
B.2.4 Local orderings
For ls, ds, Ds and, if the weights are positive integers, also for ws and
Ws, we have
Loc = , the localization of
at the maximal ideal
.
 ls:
 negative lexicographical ordering:
.  ds:
 negative degree reverse lexicographical ordering:
let
then
or
and
 Ds:
 negative degree lexicographical ordering:
let
then
or
and
 ws:
 (general) weighted reverse lexicographical ordering:
a nonzero integer,
any integer (including 0),
is defined as ds
but with
 Ws:
 (general) weighted lexicographical ordering:
a nonzero integer,
any integer (including 0),
is defined as Ds
but with
