Algebraic and Arithmetic Attributes of Hypergeometric Functions in SageMath

TL;DR

This paper presents algorithms implemented in SageMath for analyzing algebraic and arithmetic properties of hypergeometric functions across various fields, including rationals, finite fields, and p-adics.

Contribution

It introduces new implementations for deciding algebraicity, computing valuations, and finding minimal polynomials of hypergeometric functions in different algebraic settings.

Findings

Algorithms successfully determine algebraicity of hypergeometric series.

Valuations and minimal polynomials are computed efficiently in positive characteristic.

Implementations extend SageMath's capabilities for hypergeometric function analysis.

Abstract

We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and over the p-adics. Among other things, we provide implementations deciding algebraicity, computing valuations, and computing minimal polynomials in positive characteristic.