On Kahan's Rules for Determining Branch Cuts

TL;DR

This paper examines how Kahan's rules can be adapted to determine branch cuts in functions defined as solutions of differential equations, aiming to make the process more algorithmic.

Contribution

It extends Kahan's rules to the differential equation context, providing a new approach for algorithmically determining branch cuts.

Findings

Kahan's rules can be adapted for differential equations

The approach improves the algorithmic determination of branch cuts

Discussion of problems and limitations in the current methods

Abstract

In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.