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<TITLE>PolyBoRi Master Reference</TITLE>
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<h1>PolyBoRi Master Reference</h1>

<p> The core of <i>PolyBoRi</i> is a C++ library, which provides high-level data types
for Boolean polynomials and monomials, exponent vectors, as well as for the
underlying polynomial rings and subsets of the powerset of the Boolean
variables. As a unique approach, binary decision diagrams are 
used as internal storage type for polynomial structures.</p>	

<p> On top of this C++-library we provide a Python interface. This allows
parsing of complex polynomial systems, as well as sophisticated and extendable
strategies for Gr&ouml;bner base computation. <i>PolyBoRi</i> features a powerful reference
implementation for Gr&ouml;bner basis computation.</p>			

The structure of the framework is illustrated as follows.
<p><img src="images/overview.png" alt="Overview" align="middle" border="0">

<H2>Documentation</H2>
The documentation of the <i>PolyBoRi</i> framework and incorporated works can be
accessed via the following documents.

<P><A href="c++/index.html">PolyBoRi: Main Page</A>
<P><A href="cudd/index.html">CUDD: CU Decision Diagram Package
Release 2.4.1</A>


<h3>External documents</h3>
<p><a href="http://www.diveintopython.org/">
Dive into Python</a></p>
<p><a href="http://ipython.scipy.org/moin/Documentation/">
ipython Documentation</a></p>

<h2>Further Reading</h2>
See the following references for the mathematical background of the <i>PolyBoRi</i>
framework. 
 <ul>

    <li>M. Brickenstein, A. Dreyer,
      <i><i>PolyBoRi</i>: A Gr&ouml;bner Basis Framework for Boolean
	Polynomials</i>,
        <a 
         href="http://www.itwm.fhg.de/zentral/download/berichte/bericht122.pdf">
        Reports of Fraunhofer ITWM, No. 122,
        </a>
        Kaiserslautern, Germany, 2007.
      </li>

       <li>M. Brickenstein, A. Dreyer,
       <i><i>PolyBoRi</i>: A framework for Gr&ouml;bner basis computations with
	Boolean polynomials</i>,
     
        <a href="http://www.ricam.oeaw.ac.at/mega2007/openconf/electronic/electronic.html">   Electronic Proceedings of the MEGA 2007&nbsp;- Effective Methods in
 	Algebraic Geometry,
                      </a>
       Strobl, Austria, June 2007.
       </li>
       <li>M. Brickenstein,
     
        <a href="http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/35/paper_35_full.ps.gz">  
          <i>Slimgb: Gr&ouml;bner Bases with Slim Polynomials</i></a>, 
        Reports On Computer Algebra, Centre for Computer Algebra, University of         
        Kaiserslautern, Volume 25, September 2005
       </li>
       <li>Fabio Somenzi 
     
        <a href="http://vlsi.colorado.edu/~fabio/CUDD/">  
          <i> CUDD: CU Decision Diagram Package Release 2.4.1</i>
        </a>, 
        Department of Electrical and Computer Engineering,
        University of Colorado at Boulder     
       </li>
       <li>
        Gregory V. Bard,
        <a href="http://eprint.iacr.org/2006/251.pdf">  
          <i>Accelerating Cryptanalysis with the Method of Four Russians</i>
        </a>, Preprint July 22, 2006.
       </li>
</ul>

<h2>Links</h2>
<p><a href="http://polybori.sourceforge.net"> <i>PolyBoRi</i>'s home at
SourceForge</a></p>
<p> <a href="http://www.itwm.fhg.de/en/as__asprojects__PolyBoRi/PolyBoRi/"></p>	
<i>PolyBoRi</i>'s project page at Fraunhofer ITWM</a>

<P><img src="images/logo.png" alt="<i>PolyBoRi</i>" align="middle" border="0"></p>	
<P> Copyright &copy; 2007-2008 The <i>PolyBoRi</i> Team</p>	
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