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We consider logarithmic vector fields parametrized by finite collections ofweighted hyperplanes. For a finite collection of weighted hyperplanes in atwo-dimensional vector space, it is known that the set of such vector fields isa free module of rank two whose basis elements are homogeneous. We give analgorithm to construct a homogeneous basis for the module.

An Algorithm to Construct A Basis for the Module of Logarithmic Vector Fields