for the decision problem is YES if and only if the LP attains 
+an optimal and the optimal value is positive.  The dual solution (either
+an optimal solution or a dual unbounded direction) can be considered
+as a certificate for the NO answer, if the answer is NO.
+
+This function ignores {\tt matrix->representation}, and thus even if it is
+set to {\tt dd\_Generator} or {\tt dd\_Unspecified}, it treats the matrix
+as if it were inequality representation.
+
+\item[{\tt dd\_SetFamilyPtr dd\_Matrix2Adjacency(matrix, err)}]:\\
+Computes the adjacency list of input rows using
+the LP solver and without running the representation conversion.  When
+the input is H-representation, it gives the facet graph of the polyhedron.
+For V-representation, it gives the (vertex) graph of the polyhedron.
+It is required that the input matrix is a minimal representation.
+Run redundancy removal functions before calling this function,
+see the sample code adjacency.c. 
+
+
+\item[{\tt dd\_SetFamilyPtr dd\_Matrix2WeakAdjacency(matrix, err)}]:\\
+Computes the weak adjacency list of input rows using
+the LP solver and without running the representation conversion.  When
+the input is H-representation, it gives the graph where its nodes are the facets
+two nodes  are adjacent if and only if the associated facets have
+some intersection.
+For V-representation, it gives the graph where its nodes are the vertices
+and two nodes are adjacent if and only if the associated vertices
+are on a common facet.
+It is required that the input matrix is a minimal representation.
+Run redundancy removal functions before calling this function,
+see the sample code adjacency.c. 
+
+\item[{\tt dd\_MatrixPtr dd\_FourierElimination(matrix, err)}]:\\
+Eliminate the last variable from a system of linear inequalities
+given by matrix by using the Fourier's Elimination.  If the 
+input matrix is V-representation, {\tt  *err} returns
+{\tt dd\_NotAvailForV}.   This function does not
+remove redundancy  and one might want to call
+redundancy removal functions afterwards. See the sample code fourier.c.
+
+\item[{\tt dd\_MatrixPtr dd\_BlockElimination(matrix, set, err)}]:\\
+Eliminate a set of variables from a system of linear inequalities
+given by matrix by using the extreme rays of the dual linear system.
+See comments in the code cddproj.c for details.  This might be
+a faster way to eliminate variables than the repeated FourierElimination when
+the number of variables to eliminate is large. 
+If the input matrix is V-representation, {\tt  *err}  returns {\tt dd\_NotAvailForV}.
+This function does not remove redundancy  and one might want to call
+redundancy removal functions afterwards. See the sample code projection.c.
+
+
+\item[{\tt dd\_rowrange dd\_RayShooting(matrix, point, vector)}]:\\
+Finds the index of a halfspace first left by the ray starting from
+{\tt point} toward the direction {\tt vector}.  It resolves
+tie by a lexicographic perturbation.  Those inequalities violated
+by {\tt point} will be simply ignored.
+
+\end{description}
+
+
+\subsection{Data Manipulations}  \label{DataLibrary}
+
+\subsubsection{Number Assignments}
+For number assignments, one cannot use such expressions as {\tt x=(mytype)a}.
+This is because cddlib uses an abstract number type ({\tt mytype}) 
+so that it can compute with various 
+number types such as C double and GMP rational.
+User can easily add a new number type by redefining
+arithmetic operations in cddmp.h and cddmp.c.
+
+\begin{description}
+
+
+\item[{\tt void dd\_init(x)}]:\\
+This is to initialize a {\tt mytype} variable {\tt x} and to set it
+to zero.    This initialization has to be called before
+any {\tt mytype} variable to be used.
+
+\item[{\tt void dd\_clear(x)}]:\\
+This is to free the space allocated to a {\tt mytype} variable {\tt x}.
+
+\item[{\tt void dd\_set\_si(x, a)}]:\\
+This is to set a {\tt mytype} variable {\tt x} to the
+value of signed long integer {\tt a}.  
+
+\item[{\tt void dd\_set\_si2(x, a, b)}]:\\
+This is to set a {\tt mytype} variable {\tt x} to the
+value of  the rational expression {\tt a/b}, where
+{\tt a} is signed long and  {\tt b} is unsigned long
+integers.  
+
+\item[{\tt void dd\_set\_d(x, b)}]:\\
+This is to set a {\tt mytype} variable {\tt x} to the
+value of double {\tt b}.  This is available only
+when the library is compiled without {\tt -DGMPRATIONAL}
+compiler option.
+
+\end{description}
+
+
+\subsubsection{Arithmetic Operations for {\tt mytype} Numbers}
+
+Below  {\tt x}, {\tt y}, {\tt z}  are of type {\tt mytype}.
+
+\begin{description}
+
+\item[{\tt void dd\_add(x, y, z)}]:\\
+Set {\tt x} to be the sum of  {\tt y} and  {\tt z}.
+
+\item[{\tt void dd\_sub(x, y, z)}]:\\
+Set {\tt x} to be the substraction of  {\tt z}  from  {\tt y}.
+
+\item[{\tt void dd\_mul(x, y, z)}]:\\
+Set {\tt x} to be the multiplication of  {\tt y}  and  {\tt z}.
+
+\item[{\tt void dd\_div(x, y, z)}]:\\
+Set {\tt x} to be the division of  {\tt y}  over  {\tt z}.
+
+\item[{\tt void dd\_inv(x, y)}]:\\
+Set {\tt x} to be the reciplocal of  {\tt y}.
