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Computer Science > Symbolic Computation

arXiv:2412.13306 (cs)
[Submitted on 17 Dec 2024]

Title:Invariants: Computation and Applications

Authors:Irina A. Kogan
View a PDF of the paper titled Invariants: Computation and
Applications, by Irina A. Kogan
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    Abstract:Invariants withstand transformations and, therefore,
    represent the essence of objects or phenomena. In mathematics,
    transformations often constitute a group action. Since the 19th
    century, studying the structure of various types of invariants
    and designing methods and algorithms to compute them remains an
    active area of ongoing research with an abundance of
    applications. In this incredibly vast topic, we focus on two
    particular themes displaying a fruitful interplay between the
    differential and algebraic invariant theories. First, we show how
    an algebraic adaptation of the moving frame method from
    differential geometry leads to a practical algorithm for
    computing a generating set of rational invariants. Then we
    discuss the notion of differential invariant signature, its role
    in solving equivalence problems in geometry and algebra, and some
    successes and challenges in designing algorithms based on this
    notion.

                   This is a tutorial paper that appeared in the
                   proceedings of International Symposium on Symbolic
                   and Algebraic Computation 2023 (ISSAC 2023), July
Comments:          24-27, 2023, Tromso, Norway. ACM, New York, NY,
                   USA, this https URL . This is the author's version
                   of the work. It is posted here for your personal
                   use. Not for redistribution
Subjects:          Symbolic Computation (cs.SC)
MSC classes:       13A50, 14L24, 53A55
ACM classes:       I.1.2
Cite as:           arXiv:2412.13306 [cs.SC]
                   (or arXiv:2412.13306v1 [cs.SC] for this version)
                   https://doi.org/10.48550/arXiv.2412.13306
                   Focus to learn more
                   arXiv-issued DOI via DataCite (pending
                   registration)
                   ISSAC '23: Proceedings of the 2023 International
Journal reference: Symposium on Symbolic and Algebraic Computation,
                   Pages 31 - 40
                   https://doi.org/10.1145/3597066.3597149
Related DOI:       Focus to learn more
                   DOI(s) linking to related resources

Submission history

From: Irina Kogan A [view email]
[v1] Tue, 17 Dec 2024 20:18:03 UTC (104 KB)
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