In Macaulay2, one can define a polynomial ring with a certain monomial order as follows:

`R=QQ[x,y,z,MonomialOrder=>{Lex=>2,Position=>Up}]`

This means $R$ is a polynomial ring over $mathbb{Q}$ with variables $x,y,z$, using the Lexicographic monomial order, but what is the point of `Lex=>2`

? What is the `2`

for? How is this different than `Lex=>3`

? I searched everywhere and I can’t figure out what this number does…. can anyone familiar with this software tell me what is going on here? The website documentation does not seem to talk about it.