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Algorithms for orbit closure separation for invariants and semi-invariants of matrices (1801.02043v2)
Published 6 Jan 2018 in math.RA, cs.CC, and math.AC
Abstract: We consider two group actions on $m$-tuples of $n \times n$ matrices. The first is simultaneous conjugation by $\operatorname{GL}_n$ and the second is the left-right action of $\operatorname{SL}_n \times \operatorname{SL}_n$. We give efficient algorithms to decide if the orbit closures of two points intersect. We also improve the known bounds for the degree of separating invariants in these cases.