Computing with endomorphism ringsof modular representations
Journal of Symbolic Computation
Programming with algebraic structures: design of the MAGMA language
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Peakword condensation and submodule lattices: an application of the meat-axe
Journal of Symbolic Computation
Polynomial time algorithms for modules over finite dimensional algebras
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Multiplicative bases, Gröbner bases, and right Gröbner bases
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Opal: A System for Computing Noncommutative Gröbner Bases
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
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We present a new deterministic algorithm for constructing endomorphism rings of a finite dimensional module M, given via a vertex projective presentation, over finite dimensional quotients of path algebras. We use the theory of right Gröbner basis to encode M and to construct appropriate systems of equations for finding the endomorphism ring of M. The algorithm is implemented in the computer algebra system GAP and is included in HOPF, a computational package for noncommutative algebra. We compare the performance of our implementation with implementations of existing algorithms for computing endomorphism rings.