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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

\begin{displaymath}\deg(x^\alpha) < \deg(x^\beta) \Rightarrow x^\alpha < x^\beta,\end{displaymath}


\begin{displaymath}\deg(x^\alpha) > \deg(x^\beta) \Rightarrow x^\alpha > x^\beta. \end{displaymath}


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);

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