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tutorial_auxiliary.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%>
<font color=red>Auxiliary functions</font>
</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%>
<a href="tutorial_markov.html">Markov bases</a>
</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 align=left width=70%>
Generate the matrix for a hierachical model. (See <a href="tutorial_input.html">Input</a> on how to specify the model.)
</th>
<th align=left width=30%>
./genModel fileName
</th>
</tr>
<tr>
<th align=left width=70%>
Construct generators for ALL symmetries for 4-way tables and put them into "fileName.sym".<br>
(Hint: Use c=d=1 and d=1 for 2- and 3-way tables.)
</th>
<th align=left width=30%>
./genSymm a b c d fileName
</th>
</tr>
<tr>
<th align=left width=70%>
Extract circuits from Graver basis.<p>
<font color="red">Needs</font> "fileName.gra".
</th>
<th align=left width=30%>
./circuits fileName
</th>
</tr>
<tr>
<th align=left width=70%>
Compute (unweighted) Hilbert-Poincare' series of leading term ideal.<p>
<font color="red">Needs</font> "fileName.gro".<p>
This function is only available for linux at the moment.<br>
It is only a first and rough implementation to provide the
functionality in 4ti2.
</th>
<th align=left width=30%>
./output pos fileName.gro<p>
./poincare fileName.gro.pos
</th>
</tr>
<tr>
<th align=left width=70%>
Remove (most of the) computed files related to fileName.
</th>
<th align=left width=30%>
./cleanup fileName<p>
</th>
</tr>
</table>
</center>
</BODY>