H = hibiRing P
H = hibiRing(P, Strategy => "kernel")
H = hibiRing(P, Strategy => "4ti2")
The Hibi ring of $P$ is a monomial algebra generated by the monomials which generate the Hibi ideal (hibiIdeal). That is, the monomials built 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 monomials 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 $I$.
This method returns the toric quotient algebra isomorphic to the Hibi ring. The ideal is the ideal of Hibi relations. The generators of the PolynomialRing $H$ is built over are of the form $t_I$ where $I$ is an order ideal of $P$.

The Hibi ring of the $n$ chain is just a polynomial ring in $n+1$ variables.

In some cases, it may be faster to use the FourTiTwo method toricGroebner to generate the Hibi relations. Using the Strategy "4ti2" tells the method to use this approach.

The object hibiRing is a method function with options.