Singular Manual: Extra weight vector

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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