Refine
Year of publication
- 2002 (2) (remove)
Document Type
- ZIB-Report (2) (remove)
Language
- English (2)
Has Fulltext
- yes (2)
Is part of the Bibliography
- no (2)
Keywords
- conservation laws (2)
- Bi-linear algebraic systems (1)
- Computer algebra (1)
- Integrability (1)
- PDE (1)
- evolution equations (1)
- quadratic Hamiltonians (1)
- syzygies (1)
Institute
- ZIB Allgemein (2)
The purpose of the paper is to formulate and use syzygies for systems of linear PDEs. The computation of an equivalent of a GCD for linear partial differential operators will save us their factorization which is otherwise only possible algorithmically in special cases. After showing the computation with the new and the traditional method and comparing both in the next three sections, the algorithm is explained in general and an overview is given.
The talk given by the author at the CRM workshop on Superintegrability in Sep.\ 2002 and this related paper report on work in two subjects. One is the collaboration with Vladimir Sokolov and Takayuki Tsuchida in an effort to classify polynomial integrable vector evolution equations. The other is the computer algebra package {\sc Crack} which did the main computations in solving large bi-linear algebraic systems. Although originally designed to solve over-determined systems of partial differential equations a number of extensions made {\sc Crack} a powerful tool for solving systems of bi-linear algebraic equations. Such systems turn up in many different classification problems some of which were investigated by other participants of this workshop. Two additional applications are outlined. In the talk on which this article is based a method to reduce the length of equations was presented which proved to be useful in solving the bi-linear algebraic systems. Due to numerous asked questions about the computer program, a more complete overview is given in the appendix.