+
+\end{description}
+
+
+\subsubsection{Predefined  Constants} \label{constants}
+
+There are several {\tt mytype} constants defined when {\tt dd\_set\_global\_constants(void)} is called.
+Some constants depend on the double constant {\tt dd\_almostzero} which is normally set to $10^{-7}$ in cdd.h. 
+This value can be modified depending on how numerically delicate your problems are but an extra
+caution should be taken.
+
+\begin{description}
+
+\item[{\tt mytype dd\_purezero}]:\\
+This represents the mathematical zero $0$.
+
+\item[{\tt mytype dd\_zero}]:\\
+This represents the largest positive number which should be considered to be zero.  In the GMPRATIONAL
+mode, it is equal to {\tt dd\_purezero}.   In the C double mode, it is set to the value of {\tt dd\_almostzero}.
+
+\item[{\tt mytype dd\_minuszero}]:\\
+The negative of {\tt dd\_zero}.
+
+\item[{\tt mytype dd\_one}]:\\
+This represents the mathematical one $1$.
+
+
+\end{description}
+
+\subsubsection{Sign Evaluation and Comparison for {\tt mytype} Numbers}
+
+Below {\tt x}, {\tt y}, {\tt z} are of type {\tt mytype}.  
+
+\begin{description}
+
+\item[{\tt dd\_boolean dd\_Positive(x)}]:\\
+Returns {\tt dd\_TRUE} if {\tt x} is considered positive,  and  {\tt dd\_FALSE} otherwise.
+In the GMPRATIONAL mode, the positivity recognition is exact.  In the C double mode,
+this means the value is strictly larger than  {\tt dd\_zero}.
+
+{\tt dd\_boolean dd\_Negative(x)} works similarly.
+
+\item[{\tt dd\_boolean dd\_Nonpositive(x)}]:\\
+Returns the negation of {\tt dd\_Positive(x)}.   {\tt dd\_Nonnegative(x)} works similarly.
+
+\item[{\tt dd\_boolean dd\_EqualToZero(x)}]:\\
+Returns {\tt dd\_TRUE} if {\tt x} is considered zero,  and  {\tt dd\_FALSE} otherwise.
+In the GMPRATIONAL mode, the zero recognition is exact.  In the C double mode,
+this means the value is inbetween {\tt dd\_minuszero} and  {\tt dd\_zero}
+inclusive.
+
+\item[{\tt dd\_boolean dd\_Larger(x, y)}]:\\
+Returns {\tt dd\_TRUE} if {\tt x} is strictly larger than {\tt y},  and  {\tt dd\_FALSE} otherwise.
+This is implemented as {dd\_Positive(z)} where {\tt z} is the subtraction of {\tt y}
+from {\tt x}.
+{\tt dd\_Smaller(x, y)} works similarly.
+
+\item[{\tt dd\_boolean dd\_Equal(x, y)}]:\\
+Returns {\tt dd\_TRUE} if {\tt x} is considered equal to  {\tt y},  and  {\tt dd\_FALSE} otherwise.
+This is implemented as {dd\_EqualToZero(z)} where {\tt z} is the subtraction of {\tt y}
+from {\tt x}.
+\end{description}
+
+
+
+\subsubsection{Polyhedra Data Manipulation}
+\begin{description}
+
+\item[{\tt dd\_MatrixPtr dd\_PolyFile2Matrix (f, err)}]:\\
+Read a Polyhedra data from stream {\tt f} and store it in {\tt matrixdata}
+and return a pointer to the data.
+
+\item[{\tt dd\_MatrixPtr dd\_CopyInequalities(poly)}]:\\
+Copy the inequality representation pointed by poly to {\tt matrixdata}
+and return {\tt dd\_MatrixPtr}.
+
+\item[{\tt dd\_MatrixPtr dd\_CopyGenerators(poly)}]:\\ 
+Copy the generator representation pointed by poly to {\tt matrixdata}
+and return {\tt dd\_MatrixPtr}.
+
+\item[{\tt dd\_SetFamilyPtr dd\_CopyIncidence(poly)}]:\\ 
+Copy the incidence representation of the computed representation
+pointed by poly to {\tt setfamily}
+and return {\tt dd\_SetFamilyPtr}.  The computed representation is
+{\tt Inequality} if the input is {\tt Generator}, and the vice visa.
+
+\item[{\tt dd\_SetFamilyPtr dd\_CopyAdjacency(poly)}]:\\ 
+Copy the adjacency representation of the computed representation
+pointed by poly to {\tt setfamily}
+and return {\tt dd\_SetFamilyPtr}.  The computed representation is
+{\tt Inequality} if the input is {\tt Generator}, and the vice visa.
+
+\item[{\tt dd\_SetFamilyPtr dd\_CopyInputIncidence(poly)}]:\\ 
+Copy the incidence representation of the input representation
+pointed by poly to {\tt setfamily}
+and return {\tt d\_SetFamilyPtr}.
+
+\item[{\tt dd\_SetFamilyPtr dd\_CopyInputAdjacency(poly)}]:\\ 
+Copy the adjacency representation of the input representation
+pointed by poly to {\tt setfamily}
+and return {\tt d\_SetFamilyPtr}.
+
+\item[{\tt void dd\_FreePolyhedra(poly)}]:\\
+Free memory allocated to {\tt poly}.
+
+\end{description}
+
+\subsubsection{LP Data Manipulation}
+\begin{description}
+
+\item[{\tt dd\_LPPtr dd\_MakeLPforInteriorFinding(lp)}]:\\
+Set up an LP to find an interior point of the feasible region of {\tt lp}
+and return a pointer to the LP.  The new LP has one new variable
+$x_{d+1}$ and one more constraint:
+$\max x_{d+1}$ subject to $b - A x - x_{d+1} \ge 0$ and $x_{d+1} \le K$,
+where $K$ is a positive constant.
+
+\item[{\tt dd\_LPPtr dd\_Matrix2LP(matrix, err)}]:\\
+Load {\tt matrix} to {\tt lpdata} and return a pointer to the data.
+
+\item[{\tt dd\_LPSolutionPtr dd\_CopyLPSolution(lp)}]:\\
+Load the solutions of {\tt lp} to {\tt lpsolution} and
+return a pointer to the data.  This replaces the old name
+{\tt dd\_LPSolutionLoad(lp)}.
+
+\item[{\tt void dd\_FreeLPData(lp)}]:\\
+Free memory allocated as an LP data pointed by {\tt lp}.
+
+\item[{\tt void dd\_FreeLPSolution(lps)}]:\\
+Free memory allocated as an LP solution data pointed by {\tt lps}.
+
+\end{description}
+
+\subsubsection{Matrix Manipulation}
+\begin{description}
+
+\item[{\tt dd\_MatrixPtr dd\_CopyMatrix(matrix)}]:\\
+Make a copy of matrixdata pointed by {\tt matrix} and return
+a pointer to the copy.
+
+\item[{\tt dd\_MatrixPtr dd\_AppendMatrix(matrix1, matrix2)}]:\\
+Make a matrixdata by copying {\tt *matrix1} and appending
+the matrix in {\tt *matrix2} and return
+a pointer to the data.  The colsize must be equal in
+the two input matrices.  It returns a {\tt NULL} pointer
+if the input matrices are not appropriate.
+Its {\tt rowsize} is set to
+the sum of the rowsizes of {\tt matrix1} and {\tt matrix2}.
+ The new matrixdata inherits everything else
+(i.e. numbertype, representation, etc)
+from the first matrix. 
+
+\item[{\tt int dd\_MatrixAppendTo(\& matrix1, matrix2)}]:\\
+Same as {\tt dd\_AppendMatrix} except that the first matrix
+is modified to take the result.
+
+\item[{\tt int dd\_MatrixRowRemove(\& matrix, i)}]:\\
+Remove the $i$th row of {\tt matrix}.
+
+\item[{\tt dd\_MatrixPtr dd\_MatrixSubmatrix(matrix, set)}]:\\
+Generate the submatrix of {\tt matrix} by removing the
+rows indexed by {\tt set} and return a matrixdata pointer.
+
+\item[{\tt  dd\_SetFamilyPtr dd\_Matrix2Adjacency(matrix, err)}]:\\
+Return the adjacency list of the representation given by {\tt matrix}.
+The computation is done by the built-in LP solver.  The representation
+should be free of redundancy when this function is called. 
+See the function  {\tt dd\_rowset dd\_RedundantRows}
+and the example program adjacency.c.
+
+\end{description}
+
+\subsection{Input/Output Functions}  \label{IOLibrary}
+
+\begin{description}
+
+\item[{\tt dd\_MatrixPtr dd\_PolyFile2Matrix (f, err)}]:\\
+Read a Polyhedra data from stream {\tt f} and store it in {\tt matrixdata}
+and return a pointer to the data.
+
+\item[{\tt boolean dd\_DDFile2File(ifile, ofile, err)}]:\\
+Compute the representation conversion for a polyhedron given
+by a Polyhedra file ifile, and write the other representation
+in a Polyhedra file ofile.  {\tt *err}
+returns {\tt dd\_NoError} if the computation terminates normally.  Otherwise,
+it returns a value according to the error occured.
+
+\item[{\tt void dd\_WriteMatrix(f, matrix)}]:\\
+Write {\tt  matrix} to stream {\tt f}.
+
+\item[{\tt void dd\_WriteNumber(f, x)}]:\\
+Write {\tt x} to stream {\tt f}.  If {\tt x} is of GMP mpq\_t rational $p/q$,
+the output is $p/q$.  If it is of C double, it is formated as a double float
+with a decimal point.
+
+\item[{\tt void dd\_WritePolyFile(f, poly)}]:\\
+Write {tt poly} to stream {\tt f} in Polyhedra format.
+
+\item[{\tt void dd\_WriteErrorMessages(f, err)}]:\\
+Write error messages given by {\tt err} to stream {\tt f}.
+
+\item[{\tt void dd\_WriteSetFamily(f, setfam)}]:\\
+Write the set family pointed by {\tt setfam} to stream {\tt f}.
+For each set, it outputs its index, its cardinality,
+a colon ``:'' and a ordered list of its elements.
+
+\item[{\tt void dd\_WriteSetFamilyCompressed(f, setfam)}]:\\
+Write the set family pointed by {\tt setfam} to stream {\tt f}.
+For each set, it outputs its index, its cardinality or the
+negative of the cardinality, a colon ``:''
+ and the elements in the set or its complements whichever is smaller.
+Whenever it outputs the complements, the cardinality is negated
+so that there is no ambiguity.
+This will be considered standard for
+outputing incidence (*.icd, *ecd) and adjacency 
+(*.iad, *.ead) data in cddlib.   But there is some minor incompatibility
+with cdd/cdd+ standalone codes.
