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B.2.3 Global orderings
For
all these orderings: Loc K[x] = K[x]
- lp:
lexicographical ordering:
xα < xβ ⇔∃ 1 ≤ i ≤ n : α1 = β1,…,αi−1 = βi−1,αi < βi.
- rp:
reverse lexicographical ordering:
xα < xβ ⇔∃ 1 ≤ i ≤ n : αn = βn,…,αi+1 = βi+1,αi > βi.
- dp:
degree reverse lexicographical ordering:
let deg(xα) = α1 + + αn, then
xα < xβ ⇔ deg(xα) < deg(xβ) or
deg(xα) = deg(xβ) and ∃ 1 ≤ i ≤ n : αn = βn,…,αi+1 = βi+1,αi > βi.
- Dp:
degree lexicographical ordering:
let deg(xα) = α1 + + αn, then
xα < xβ ⇔ deg(xα) < deg(xβ) or
deg(xα) = deg(xβ) and
∃ 1 ≤ i ≤ n : α1 = β1,…,αi−1 = βi−1,αi < βi.
- wp:
weighted reverse lexicographical ordering:
let w1,…,wn be positive integers. Then wp(w1,…,wn)
is defined as dp
but with
deg(xα) = w1α1 + + wnαn.
- Wp:
weighted lexicographical ordering:
let w1,…,wn be positive integers. Then Wp(w1,…,wn)
is defined as Dp
but with
deg(xα) = w1α1 + + wnαn.
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