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tutorial_markov.html
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<HTML>
<HEAD>
<TITLE>4ti2 -- Computation of Hilbert bases, Graver bases, toric Gröbner bases, and more</TITLE>
</HEAD>
<BODY background="back.jpg"
bgcolor = "#EEEEFF"
TEXT=FFCC00
LINK=FFFFF
VLINK=#FFFCC
ALINK=#000066>
<center>
<table border=0 width=90% cellspacing=5 cellpadding=5>
<tr>
<th>
<font size=6 color=red>4ti2 tutorial</font>
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th width=33%>
<a href="tutorial_input.html">Input</a>
</th>
<th width=34%>
<a href="tutorial_auxiliary.html">Auxiliary functions</a>
</th>
<th width=33%>
<a href="tutorial_output.html">Output management</a>
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th width=20%>
<a href="tutorial_hilbert.html">Hilbert bases</a>
</th>
<th width=20%>
<a href="tutorial_graver.html">Graver bases</a>
</th>
<th width=20%>
<a href="tutorial_groebner.html">Gröbner bases</a>
</th>
<th width=20%>
<font color=red>Markov bases</font>
</th>
<th width=20%>
<a href="tutorial_minimize.html">Minimization</a>
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th>
'markov' extracts a minimal generating set from a graded Gröbner basis.<p>
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th align=left width=70%>
Extract Markov basis from Gröbner basis in fileName.gro.<p>
If "fileName.gro" does not exist, the project-and-lift algorithm is used
to compute a generating set of the lattice ideal and to extract a Markov
basis of it.
</th>
<th align=left width=30%>
./markov fileName
</th>
</tr>
</table>
<table border=0 width=90% cellspacing=5 cellpadding=5>
<tr>
<th align=right>
<a href="http://www.4ti2.de">back to www.4ti2.de</a>
</th>
</tr>
</table>
</center>
</BODY>