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tutorial_groebner.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%>
<font color=red>Gröbner bases</font>
</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>
'groebner' computes Gröbner bases of graded lattice ideals of lattices L
given<br>
as ker(A) for given matrix A<br>
or<br>
by lattice generators.<p>
Returned is a degrevlex Gröbner basis with x[1]<...<x[n], unless cost vector is specified.
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th align=left width=70%>
Gröbner basis from matrix<p>
If present, lattice generators will be read automatically from
"fileName.lat".<p>
If present, cost vector will be read automatically from
"fileName.cost".
</th>
<th align=left width=30%>
./groebner fileName
</th>
</tr>
</table>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th>
The new 'groebner' is far more flexible than the one in version 1.1. You may
call it also via:<p>
./groebner [option] fileName<p>
With no option set, 'groebner' behaves as in version 1.1. However, the
new project-and-lift algorithm is used for the computation. For more details,
please wait for the full release at the end of August 2005.<p>
As options are possible:<p>
<table border=5 width=90% cellspacing=5 cellpadding=5>
<tr>
<th align=left width=30%>
--groebner
</th>
<th align=left width=70%>
Compute a Groebner basis.
</th>
</tr>
<tr>
<th align=left width=30%>
--saturation
</th>
<th align=left width=70%>
Use the Saturation algorithm.
</th>
</tr>
<tr>
<th align=left width=30%>
--project-and-lift
</th>
<th align=left width=70%>
Use the Project-and-Lift algorithm.
</th>
</tr>
<tr>
<th align=left width=30%>
--normal
</th>
<th align=left width=70%>
Use the straight-forward completion procedure.
</th>
</tr>
<tr>
<th align=left width=30%>
--graded
</th>
<th align=left width=70%>
Use the graded completion procedure.
</th>
</tr>
<tr>
<th align=left width=30%>
--gebauer-moeller
</th>
<th align=left width=70%>
Use the Gebauer and Moeller criteria.
</th>
</tr>
<tr>
<th align=left width=30%>
--auto-reduce-freq=n
</th>
<th align=left width=70%>
Set the frequency of auto reduction to 'n' iterations.
</th>
</tr>
</table>
<tr>
<th align=left width=30%>
--silent
</th>
<th align=left width=70%>
Surpresses all output.
</th>
</tr>
</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>