  This short paper presents saturation-based algorithms for homogenization and
elimination. This algorithm can compute elimination ideals by using syzygies
and ideal membership test, hence it works with any} monomial order, in
particular without the use of block-elimination orders. The used saturation is
a translation of the geometric fact that the projective closure of an affine
scheme has no components in the hyperplane at infinity.

Commutative Algebra