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The problem of finding a positive distribution, which corresponds to a givencomplex density, is studied. By the requirement that the moments of thepositive distribution and of the complex density are equal, one can reduce theproblem to solving the matching conditions. These conditions are a set ofquadratic equations, thus Groebner basis method was used to find its solutionswhen it is restricted to a few lowest-order moments. For a Gaussian complexdensity, these approximate solutions are compared with the exact solution, thatis known in this special case.

Satisfying positivity requirement in the Beyond Complex Langevin approach