### 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

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