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Study of complexity of two algorithms computing some families of nilpotent and solvable Lie algebras

Desamparados Fernández-Ternero, Juan Núñez, Ángel f. Tenorio

Abstract



In this paper, we compare two algorithms (introducing their respective implementations with Maple for this reason) which compute, respectively, the commutator relations of two special families of complex Lie algebras: the solvable Lie algebras s_n of nXn complex upper-triangular matrices and the nilpotent Lie algebras n_n of nXn complex strictly uppertriangular matrices. Starting from the source code of the implementation introduced here
for both algorithms, we study some computational differences between them, regarding the computing time and memory used in these implementations, and we also give some numerical data which exemplify them. Finally, the complexity of both algorithms is studied and compared by means of their implementations.

Keywords


Nilpotent Lie algebra, solvable Lie algebra, algorithm, complexity.

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