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<A NAME=Groebner_bases>

<TITLE>Groebner_bases</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>GROEBNER BASES</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>introduction</B><P>
<P>
 
The GROEBNER package calculates <em>Groebner bases</em> using the 
 <em>Buchberger algorithm</em> and provides related algorithms 
for arithmetic with ideal bases, such as ideal quotients, 
Hilbert polynomials ( <em>Hollmann algorithm</em>), 
basis conversion ( 
 <em>Faugere-Gianni-Lazard-Mora algorithm</em>), independent 
variable set ( <em>Kredel-Weispfenning algorithm</em>). 
<P>
<P>
Some routines of the Groebner package are used by 
<A HREF=r37_0179.html>solve</A> - in 
that context the package is loaded automatically. However, if you 
want to use the package by explicit calls you must load it by 
<P><PRE><TT>
    load_package groebner;
</TT></PRE><P><P>
<P>
For the common parameter setting of most operators in this package 
see 
<A HREF=r37_0352.html>ideal parameters</A>. 
<P>
<P>