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B.2.7 Product orderings

Let be two ordered sets of variables,

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

In , 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.


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