One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this distribution. After giving some counterexamples, we prove that this is the case for the vast majority of configurations.In the second part of the paper, the distribution of areas of sub-triangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.
This paper gives an algorithm for computing invariant rings of reductive groups in arbitrary characteristic. Previously, only algorithms for linearly reductive groups and for finite groups have been known. The key step is to find a separating set of invariants.
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