Weil–Petersson Volumes and $\psi$-Class Intersection Numbers via Mirzakhani Recursion

Mirzakhani-style recursion for intersection numbers with exact rational arithmetic and parallelization.

Install (editable)

pip install -e .

Quickstart

Open notebooks/Intersection_Numbers_Tutorial.ipynb. It:

• Verifies the core API.
• Builds the normalized table R_X(g,n,alpha) via iterate(...).
• Shows how to convert to intersection numbers ⟨τ_{d1}⋯τ_{dn}⟩_g using x_from_rx(...).
• Provides helper utilities to query arbitrary (g, n, alpha) tuples.

Minimal API

import wp

# Fill cache up to a degree bound and return a dict { (g,n,alpha): Fraction }
rx = wp.iterate(dmax=6, cache_path="data/wp_rx.pkl", max_workers=None, fill_missing=True)

# Convert normalized value to the actual intersection number
from fractions import Fraction
g, n, alpha = 0, 4, (1,0,0,0)
X = wp.x_from_rx(g, n, alpha, rx[(g,n,tuple(sorted(alpha, reverse=True)))])
assert X == Fraction(1,1)  # ⟨τ_1 τ_0^3⟩_0 = 1

Notes

• Cache file defaults to data/wp_rx.pkl