TL;DR
This paper introduces a differential analog of integral closure for algebraic function fields and presents an algorithm to compute it, extending van Hoeij's algebraic integral basis algorithm to differential operators.
Contribution
It develops a novel differential analog of integral closure and provides an algorithm for computing the integral closure of algebras defined by linear differential operators.
Findings
Algorithm successfully computes integral closures for differential algebraic structures.
Extends van Hoeij's algebraic integral basis algorithm to differential operators.
Provides a theoretical framework for differential integral closure.
Abstract
We propose a differential analog of the notion of integral closure of algebraic function fields. We present an algorithm for computing the integral closure of the algebra defined by a linear differential operator. Our algorithm is a direct analog of van Hoeij's algorithm for computing integral bases of algebraic function fields.
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