+
+\item[{\tt void dd\_WriteProgramDescription(f)}]:\\
+Write the cddlib version information to stream {\tt f}.
+
+\item[{\tt void dd\_WriteDDTimes(f, poly)}]:\\
+Write the representation conversion time information on {\tt poly}
+ to stream {\tt f}.
+
+\end{description}
+
+\subsection{Obsolete Functions}  \label{ObsoleteFunctions}
+\begin{description}
+\item[{\tt boolean dd\_DoubleDescription(poly, err)}]: 
+(removed in Version 0.90c)\\
+The new function
+{\tt dd\_DDMatrix2Poly(matrix, err)} (see Section~\ref{CoreLibrary}) 
+replaces (and actually combines) both this and 
+{\tt dd\_Matrix2Poly(matrix, err)}.
+
+\item[{\tt dd\_PolyhedraPtr dd\_Matrix2Poly(matrix, err)}]: 
+(removed in Version 0.90c)\\
+See above for the reason for removal.
+
+\item[{\tt dd\_LPSolutionPtr dd\_LPSolutionLoad(lp)}]:
+(renamed in Version 0.90c)\\
+This function is now called {\tt dd\_CopyLPSolution(lp)}.
+
+\end{description}
+
+
+\subsection{Set Functions in {\tt setoper} library}  \label{SetFunctions}
+
+The cddlib comes with a simple set operation library {\tt setoper}.  The key
+type defined is {\tt set\_type}.   A set is represented by a fixed length
+binary strings.  Thus, the maximum length of a set must be declared when
+it is initialized.
+
+Below the symbols {\tt a},   {\tt b},  {\tt c} are
+of type  {\tt set\_type}.   The symbols {\tt aP} is a
+pointer to type  {\tt set\_type}, and {\tt s}, {\tt t} are of type {\tt long}.
+Here are some of the functions defined.  See {\tt setoper.h} for a
+complete listing.
+
+\begin{description}
+
+\item[{\tt void set\_initialize(aP, s)}]:\\
+Allocate a {\tt set\_type} space of maximum cardinality {\tt s}
+ and make it pointed by {\tt aP}.  The set is initialized as empty set.
+
+\item[{\tt void set\_free(a)}]:\\
+Free the  {\tt set\_type} space allocated for {\tt a}.
+
+\item[{\tt void set\_copy(a, b))}]:\\
+Set {\tt a} to be {\tt b}.   The set {\tt a} must be pre-initialized
+with the same maximum cardinality as that of {\tt b}.  
+
+\item[{\tt void set\_addelem(a, t))}]:\\
+Add an element  {\tt t} to a set {\tt a}.    The set  {\tt a} stays unchanged
+if it contains the element {\tt t}.
+
+\item[{\tt long set\_card(a))}]:\\
+Return the cardinality of set {\tt a}. 
+
+\item[{\tt int set\_member(t, a))}]:\\
+Return $1$ if  {\tt t} is a member of set {\tt a}, and $0$ otherwise.
+
+
+\item[{\tt void set\_write(a))}]:\\
+Print out the elements of set {\tt a} to {\tt stdout}.  The function {\tt void set\_fwrite(f, a))} output
+to stream {\tt f}.
+
+\end{description}
+
+\section{An Extension of the CDD Library in GMP mode}  \label{GMPLIB}
+
+Starting from the version 093, the GMP version of cddlib, {\tt libcddgmp.a}, contains
+all cdd library functions in two arithmetics.   All functions with the standard prefix {\tt dd\_}
+are computed with the GMP rational arithmetic as before.  The same fuctions with
+the new prefix {\tt ddf\_} are now added to the library  {\tt libcddgmp.a} that are based
+on the C  double floating-point arithmetic.  Thus these functions are equivalent to
+ {\tt libcdd.a} functions, except that all functions and  variable types are with prefix  {\tt ddf\_} and
+the variable type {\tt mytype} is replaced by {\tt myfloat}.
+
+In this sense,  {\tt libcdd.a} is a proper subset of  {\tt libcddgmp.a} and in principle one can
+do everything with  {\tt libcddgmp.a}.   See how the new {\tt dd\_LPSolve} is written in
+cddlp.c.
+
+
+\section{Examples}  \label{EXAMPLES}
+
+See example codes such as testcdd*.c , testlp*.c, redcheck.c, adjacency.c, allfaces,c
+and simplecdd.c 
+in the {\tt src} and {\tt src-gmp} subdirectories of the source
+distribution.
+
+\section{Numerical Accuracy}  \label{accuracy}
+ A little caution is in order.  Many people have observed 
+numerical problems of cddlib when the floating version of cddlib
+is used.   As we all know, floating-point computation
+might not give a correct answer, especially when an input
+data is very sensitive to a small perturbation.  When
+some strange behavior is observed, it is always wise
+to create a rationalization of the input
+(for example, one can replace 0.3333333 with 1/3)
+and to compute it with cddlib compiled with gmp rational
+to see what a correct behavior should be.  Whenever the time
+is not important, it is safer to use gmp rational arithmetic.
+
+If you need speedy computation with floating-point arithmetic,
+you might want to ``play with'' the constant {\tt dd\_almostzero} 
+defined in cdd.h:
+
+\begin{verbatim}
+   #define dd_almostzero  1.0E-7
+\end{verbatim}
+\noindent
+This number is used to recognize whether a number is zero:  
+a number whose absolute value is smaller
+than {\tt dd\_almostzero} is considered zero, and nonzero otherwise.
