Suppose that we seek to factor a multivariate polynomial
a
ε
R
= Z[
x
1
, ...,
x
n
] and
a
=
fg
with
f, g
in
R
. The multivariate Hensel lifting algorithm (MHL) developed by Wang [1] uses a prime number
p
and an ideal
I
= 〈
x
2
− α
2
, ...,
x
n
− α
n
〉 of Z
p
[
x
1
, ...,
x
n
] where α
2
, α
3
, ..., α
n
ε Z
p
is an evaluation point chosen by the algorithm.
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