An algorithm for finding symmetric Grobner bases in infinite dimensional rings

Authors:
Matthias Aschenbrenner;Christopher J. Hillar
Affiliations:
University of California, Los Angeles, Los Angeles, CA, USA;Texas A&M University, College Station, TX, USA
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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Abstract

A symmetric ideal I ⊂ R = K[x1,x2,...] is an ideal that is invariant under the natural action of the infinite symmetric group. We give an explicit algorithm to find Grobner bases for symmetric ideals in the infinite dimensional polynomial ring R. This allows for symbolic computation in a new class of rings. In particular, we solve the ideal membership problem for symmetric ideals of R.