+You can change this to modify the behavior of cddlib.  One might
+consider the default setting is rather large for double
+precision arithmetic.  This is because cddlib is made
+to deal with highly degenerate data and it works better
+to treat a relatively large ``epsilon'' as zero.
+
+Another thing one can do is scaling.  If the values in one column of
+an input is of smaller magnitude than those in another column, 
+scale one so that they become comparable.
+
+\section{Other Useful Codes}  \label{CODES}
+There are several other useful codes available for vertex enumeration and/or
+convex hull computation  such as lrs, qhull, porta and irisa-polylib.
+The pointers to these codes are available at
+\begin{enumerate}
+\item lrs by D. Avis \cite{a-lrshome-01} (C implementation of the reverse search algorithm 
+\cite{af-pachv-92}). 
+
+\item qhull by C.B. Barber \cite{bdh-qach-03} (C implementation of
+the beneath-beyond method, see \cite{e-acg-87,m-cg-94},
+which is the dual of the dd method). 
+
+\item porta by T. Christof and A. L{\"o}bel \cite{cl-porta-97} (C implementation
+of the Fourier-Motzkin elimination).
+
+\item IRISA polyhedral library by D.K. Wilde
+\cite{w-ldpo-93b} (C implementation
+of a variation of the dd algorithm).
+
+\item PPL: the Parma Polyhedra Library \cite{b-pplhome} by R. Bagnara (C++ implementation of
+a variation of the dd algorithm).
+
+\item {\tt pd} by A. Marzetta \cite{m-pdcip-97} (C implementation of the primal-dual algorithm 
+\cite{bfm-pdmvf-97}). 
+
+ \item Geometry Center Software List by N. Amenta \cite{a-dcg}.
+
+ \item Computational Geometry Pages by J. Erickson \cite{e-cgp}.
+
+ \item Linear Programming FAQ by R. Fourer and J. Gregory \cite{fg-lpfaq}.
+
+ \item ZIB Berlin polyhedral software list:\\
+ \htmladdnormallink{ftp://elib.zib-berlin.de/pub/mathprog/polyth/index.html}
+{ftp://elib.zib-berlin.de/pub/mathprog/polyth/index.html}.
+
+
+\item Polyhedral Computation FAQ \cite{f-pcfaq-98}.
+\end{enumerate}
+
+\section{Codes Using Cddlib}  \label{USERCODES}
+
+There are quite a few nice programs using some functions of cddlib.  
+Here are some of them.
+
+
+\begin{enumerate}
+
+\item {\tt LattE} \cite{dhhhty-latte-05} computes the number of lattice points
+in a convex polytope.
+
+\item {\tt Minksum} \cite{w-msv-05} is a program to compute the V-representation
+(i.e. the set of vertices) of the Minkowski addition of several convex polytopes
+given by their V-representation in $\R^d$.  It is an implementation in C++ language 
+of the reverse search algorithm \cite{f-fzctmacp-04} whose time complexity is
+polynomially bounded by the sizes of input and output.
+
+\item {\tt Gfan} \cite{j-gvum-05} is a program to list all reduced Gr\"obner
+bases of a general polynomial ideal given by a set of generating polynomials
+in $n$-variables.   It is an implementation in C++ language 
+of the reverse search algorithm \cite{fjt-cgf-05}.
+
+
+\item {\tt TOPCOM} \cite{r-topcom-05} computes the combinatorial structure
+(the oriented matroid) of a point configuration and enumerates all triangulations
+of a point set.   It detects the regularlity of a triangulation using cddlib.
+
+\end{enumerate}
+
+
+\section*{Acknowledgements.} 
+I am  grateful to Tom  Liebling who
+provided me with an ideal opportunity to visit EPFL
+for the academic year 1993-1994.  Later, Hans-Jakob L\"uthi (ETHZ) and 
+Emo Welzl  (ETHZ) joined to support the 
+the development of cdd codes (cdd, cdd+, cddlib).
+Without their generous and continuing support, the present form of 
+this program would not have existed.
+
+There are many other people who helped me to improve cdd, in particular,
+I am indebted to  David Avis, 
+Alexander Bockmayr, David Bremner, Henry Crapo, Istvan Csabai, 
+Francois Margot, Marc Pfetsch, Alain Prodon, J\"org Rambau, Dima Pasechnik,
+Shawn Rusaw, Matthew Saltzman, Masanori Sato, Anders Jensen,
+Ruriko Yoshida, Charles Geyer, Michal Kvasnica, Sven Verdoolaege
+ (listed in arbitrary order) and those listed
+in the HISTORY file.
