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tutorial_input.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%>
<font color=red>Input</font>
</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%>
<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=50%>
Matrix
</th>
<th align=left width=20%>
fileName<p>
</th>
<th align=left width=30%>
2 4<br>
1 1 1 1<br>
1 2 3 4<br>
</th>
</tr>
<tr>
<th align=left width=50%>
Lattice generators
</th>
<th align=left width=20%>
fileName.lat<p>
</th>
<th align=left width=30%>
3 4<br>
-2 1 0 0<br>
-3 0 1 0<br>
-4 0 0 1<br>
</th>
</tr>
<tr>
<th align=left width=50%>
Cost vector<p>
Upper bounds vector<p>
Feasible solution
</th>
<th align=left width=20%>
fileName.cost<p>
fileName.tru<p>
fileName.feas
</th>
<th align=left width=30%>
1 5<br>
3 4 11 22 17<br>
</th>
</tr>
<tr>
<th align=left width=50%>
Generators of symmetry group (permutations of columns)
</th>
<th align=left width=20%>
fileName.sym
</th>
<th align=left width=30%>
4 9<br>
2 3 1 5 6 4 8 9 7<br>
2 1 3 5 4 6 8 7 9<br>
4 5 6 7 8 9 1 2 3<br>
4 5 6 1 2 3 7 8 9<br>
</th>
</tr>
<tr>
<th align=left width=70%>
Simplicial complex for hierachical model given by<br>
- number of nodes and number of levels attached to them, and<br>
- number of faces, and<br>
- list of faces, where each face is given by number of nodes and the list of nodes.<p>
Example here: binary model on bipartite graph K_{2,3}.
</th>
<th align=left width=0%>
</th>
<th align=left width=30%>
5<br>
2 2 2 2 2<br>
6<br>
2 1 3<br>
2 1 4<br>
2 1 5<br>
2 2 3<br>
2 2 4<br>
2 2 5<br>
</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>