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Equivariant Gröbner bases Krone, Robert


Families of polynomial ideals in high dimension but with symmetry often exhibit certain stabilization even as the dimension grows, for example being generated by the orbits of a short list of polynomials. Similarly an equivariant Gröbner basis of an ideal is a set of polynomials whose orbits form a Gröbner basis, which is a useful computational tool for working with these families of ideals. We describe the current state of equivariant Gröbner basis algorithms including criteria for guaranteeing termination and strategies for speeding up computation. This is joint work with Chris Hillar and Anton Leykin.

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