
PROGRAM LIBRARY JINRLIBDWSGCoeff, FPLSA, LieCohomology  programs for study of noncommutative and nonassociative structures in problems of mathematical physicsAuthor: V.V.Kornyak 

Language: C
DWSGCoeff  computation of DeWittSeeleyGilky coefficients; DWSGCoeff  COMPUTATION OF DEWITTSEELEYGILKY COEFFICIENTS The DWSGCoeff program is intended for calculation of asymptotic spectral invariants (heat kernel coefficients) of elliptic differential operators acting on compact closed curved manifolds with torsion and gauge connection. The program (file DWSG.c), the instruction on compilation and use, examples of input files can be received from the author. Method: The algorithm of calculation is based on the Vidom's covariant
generalization of pseudodifferential calculus. References:
FPLSA  COMPUTATION OF FINITELY PRESENTED LIE ALGEBRAS Authors: V.P.Gerdt, V.V. Kornyak The FPLSA program is intended for constructing the complete system of relations (Groebner basis), basis elements and commutator table for Lie algebras and superalgebras defined by finite set of generators satisfying to finite set of relations. The program outputs also the Hilbert series of the constructed algebra and, in the case the input data contain arbitrary parameters, the list of parametric expressions which zero values may cause branching in the structure of the algebra. The program (file FPLSA4.c) and auxiliary files (initiating file  FPLSA4.ini, message file  FPLSA4.msg, examples of input data, the instruction on compilation and use) are available from the author. Method: Computation of noncommutative and nonassociative Groebner basis of ideal in free Lie (super)algebra. As a basis of free Lie (super)algebra the Hall regular monomials are used. References:
LieCohomology  COMPUTATION OF COHOMOLOGIES OF LIE ALGEBRAS AND Author: V.V. Kornyak The LieCohomology program is intended for computing nontrivial cohomology classes of finitedimensional and graded infinitedimensional Lie algebras and superalgebras with coefficients in the trivial, adjoint and coadjoint modules. The algebra can be defined via basis elements and commutator table. For some Lie (super)algebras of vector fields (general W(nm) and special S(nm) vectorial algebras; Poisson algebra Po(2nm), Hamilton H(2nm) and special Hamilton algebra SH(0m); contact algebra K(2n+1m); Buttin B(n), Leites Le(n) algebras and their special forms SB(n) and SLe(n); odd contact algebra M(n) and its special form SM(n)) the program constructs basis elements and their commutators automatically. The program (file LieCoho1.c) and auxiliary files (initiating file  LieCoho1.ini, message file  LieCoho1.msg, examples of input data, the instruction on compilation and use) are available from the author. Method: Construction of the part of cochain complex, corresponding to given cohomological dimension (cochain degree) and grade, and computation of basis elements of the quotient space of the cocycle space with respect to subspace of coboundaries. References:
