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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,i1 = βi1i < βi.

rp:

reverse lexicographical ordering:
xα < xβ ⇔∃ 1 i n : αn = βn,i+1 = βi+1i > 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,i+1 = βi+1i > 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,i1 = βi1i < 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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