Das, SuprajoSuprajoDasDubey, SaipriyaSaipriyaDubeyRoy, SudeshnaSudeshnaRoyVerma, Jugal K.Jugal K.Verma2025-10-212025-10-212025-11-0110.1016/j.jpaa.2025.1081072-s2.0-105018122882http://repository.iitgn.ac.in/handle/IITG2025/33305This article investigates the computational aspects of the ε-multiplicity. Primarily, we show that the ε-multiplicity of a homogeneous ideal I in a two-dimensional standard graded domain of finite type over an algebraically closed field of arbitrary characteristic, is always a rational number. In this situation, we produce a formula for the ε-multiplicity of I in terms of certain mixed multiplicities associated to I. In any dimension, under the assumptions that the saturated Rees algebra of I is finitely generated, we give a different expression of the ε-multiplicity in terms of mixed multiplicities by using the Veronese degree. This enabled us to make various explicit computations of ε-multiplicities. We further write a Macaulay2 algorithm to compute ε-multiplicity (under the Noetherian hypotheses) even when the base ring is not necessarily standard graded.falseEpsilon multiplicity | Hilbert functions | Local cohomology | Mixed multiplicitiesArticleNovember 202501081071WOS:001594386000001