An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings

Details An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings

2008-01-29

arxiv.org/abs/0801.4439v1

Mathematics

Commutative Algebra

preliminary abstract, 10 pages

Scientific paper

A \textit{symmetric ideal} $I \subseteq R = K[x_1,x_2,...]$ is an ideal that is invariant under the natural action of the infinite symmetric group. We give an explicit algorithm to find Gr\"obner 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 $R$.

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