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tutorial_hilbert.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%>
<font color=red>Hilbert bases</font>
</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>
'hilbert' computes (truncated) Hilbert bases of cones of the form lattice
L \cap R^n_+<br>
where L is given<br>
as ker(A) for given matrix A<br>
or<br>
by lattice generators.</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th align=left width=70%>
Hilbert basis from matrix<p>
If present, lattice generators will be read automatically from
"fileName.lat".<p>
If present, upper bound vector will <font color="red">NOT</font> be read automatically from
"fileName.tru".
</th>
<th align=left width=30%>
./hilbert fileName
</th>
</tr>
<tr>
<th align=left width=70%>
Truncated Hilbert basis from matrix<p>
If present, lattice generators will be read automatically from
"fileName.lat".<p>
<font color="red">Needs</font> upper bounds in "fileName.tru".
</th>
<th align=left width=30%>
./hilbert tru fileName
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th>
Note that the option 'inf 0' surpresses most of the output of 'hilbert'.
</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>