swMATH ID: 7776
Software Authors: Blinkov Y, Cid C, Gerdt V, Plesken W, Robertz D
Description: The Maple package Janet implements the involutive basis technique of V. P. Gerdt and Y. A. Blinkov for computing Janet bases and Janet-like Gröbner bases for linear systems of partial differential equations. It works with left modules over differential algebras defined over differential fields of characteristic zero which exist in Maple. Janet also provides a number of tools for dealing with differential expressions and differential operators. A generic linearization for a non-linear system of partial differential equations can be computed. Some procedures translate differential expressions into jet notation and vice versa. For the Weyl algebra representing ordinary differential operators in characteristic zero whose coefficients are rational functions, an elementary divisor algorithm [Rehm 2001/2002], [Cohn 1985] is implemented to compute the Jacobson normal form of a matrix with entries in this Weyl algebra. Among the orderings for differential monomials which are available in Janet are the degree reverse lexicographical one, the pure lexicographical one, block orderings and their extensions to the case of more than one dependent variable which correspond to ”term over position” and ”position over term” orderings in the polynomial case. Four involutive criteria are implemented to avoid unnecessary reductions during involutive basis computations.
Homepage: http://wwwb.math.rwth-aachen.de/Janet/janet.html
Dependencies: Maple
Related Software: SINGULAR; Maple; OreModules; Macaulay2; Plural; Magma; DifferentialThomas; RegularChains; Ginv; QuillenSuslin; homalg; OreMorphisms; DIFFALG; JanetOre; SADE; GeM; AlgebraicThomas; CRACK; CoCoA; TDDS
Cited in: 37 Documents

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