Knowledge-based interoperability for mathematical software systems

Michael Kohlhase, Luca De Feo, Dennis Müller, Markus Johannes Pfeiffer, Florian Rabe, Nicolas Thiéry, Victor Vasilyev, Tom Wiesing

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)
2 Downloads (Pure)


There is a large ecosystem of mathematical software systems. Individually, these are optimized for particular domains and functionalities, and together they cover many needs of practical and theoretical mathematics. However, each system specializes on one area, and it remains very difficult to solve problems that need to involve multiple systems. Some integrations exist, but the are ad-hoc and have scalability and maintainability issues. In particular, there is not yet an interoperability layer that combines the various systems into a virtual research environment (VRE) for mathematics.

The OpenDreamKit project aims at building a toolkit for such VREs. It suggests using a central system-agnostic formalization of mathematics (Math-in-the-Middle, MitM) as the needed interoperability layer. In this paper, we conduct the first major case study that instantiates the MitM paradigm for a concrete domain as well as a concrete set of systems. Specifically, we integrate GAP, Sage, and Singular to perform computation in group and ring theory.

Our work involves massive practical efforts, including a novel formalization of computational group theory, improvements to the involved software systems, and a novel mediating system that sits at the center of a star-shaped integration layout between mathematical software systems.
Original languageEnglish
Title of host publicationMathematical Aspects of Computer and Information Sciences
Subtitle of host publication7th International Conference, MACIS 2017, Vienna, Austria, November 15-17, 2017, Proceedings
EditorsJohannes Blömer, Ilias Kotsireas, Temur Kutsia, Dimitris E. Simos
Place of PublicationCham
ISBN (Electronic)9783319724539
ISBN (Print)9783319724522
Publication statusPublished - 2017
Event7th International Conference on Mathematical Aspects of Computer and Information Sciences - University of Applied Sciences Technikum Wien, Vienna, Austria
Duration: 15 Nov 201717 Nov 2017
Conference number: 7

Publication series

NameLecture Notes in Computer Science (Theoretical Computer Science and General Issues)
ISSN (Print)0302-9743


Conference7th International Conference on Mathematical Aspects of Computer and Information Sciences
Abbreviated titleMACIS
Internet address


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