H = hibiIdeal P
The Hibi ideal of $P$ is a MonomialIdeal built over a ring in $2n$ variables $x_0, \ldots, x_{n1}, y_0, \ldots, y_{n1}$, where $n$ is the size of the ground set of $P$. The generators of the ideal are in bijection with order ideals in $P$. Let $I$ be an order ideal of $P$. Then the associated monomial is the product of the $x_i$ associated with members of $I$ and the $y_i$ associated with nonmembers of $I$.

The object hibiIdeal is a method function with options.