Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra
Clemens Hofstadler,
Thibaut Verron
Abstract:Signature-based algorithms have become a standard approach for computing Gröbner bases in commutative polynomial rings. However, so far, it was not clear how to extend this concept to the setting of noncommutative polynomials in the free algebra. In this paper, we present a signature-based algorithm for computing Gröbner bases in precisely this setting. The algorithm is an adaptation of Buchberger's algorithm including signatures. We prove that our algorithm correctly enumerates a signature Gröbner basis as we… Show more
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