On the Structure and Generators of Differential Invariant Algebras

Peter J. Olver

doi:10.1007/978-3-031-41724-5_16

On the Structure and Generators of Differential Invariant Algebras

Peter J. Olver

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The structure of algebras of differential invariants, particularly their generators, is investigated using the symbolic invariant calculus provided by the method of equivariant moving frames. We develop a computational algorithm that will, in many cases, determine whether a given set of differential invariants is generating. As an example, we establish a new result that the Gaussian curvature generates all the differential invariants for Euclidean surfaces in three-dimensional space.

Original language	English (US)
Title of host publication	Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings
Editors	François Boulier, Matthew England, Ilias Kotsireas, Timur M. Sadykov, Evgenii V. Vorozhtsov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	292-311
Number of pages	20
ISBN (Print)	9783031417238
DOIs	https://doi.org/10.1007/978-3-031-41724-5_16
State	Published - 2023
Event	25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023 - Havana, Cuba Duration: Aug 28 2023 → Sep 1 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14139 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023
Country/Territory	Cuba
City	Havana
Period	8/28/23 → 9/1/23

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Differential invariant
Generating set
Moving frame
Recurrence formula

Publisher link

10.1007/978-3-031-41724-5_16

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Cite this

Olver, P. J. (2023). On the Structure and Generators of Differential Invariant Algebras. In F. Boulier, M. England, I. Kotsireas, T. M. Sadykov, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings (pp. 292-311). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14139 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-41724-5_16

On the Structure and Generators of Differential Invariant Algebras. / Olver, Peter J.
Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings. ed. / François Boulier; Matthew England; Ilias Kotsireas; Timur M. Sadykov; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2023. p. 292-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14139 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Olver, PJ 2023, On the Structure and Generators of Differential Invariant Algebras. in F Boulier, M England, I Kotsireas, TM Sadykov & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14139 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 292-311, 25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023, Havana, Cuba, 8/28/23. https://doi.org/10.1007/978-3-031-41724-5_16

Olver PJ. On the Structure and Generators of Differential Invariant Algebras. In Boulier F, England M, Kotsireas I, Sadykov TM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 292-311. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-41724-5_16

Olver, Peter J. / On the Structure and Generators of Differential Invariant Algebras. Computer Algebra in Scientific Computing - 25th International Workshop, CASC 2023, Proceedings. editor / François Boulier ; Matthew England ; Ilias Kotsireas ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2023. pp. 292-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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