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B.2.7 Product orderings
Let
x = (x1,…,xn) and y = (y1,…,ym)
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:
xayb < xAyB ⇔ xa < 1xA or (xa = xA and yb < 2yB).
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.
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