+
+\bibliographystyle{plain}
+
+\bibliography{fukuda1,fukuda2}
+
+\end{document}
+
+

third_party/cddlib/doc/cddlibman.toc

diff --git a/third_party/cddlib/doc/cddlibman.toc b/third_party/cddlib/doc/cddlibman.toc
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@@ -0,0 +1,22 @@
+\contentsline {section}{\numberline {1}Introduction}{2}
+\contentsline {section}{\numberline {2}Polyhedra H- and V-Formats (Version 1999)}{3}
+\contentsline {section}{\numberline {3}Basic Object Types (Structures) in cddlib}{4}
+\contentsline {section}{\numberline {4}Library Functions}{7}
+\contentsline {subsection}{\numberline {4.1}Library Initialization}{7}
+\contentsline {subsection}{\numberline {4.2}Core Functions}{7}
+\contentsline {subsection}{\numberline {4.3}Data Manipulations}{11}
+\contentsline {subsubsection}{\numberline {4.3.1}Number Assignments}{11}
+\contentsline {subsubsection}{\numberline {4.3.2}Arithmetic Operations for {\tt mytype} Numbers}{11}
+\contentsline {subsubsection}{\numberline {4.3.3}Predefined Constants}{12}
+\contentsline {subsubsection}{\numberline {4.3.4}Sign Evaluation and Comparison for {\tt mytype} Numbers}{12}
+\contentsline {subsubsection}{\numberline {4.3.5}Polyhedra Data Manipulation}{12}
+\contentsline {subsubsection}{\numberline {4.3.6}LP Data Manipulation}{13}
+\contentsline {subsubsection}{\numberline {4.3.7}Matrix Manipulation}{13}
+\contentsline {subsection}{\numberline {4.4}Input/Output Functions}{14}
+\contentsline {subsection}{\numberline {4.5}Obsolete Functions}{15}
+\contentsline {subsection}{\numberline {4.6}Set Functions in {\tt setoper} library}{15}
+\contentsline {section}{\numberline {5}An Extension of the CDD Library in GMP mode}{16}
+\contentsline {section}{\numberline {6}Examples}{16}
+\contentsline {section}{\numberline {7}Numerical Accuracy}{16}
+\contentsline {section}{\numberline {8}Other Useful Codes}{16}
+\contentsline {section}{\numberline {9}Codes Using Cddlib}{17}

third_party/cddlib/doc/html.sty

diff --git a/third_party/cddlib/doc/html.sty b/third_party/cddlib/doc/html.sty
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+% LaTeX2HTML Version 95.1 : html.sty
+%
+%  WARNING:  This file requires LaTeX2e.  A LaTeX 2.09 version
+%	is also provided, but with restricted functionality.
+%
+% This file contains definitions of LaTeX commands which are
+% processed in a special way by the translator. 
+% For example, there are commands for embedding external hypertext links,
+% for cross-references between documents or for including
+% raw HTML.
+% This file includes the comments.sty file v2.0 by Victor Eijkhout
+% In most cases these commands do nothing when processed by LaTeX.
+
+% Modifications:
+%
+%  nd = Nikos Drakos <nikos@cbl.leeds.ac.uk>
+%  jz = Jelle van Zeijl <jvzeijl@isou17.estec.esa.nl>
+%  hs = Herb Swan <dprhws@edp.Arco.com>
+
+% hs 31-JAN-96 - Added support for document segmentation
+% hs 10-OCT-95 - Added \htmlrule command
+% jz 22-APR-94 - Added support for htmlref
+% nd  - Created
+%%%%MG added
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{html}
+          [1996/02/01 v1.0 hypertext commands for latex2html (nd, hs)]
+%%%%MG
+% Exit if the style file is already loaded
+% (suggested by Lee Shombert <las@potomac.wash.inmet.com>
+\ifx \htmlstyloaded\relax \endinput\else\let\htmlstyloaded\relax\fi
+
+%%% LINKS TO EXTERNAL DOCUMENTS
+%
+% This can be used to provide links to arbitrary documents.
+% The first argumment should be the text that is going to be
+% highlighted and the second argument a URL.
+% The hyperlink will appear as a hyperlink in the HTML 
+% document and as a footnote in the dvi or ps files.
+%
+\newcommand{\htmladdnormallinkfoot}[2]{#1\footnote{#2}} 
+
+% This is an alternative definition of the command above which
+% will ignore the URL in the dvi or ps files.
+\newcommand{\htmladdnormallink}[2]{#1}
+
+% This command takes as argument a URL pointing to an image.
+% The image will be embedded in the HTML document but will
+% be ignored in the dvi and ps files.
+%
+\newcommand{\htmladdimg}[1]{}
+
+%%% CROSS-REFERENCES BETWEEN (LOCAL OR REMOTE) DOCUMENTS
+%
+% This can be used to refer to symbolic labels in other Latex 
+% documents that have already been processed by the translator.
+% The arguments should be:
+% #1 : the URL to the directory containing the external document
+% #2 : the path to the labels.pl file of the external document.
+% If the external document lives on a remote machine then labels.pl 
+% must be copied on the local machine.
+%
+%e.g. \externallabels{http://cbl.leeds.ac.uk/nikos/WWW/doc/tex2html/latex2html}
+%                    {/usr/cblelca/nikos/tmp/labels.pl}
+% The arguments are ignored in the dvi and ps files.
+%
+\newcommand{\externallabels}[2]{}
+
+%
+% This complements the \externallabels command above. The argument
+% should be a label defined in another latex document and will be
+% ignored in the dvi and ps files.
+%
+\newcommand{\externalref}[1]{}
+
+% This command adds a horizontal rule and is valid even within
+% a figure caption.
+%
+\newcommand{\htmlrule}{}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% The following commands pertain to document segmentation, and
+% were added by Herbert Swan <dprhws@edp.Arco.com> (with help from
+% Michel Goossens <goossens@cern.ch>):
+%
+%
+% This command inputs internal latex2html tables so that large
+% documents can to partitioned into smaller (more manageable)
+% segments.
+%
+\newcommand{\internal}[2][internals]{}
+
+%
+%  Define a dummy stub \htmlhead{}.  This command causes latex2html
+%  to define the title of the start of a new segment.  It is not
+%  normally placed in the user's document.  Rather, it is passed to
+%  latex2html via a .ptr file written by \segment.
