A SageMath program for calculations in the tautological ring of $$\overline{\mathcal{M}}_{g,n}$$ and computation of cycles of admissible covers
Authors
Vincent Delecroix, Johannes Schmitt and Jason van Zelm
Many functions of the program rely on an earlier implementation of tautological computations by Aaron Pixton. We want to thank Samuel Lelièvre for help and advice.
Overview
The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring. This includes lists of generators and their products, intersection numbers and verification of tautological relations. Maps between tautological rings induced by functoriality, that is pushforwards and pullbacks under gluing and forgetful maps, are implemented. Furthermore, many interesting cycle classes, such as the double ramification cycles, strata of k-differentials and hyperelliptic or bielliptic cycles are available.