|  |  B.2.7 Product orderings 
Let
 and  be two ordered sets of variables,  a monomial
ordering on ![$K[x]$](sing_512.png) and  a monomial ordering on ![$K[y]$](sing_574.png) .   The product
ordering (or block ordering)  on ![$K[x,y]$](sing_576.png) is the following: 
  or (  and  ). 
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:lpon the first 3 variables, the matrix orderingM(1, 2, 3, 1, 1, 1, 1, 0, 0)on the next 3 variables,dson the next 4 variables andws(1,2,3)on the last 3 variables. 
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