+%
+\newcommand{\htmlhead}[2]{}
+
+%
+%  The dummy command \endpreamble is needed by latex2html to
+%  mark the end of the preamble in document segments that do
+%  not contain a \begin{document}
+%
+\newcommand{\startdocument}{}
+
+%
+%  Allocate a new set of section counters, which will get incremented
+%  for "*" forms of sectioning commands, and for a few miscellaneous
+%  commands.
+%
+
+\newcounter{lpart}
+\newcounter{lchapter}[part]
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+\newcounter{lsubsubsection}[subsection]
+\newcounter{lparagraph}[subsubsection]
+\newcounter{lsubparagraph}[paragraph]
+\newcounter{lsubsubparagraph}[subparagraph]
+\newcounter{lequation}
+%
+%  Redefine "*" forms of sectioning commands to increment their
+%  respective counters.
+%
+\let\Hpart=\part
+\let\Hchapter=\chapter
+\let\Hsection=\section
+\let\Hsubsection=\subsection
+\let\Hsubsubsection=\subsubsection
+\let\Hparagraph=\paragraph
+\let\Hsubparagraph=\subparagraph
+\let\Hsubsubparagraph=\subsubparagraph
+
+%
+%  The following definitions are specific to LaTeX2e:
+%  (They must be commented out for LaTeX 2.09)
+%
+\def\part{\@ifstar{\stepcounter{lpart}\Hpart*}{\Hpart}}
+\def\chapter{\@ifstar{\stepcounter{lchapter}\Hchapter*}{\Hchapter}}
+\def\section{\@ifstar{\stepcounter{lsection}\Hsection*}{\Hsection}}
+\def\subsection{\@ifstar{\stepcounter{lsubsection}\Hsubsection*}{\Hsubsection}}
+\def\subsubsection{\@ifstar{\stepcounter{lsubsubsection}\Hsubsubsection*}{\Hsubsubsection}}
+\def\paragraph{\@ifstar{\stepcounter{lparagraph}\Hparagraph*}{\Hparagraph}}
+\def\subparagraph{\@ifstar{\stepcounter{lsubparagraph}\Hsubparagraph*}{\Hsubparagraph}}
+\def\subsubparagraph{\@ifstar{\stepcounter{lsubsubparagraph}\Hsubsubparagraph*}{\Hsubsubparagraph}}
+%
+%  Define a helper macro to dump a single \secounter command to a file.
+%
+\newcommand{\DumpPtr}[2]{%
+\count255=\arabic{#1} \advance\count255 by \arabic{#2}
+\immediate\write\ptrfile{%
+\noexpand\setcounter{#1}{\number\count255}}}
+
+%
+%  Define a helper macro to dump all counters to the file.
+%  The value for each counter will be the sum of the l-counter
+%      actual LaTeX section counter.
+%  Also dump an \htmlhead{section-command}{section title} command
+%      to the file.
+%
+
+\def\DumpCounters#1#2#3{\newwrite\ptrfile
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+\DumpPtr{part}{lpart}
+\ifx\Hchapter\undefined\relax\else\DumpPtr{chapter}{lchapter}\fi
+\DumpPtr{section}{lsection}
+\DumpPtr{subsection}{lsubsection}
+\DumpPtr{subsubsection}{lsubsubsection}
+\DumpPtr{paragraph}{lparagraph}
+\DumpPtr{subparagraph}{lsubparagraph}
+\DumpPtr{equation}{lequation}
+\immediate\write\ptrfile{\noexpand\htmlhead{#2}{#3}}
+\immediate\closeout\ptrfile}
+
+%
+%  Define the \segment{file}{section-command}{section-title} command,
+%  and its helper macros.  This command does four things:
+%	1)  Begins a new LaTeX section;
+%	2)  Writes a list of section counters to file.ptr, each
+%	    of which represents the sum of the LaTeX section
+%	    counters, and the l-counters, defined above;
+%	3)  Write an \htmlhead{section-title} command to file.ptr;
+%	4)  Inputs file.tex.
+%
+
+%%%%MG changed
+\def\segment{\@ifstar{\@@htmls}{\@@html}}
+\def\@@htmls#1#2#3{\csname #2\endcsname* {#3}%
+                   \DumpCounters{#1}{#2*}{#3}\input{#1}}
+\def\@@html#1#2#3{\csname #2\endcsname {#3}%
+                   \DumpCounters{#1}{#2}{#3}\input{#1}}
+%%%%MG 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Comment.sty   version 2.0, 19 June 1992
+% selectively in/exclude pieces of text: the user can define new
+% comment versions, and each is controlled separately.
+% This style can be used with plain TeX or LaTeX, and probably
+% most other packages too.
+%
+% Examples of use in LaTeX and TeX follow \endinput
+%
+% Author
+%    Victor Eijkhout
+%    Department of Computer Science
+%    University Tennessee at Knoxville
+%    104 Ayres Hall
+%    Knoxville, TN 37996
+%    USA
+%
+%    eijkhout@cs.utk.edu
+%
+% Usage: all text included in between
+%    \comment ... \endcomment
+% or \begin{comment} ... \end{comment}
+% is discarded. The closing command should appear on a line
+% of its own. No starting spaces, nothing after it.
+% This environment should work with arbitrary amounts
+% of comment.
