 Elementary Uses of Gröbner Bases in Macaulay2

Official Macaulay2 documentation tutorial: www.macaulay2.com/doc/Macaulay2-1.23/share/doc/Macaulay2/Macaulay2Doc/html/___Tutorial_co_sp__Elementary_spuses_spof_sp__Groebner_spbases.html . The projective-closure discussion explains why homogenizing a chosen generating set can leave components at infinity and how saturation removes them.