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**An implementation for the algorithm of Janet bases of linear differential ideals in the Maple system.**
*(English)*
Zbl 1138.35300

Summary: 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 judgment of involutive divisor and reducible, the judgment of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction algorithms 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.

### MSC:

35-04 | Software, source code, etc. for problems pertaining to partial differential equations |

13P99 | Computational aspects and applications of commutative rings |

35A30 | Geometric theory, characteristics, transformations in context of PDEs |

68W30 | Symbolic computation and algebraic computation |

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\textit{S. Zhang} and \textit{Z. Li}, Acta Math. Appl. Sin., Engl. Ser. 20, No. 4, 605--616 (2004; Zbl 1138.35300)

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### References:

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