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Journal of the London Mathematical Society 1996 54(2):323-345; doi:10.1112/jlms/54.2.323
© 1996 by London Mathematical Society
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© The London Mathematical Society

A Simple Criterion for Involutivity

Elizabeth L. Mansfield

Institute of Mathematics and Statistics, University of Kent Canterbury CT2 7NF E-mail: E.L.Mansfield{at}ukc.ac.uk

Received 4 May 1993. Revision received 18 March 1994.

A simple criterion for the involutivity of a system of partial differential equations of polynomial type is proved. The criterion involves the equations themselves and does not require the system to be in orthonomic form. It is proved that a system of partial differential equations is involutive if it is a differential Gröbner basis with respect to a total degree ordering, and if the compatibility conditions of the symbol equations of the system consist of equations of degree one. An algorithm for calculating these compatibility conditions is given.

Research partially supported by the SERC.


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