Given a polynomial ring $S$ over a field of characteristic zero and an Artinian ring $A = S/I$ where $I$ is a monomial ideal, we build a new polynomial ring $S_{I}$ with the variables being the nonzero monomials of $A$. For every degree $i$, we define two ideals in $S_{I}$ such that their analytic spread detects the WLP property of $A$ in degree $i$:

1. The jacobian ideal of a hyperplane arrangement, when $I$ is any monomial ideal

2. The edge ideal of a hypergraph, when all the nonzero monomials of $A$ are squarefree.

In particular, when all the nonzero monomials of $A$ are squarefree, we see the connections between birational maps and the failure of WLP in positive characteristics.