B.2.8 Extra weight vector
-------------------------

${\tt a}(w_1, \ldots, w_n),\; $
$w_1,\ldots,w_n$
any integers (including 0), defines
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n$
and


    $$\deg(x^\alpha) < \deg(x^\beta) \Rightarrow x^\alpha < x^\beta,$$
    $$\deg(x^\alpha) > \deg(x^\beta) \Rightarrow x^\alpha > x^\beta. $$

An extra weight vector does not define a monomial ordering by itself:
it can only be used in combination with other orderings
to insert an extra line of weights into the ordering
matrix.


Example:
ring r = 0, (x,y,z),  (a(1,2,3),wp(4,5,2));
ring s = 0, (x,y,z),  (a(1,2,3),dp);
ring q = 0, (a,b,c,d),(lp(1),a(1,2,3),ds);

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

</body>
</html>
