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An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System

Abstract

In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division, Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package.

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Correspondence to Shan-qing Zhang.

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Supported by the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20020269003).

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Zhang, Sq., Li, Zb. An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System. Acta Mathematicae Applicatae Sinica, English Series 20, 605–616 (2004). https://doi.org/10.1007/s10255-004-0198-3

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  • DOI: https://doi.org/10.1007/s10255-004-0198-3

Keywords

  • Involutive bases
  • Janet bases
  • Gröbner bases
  • symbolic computation and algebraic computation
  • partial differential equations

2000 MR Subject Classification

  • 35-04
  • 68W30