tutorial_groebner.html

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<TITLE>4ti2 -- Computation of Hilbert bases, Graver bases, toric Gröbner bases, and more</TITLE>
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    <font size=6 color=red>4ti2 tutorial</font>
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<a href="tutorial_input.html">Input</a>
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<a href="tutorial_auxiliary.html">Auxiliary functions</a>
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<a href="tutorial_output.html">Output management</a>
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<a href="tutorial_hilbert.html">Hilbert bases</a>
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<a href="tutorial_graver.html">Graver bases</a>
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<font color=red>Gröbner bases</font>
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<a href="tutorial_markov.html">Markov bases</a>
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<a href="tutorial_minimize.html">Minimization</a>
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'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]&lt;...&lt;x[n], unless cost vector is specified. 
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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".
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./groebner fileName
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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>

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--groebner
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Compute a Groebner basis.
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--saturation
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Use the Saturation algorithm. 
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--project-and-lift
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Use the Project-and-Lift algorithm. 
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--normal
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Use the straight-forward completion procedure. 
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--graded
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Use the graded completion procedure. 
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--gebauer-moeller
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Use the Gebauer and Moeller criteria. 
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--auto-reduce-freq=n
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Set the frequency of auto reduction to 'n' iterations.
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--silent
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Surpresses all output.
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