HypIgu

Author: Joshua Maglione.

Documentation for the HypIgu package for SageMath.

Purpose

The goal of HypIgu (HYPerplane IGUsa) is to provide SageMath with the functionality to compute various zeta functions associated with hyperplane arrangements. Included are common constructions for hyperplane arrangements and specializations of the flag Hilbert–Poincaré series defined in Maglione–Voll. Mathematical details are given in Maglione–Voll. We outline the functions included in HypIgu and provide example cases.

Setup

The simplest way to install HypIgu is to run the following 

$ sage --pip install hypigu

Alternatively, one can download the latest release and unzip it into a directory that SageMath can find for importing.

To update an older version of HypIgu to the latest version, run the following 

$ sage --pip install hypigu --upgrade

HypIgu has no external dependencies and is compatible with SageMath 9.6 and later. It may work just fine with earlier versions of SageMath, but these have not been tested.

Importing

Import HypIgu during your SageMath run with the following

import hypigu as hi

Throughout this documentation, we use hi for the reference name of hypigu.

Funding

This work was supported in part by DFG-grant 373111162.

References

  1. Joshua Maglione and Christopher Voll. Flag Hilbert–Poincaré series of hyperplane arrangements and Igusa zeta functions, to appear in Israel J. Math. 2021. arXiv:2103:03640.