+%
+% Other 'comment' environments are defined by
+% and are selected/deselected with
+% \includecomment{versiona}
+% \excludecoment{versionb}
+%
+% These environments are used as
+% \versiona ... \endversiona
+% or \begin{versiona} ... \end{versiona}
+% with the closing command again on a line of its own.
+%
+% Basic approach:
+% to comment something out, scoop up  every line in verbatim mode
+% as macro argument, then throw it away.
+% For inclusions, both the opening and closing comands
+% are defined as noop
+%
+% Changed \next to \html@next to prevent clashes with other sty files
+% (mike@emn.fr)
+% Changed \html@next to \htmlnext so the \makeatletter and
+% \makeatother commands could be removed (they were causing other
+% style files - changebar.sty - to crash) (nikos@cbl.leeds.ac.uk)
+% Changed \htmlnext back to \html@next...
+
+\makeatletter
+\def\makeinnocent#1{\catcode`#1=12 }
+\def\csarg#1#2{\expandafter#1\csname#2\endcsname}
+
+\def\ThrowAwayComment#1{\begingroup
+    \def\CurrentComment{#1}%
+    \let\do\makeinnocent \dospecials
+    \makeinnocent\^^L% and whatever other special cases
+    \endlinechar`\^^M \catcode`\^^M=12 \xComment}
+{\catcode`\^^M=12 \endlinechar=-1 %
+ \gdef\xComment#1^^M{\def\test{#1}
+      \csarg\ifx{PlainEnd\CurrentComment Test}\test
+          \let\html@next\endgroup
+      \else \csarg\ifx{LaLaEnd\CurrentComment Test}\test
+            \edef\html@next{\endgroup\noexpand\end{\CurrentComment}}
+      \else \let\html@next\xComment
+      \fi \fi \html@next}
+}
+\makeatother
+
+\def\includecomment
+ #1{\expandafter\def\csname#1\endcsname{}%
+    \expandafter\def\csname end#1\endcsname{}}
+\def\excludecomment
+ #1{\expandafter\def\csname#1\endcsname{\ThrowAwayComment{#1}}%
+    {\escapechar=-1\relax
+     \csarg\xdef{PlainEnd#1Test}{\string\\end#1}%
+     \csarg\xdef{LaLaEnd#1Test}{\string\\end\string\{#1\string\}}%
+    }}
+
+\excludecomment{comment}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% RAW HTML 
+% 
+% Enclose raw HTML between a \begin{rawhtml} and \end{rawhtml}.
+% The html environment ignores its body
+%
+\excludecomment{rawhtml}
+
+%%% HTML ONLY
+%
+% Enclose LaTeX constructs which will only appear in the 
+% HTML output and will be ignored by LaTeX with 
+% \begin{htmlonly} and \end{htmlonly}
+%
+\excludecomment{htmlonly}
+% Shorter version
+\newcommand{\html}[1]{}
+
+
+%%% LaTeX ONLY
+% Enclose LaTeX constructs which will only appear in the 
+% DVI output and will be ignored by latex2html with 
+%\begin{latexonly} and \end{latexonly}
+%
+\newenvironment{latexonly}{}{}
+% Shorter version
+\newcommand{\latex}[1]{#1}
+
+%%% HYPERREF 
+% Suggested by Eric M. Carol <eric@ca.utoronto.utcc.enfm>
+% Similar to \ref but accepts conditional text. 
+% The first argument is HTML text which will become ``hyperized''
+% (underlined).
+% The second and third arguments are text which will appear only in the paper
+% version (DVI file), enclosing the fourth argument which is a reference to a label.
+%
+%e.g. \hyperref{using the tracer}{using the tracer (see Section}{)}{trace}
+% where there is a corresponding \label{trace}
+%
+\newcommand{\hyperref}[4]{#2\ref{#4}#3}
+
+%%% HTMLREF
+% Reference in HTML version only.
+% Mix between \htmladdnormallink and \hyperref.
+% First arg is text for in both versions, second is label for use in HTML
+% version.
+\newcommand{\htmlref}[2]{#1}
+
+%%% HTMLIMAGE
+% This command can be used inside any environment that is converted
+% into an inlined image (eg a "figure" environment) in order to change
+% the way the image will be translated. The argument of \htmlimage
+% is really a string of options separated by commas ie 
+% [scale=<scale factor>],[external],[thumbnail=<reduction factor>
+% The scale option allows control over the size of the final image.
+% The ``external'' option will cause the image not to be inlined 
+% (images are inlined by default). External images will be accessible
+% via a hypertext link. 
+% The ``thumbnail'' option will cause a small inlined image to be 
+% placed in the caption. The size of the thumbnail depends on the
+% reduction factor. The use of the ``thumbnail'' option implies
+% the ``external'' option.
+%
+% Example:
+% \htmlimage{scale=1.5,external,thumbnail=0.2}
+% will cause a small thumbnail image 1/5th of the original size to be
+% placed in the final document, pointing to an external image 1.5
+% times bigger than the original.
+% 
+\newcommand{\htmlimage}[1]{}
+
+%%% HTMLADDTONAVIGATION
+% This command appends its argument to the buttons in the navigation
+% panel. It is ignored by LaTeX.
+%
+% Example:
+% \htmladdtonavigation{\htmladdnormallink
+%              {\htmladdimg{http://server/path/to/gif}}
+%              {http://server/path}}
+\newcommand{\htmladdtonavigation}[1]{}
+
+\endinput
\ No newline at end of file