Skip to main content
SpringerLink
Log in

Involutive Divisions. Graphs

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

A new approach to the theory of involutive divisions is suggested. The application of this approach simplifies the formulation of definitions and properties and makes it possible to obtain new involutive divisions. The latter feature is important in light of the results discussed in [1]. An involutive division graph is defined, and the notions of its completeness and projection are introduced. Criteria for being global and Noetherian and a sufficient condition for the completeness are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Gerdt, V.P. and Blinkov, Yu.A., Involutive Bases of Polynomial Ideals, Math. Comput. Simulation, 1998, vol. 45, pp. 519–542.

    Google Scholar 

  2. Janet, M., Sur les Systemes d'Equations aux Derivees Partielles, J. Math. Pure et Appl., 1920, vol. 3, pp. 65–151.

    Google Scholar 

  3. Thomas, J., Differential Systems, New York: AMS, 1937.

    Google Scholar 

  4. Pommaret, J.F., Systems of Partial Differential Equations and Lie Pseudogroups, New York: Gordon & Breach, 1978.

    Google Scholar 

  5. Astrelin, A.V., Golubitsky, O.D., and Pankratiev, E.V., Gröbner Bases and Involutive Bases, Proc. of the Int. Algebraic Conf. on the Occasion of the 90th Birthday of A.G. Kurosh (Moscow, 1998), Berlin: Walter Gruyter, 2000, pp. 49–55.

    Google Scholar 

  6. Chen, Yu-Fu and Gao, X.-S., Involutive Directions and New Involutive Divisions, Comput. Math. Appl., 2001, vol. 41,nos. 7–8, pp. 945–956.

    Google Scholar 

  7. Gerdt, V.P. and Blinkov, Yu.A., Minimal Involutive Bases, Math. Comput. Simulation, 1998, vol. 45, pp. 543–560.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Vorob'evy gory, Moscow, 119992, Russia

    E. S. Shemyakova

Authors
  1. E. S. Shemyakova
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shemyakova, E.S. Involutive Divisions. Graphs. Programming and Computer Software 30, 68–74 (2004). https://doi.org/10.1023/B:PACS.0000021263.97826.ef

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:PACS.0000021263.97826.ef

Keywords

Search

Navigation