Complexity of the Inversion Algorithm of Polynomial Mappings

In this paper we will recall the inversion algorithm described in [1]. The algorithm classifies polynomial automorphisms into two sets: Pascal finite and Pascal infinite. In this article the complexity of the inversion algorithm will be estimated. To do so, we will present two popular ways how Computer Algebra Systems (CASes) keep the information about multivariate polynomials. We will define the complexity as the amount of simple operations performed by the algorithm as a function of the size of the input. We will define simple operations of the algorithm. Then we will estimate complexity of checking that the polynomial map is not a polynomial automorphism. To do so we will use theorem 3.1 from [1].

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).