An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System |
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Authors: | Email author" target="_blank">Shan-qing?ZhangEmail author Zhi-bin?Li |
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Institution: | (1) Department of Computer Science, East China Normal University, Shanghai, 200062, China |
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Abstract: | 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.
Supported by the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20020269003). |
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Keywords: | Involutive bases Janet bases Gr?bner bases symbolic computation and algebraic computation partial differential equations |
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