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<A NAME=gmodule>

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



<B>GMODULE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>variable</B><P>
<P>
 
The vectors of a free 
<A HREF=r37_0400.html>module</A> over a polynomial ring R 
are encoded as linear combinations with unit vectors of 
M which are represented by auxiliary variables. These 
must be collected in the variable <em>gmodule</em> before 
any call to an operator of the Groebner package. 
<P>
<P>
<P><PRE><TT>
   torder({x,y,v1,v2,v3})$
   gmodule := {v1,v2,v3}$
   g:=groebner({x^2*v1 + y*v2,x*y*v1 - v3,2y*v1 + y*v3});
</TT></PRE><P>compute the Groebner basis of the submodule 
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<P>
<P><PRE><TT>
      ([x^2,y,0],[xy,0,-1],[0,2y,y])
</TT></PRE><P>The members of the list <em>gmodule</em> are automatically 
appended to the end of the variable list, if they are not 
yet members there. They take part in the actual term ordering. 
<P>
<P>