Abstract
Data plays an increasing role in applied and even pure mathematics: datasets of concrete mathematical objects proliferate and increase in size, reaching up to 1 TB of uncompressed data and millions of objects. Most of the datasets, especially the many smaller ones, are maintained and shared in an ad hoc manner. This approach, while easy to implement, suffers from scalability and sustainability problems as well as a lack of interoperability both among datasets and with computation systems.
In this paper we present another substantial step towards a unified infrastructure for mathematical data: a storage and sharing system with math-level APIs and UIs that makes the various collections findable, accessible, interoperable, and re-usable. Concretely, we provide a high-level data description framework from which database infrastructure and user interfaces can be generated automatically. We instantiate this infrastructure with several datasets previously collected by mathematicians. The infrastructure makes it relatively easy to add new datasets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The data set might already have a pre-existing ID-like field, which is not a UUID. In this case we need to add a declaration for a custom index key.
- 2.
We can only hope to duplicate the generic parts of the user interface. Websites like the these four major mathematical database provide a lot of customized mathematical user functionality, which we cannot hope to reproduce generically.
References
Berčič, K.: Math databases table. https://mathdb.mathhub.info/. Accessed 15 Jan 2019
Berčič, K.: Math databases wiki. https://github.com/MathHubInfo/Documentation/wiki/Math-Databases. Accessed 15 Jan 2019
Gelbart, S., Bernstein, J. (eds.): An Introduction to the Langlands Program. Birkhäuser, Basel (2003). ISBN: 3-7643-3211-5
Babai, L., Luks, E.M.: Canonical labeling of graphs. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC 1983, pp. 171–183. ACM, New York (1983). https://doi.org/10.1145/800061.808746. ISBN: 0-89791-099-0
Brinkmann, G., et al.: House of graphs: a database of interesting graphs. Discrete Appl. Math. 161(1–2), 311–314 (2013). https://doi.org/10.1016/j.dam.2012.07.018. ISSN: 0166–218X
Berg, C., Stump, C., et al.: FindStat: the combinatorial statistic finder (2014). http://www.FindStat.org. Accessed 31 Aug 2016
Berčič, K., Vidali, J.: DiscreteZOO: a fingerprint database of discrete objects (2018). arXiv:1812.05921
European Commission Expert Group on FAIR Data: Turning FAIR into reality (2018). https://doi.org/10.2777/1524
Kohlhase, M., et al.: Knowledge-based interoperability for mathematical software systems. In: Blömer, J., Kotsireas, I.S., Kutsia, T., Simos, D.E. (eds.) MACIS 2017. LNCS, vol. 10693, pp. 195–210. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72453-9_14
The L-functions and modular forms database. http://www.lmfdb.org. Accessed 02 Jan 2016
MBGen description, links demos and code repositories. https://github.com/MathHubInfo/Documentation/wiki/MBGen. Accessed 05 Mar 2019
McKay, B.: Description of graph6, sparse6 and digraph6 encodings. http://users.cecs.anu.edu.au/~bdm/data/formats.txt
MathHub.info: Active mathematics. http://mathhub.info. Accessed 28 Jan 2014
Müller, D., Rabe, F., Kohlhase, M.: Theories as types. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 575–590. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_38
The on-line encyclopedia of integer sequences. http://oeis.org. Accessed 28 May 2017
Rabe, F.: A query language for formal mathematical libraries. In: Jeuring, J., et al. (eds.) CICM 2012. LNCS (LNAI), vol. 7362, pp. 143–158. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31374-5_10. arXiv: 1204.4685. ISBN: 978-3-642-31373-8
Rabe, F.: How to identify, translate, and combine logics? J. Logic Comput. 27(6), 1753–1798 (2017)
Rabe, F., Kohlhase, M.: A scalable module system. Inf. Comput. 230(1), 1–54 (2013)
Slick, functional relational mapping for scala. http://slick.lightbend.com/. Accessed 16 Mar 2019
Rabe, F., Berčič, K.: Schema theories repository for the prototyper. https://gl.mathhub.info/ODK/discretezoo. Accessed 14 Mar 2019
Wiesing, T., Kohlhase, M., Rabe, F.: Virtual theories – a uniform interface to mathematical knowledge bases. In: Blömer, J., Kotsireas, I.S., Kutsia, T., Simos, D.E. (eds.) MACIS 2017. LNCS, vol. 10693, pp. 243–257. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72453-9_17
Acknowledgements
The authors gratefully acknowledge helpful discussions with Tom Wiesing on MathHub integration and virtual theories. Discussions with Gabe Cunningham on concrete examples of questions a researcher might have and descriptions of tools that would help them helped shape our intuitions. The work presented here was supported by EU grant Horizon 2020 ERI 676541 OpenDreamKit.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Berčič, K., Kohlhase, M., Rabe, F. (2019). Towards a Unified Mathematical Data Infrastructure: Database and Interface Generation. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-23250-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23249-8
Online ISBN: 978-3-030-23250-4
eBook Packages: Computer ScienceComputer Science (R0)