| Summary: | The computation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-primality has been object of study, mainly, for numerical semigroups due to its multiple applications to the Factorization Theory. However, its asymptotic version is less well known. In this work, we study the asymptotic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-primality for finitely generated cancelative commutative monoids. By using discrete geometry tools and the Python programming language we present an algorithm to compute this parameter. Moreover, we improve the proof of a known result for numerical semigroups.
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