We begin by giving the definition of pure lex order on
given in §2.2 of [CLS]. This order
will play a central role in defining pure lex and
multilex orders on the monic monomials of
K[
x
,
...,
x
].
Definition C.6 [CLS], Pure lex on
N
Let 
=
(a , ...,
a)
N
and
=
(b , ...,
b)
N.
We say that
is greater than
if, in the vector difference
-
Z,
the left-most nonzero entry is positive.