Operadic Gröbner Bases: An Implementation
- Cite this paper as:
- Dotsenko V., Vejdemo-Johansson M. (2010) Operadic Gröbner Bases: An Implementation. In: Fukuda K., Hoeven J..., Joswig M., Takayama N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg
In an upcoming paper , the first author and Anton Khoroshkin define the concept of a Gröbner basis for finitely presented operads, prove the diamond lemma for these Gröbner bases, and demonstrate that having a quadratic Gröbner basis is equivalent to the existence of a Poincaré-Birkhoff-Witt basis. As demonstrated by Eric Hoffbeck , an operad with a PBW basis is Koszul. Thus, out of this emerges an entirely computational framework for proving Koszulness, as well as the possibility to build tools for exploration of operads by means of explicit calculation.
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