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MiS Preprint
90/2018
Sampling from the uniform distribution on an algebraic manifold
Let $\mathcal M$ be an open submanifold of an affine algebraic variety. We can pick a point from $\mathcal M$ by first choosing an affine-linear space $\mathcal L$ of complementary dimension and then choosing one of the intersection points $x$. We propose distributions on the set of linear spaces $\mathcal L$ and on the sets $\mathcal M \cap \mathcal L$ of intersection points such that the points $x$ chosen with the procedure above are uniformly distributed. We do the same for the projective setting and demonstrate the proposed method in the context of topological data analysis.