I am trying to determine the set that generates a monomial ideal. Namely, the ideal $(xy,yz,xz)^3$.
I know it will have terms $x^3y^3$, $z^3y^3$, $x^3z^3$. For the other terms that generate, I do not know how to determine them (it should be some sort of combination of two of the terms, such that their powers sum to 6, correct?)
Also, is mathematica able to compute this?