how to check that an ideal is a monomial ideal?

Dear Users,

is there a way to check in Singular that an ideal in a polynomial ring (say in two variables) has a monomial basis?

Maybe even to see this basis explicitly?

(My knowledge of Groebner bases is infinitesimal, sorry if the question is stupid.)

If an ideal I is generated by monomials then these monomials are a GB of I with respect to any monomial ordering. Since the reduced GB of an ideal is unique (only depending on the ordering), I is a monomial ideal iff the reduced GB of I w.r.t. any monomial ordering consists of monomials.

Thanks, it works! :D