This report presents the algorithms for computing the Hadamard product, its residual, and its dual residual between formal power series in the dioid of counters (which is isomorphic to). The algorithms have been implemented in the C ++ toolbox ETVO ((Event-Time)-Variant Operators) [3], which, in turn, is based on the toolbox Min-Maxgd [5]. In this report, after the preliminaries (Section 1) and the definition of the Hadamard product and its residuals (Section 2), we present the algorithms and the proofs of their correctness (Section 3). Sections 1 and 2 are taken from [7], as well as the introduction of Section 3. The last part of the report (Section 4) constitutes a user guide for the C ++ implementation of the algorithms in ETVO, which is available at [6].
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