Problem statement

Each of the following polynomials is written with its monomials ordered according to (exactly) one of lex, grlex, or grevlex order. Determine which monomial order was used in each case.

1. $f(x, y, z) = 7x^2y^4z - 2xy^6 + x^2y^2$.
2. $f(x, y, z) = xy^3z + xy^2z^2 + x^2z^3$.
3. $f(x, y, z) = x^4y^5z + 2x^3y^2z - 4xy^2z^4$.

Solution

1. Grlex
2. Grevlex
3. Lex