Home Online Manual
Top
Back: Matrix orderings
Forward: Extra weight vector
FastBack: Representation of mathematical objects
FastForward: Mathematical background
Up: Monomial orderings
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

B.2.7 Product orderings

Let $x = (x_1, \ldots, x_n)$ and $y = (y_1, \ldots, y_m)$be two ordered sets of variables, $<_1$ a monomial ordering on $K[x]$ and $<_2$ a monomial ordering on $K[y]$. The product ordering (or block ordering) $<\ := (<_1,<_2)$ on $K[x,y]$ is the following:
         $x^a y^b < x^A y^B \Leftrightarrow x^a <_1 x^A $ or ($x^a = x^A$ and $y^b <_2 y^B$).

Inductively one defines the product ordering of more than two monomial orderings.

In SINGULAR, any of the above global orderings, local orderings or matrix orderings may be combined (in an arbitrary manner and length) to a product ordering. E.g., (lp(3), M(1, 2, 3, 1, 1, 1, 1, 0, 0), ds(4), ws(1,2,3)) defines: lp on the first 3 variables, the matrix ordering M(1, 2, 3, 1, 1, 1, 1, 0, 0) on the next 3 variables, ds on the next 4 variables and ws(1,2,3) on the last 3 variables.