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In this paper, we present a modular strategy which describes key propertiesof the absolute primary decomposition of an equidimensional polynomial idealdefined by polynomials with rational coefficients. The algorithm we design isbased on the classical technique of elimination of variables and colon idealsand uses a tricky choice of prime integers to work with. Thanks to thistechnique, we can obtain the number of absolute irreducible components, theirdegree, multiplicity and also the affine Hilbert function of the reducedcomponents (namely, their initial ideal w.r.t. a degree-compatible termordering) .

Modular absolute decomposition of equidimensional polynomial ideals