TY - JOUR
TI - Complexity of the Inversion Algorithm of Polynomial Mappings
AU - Bogdan, Paweł
TI - Complexity of the Inversion Algorithm of Polynomial Mappings
AB - 
	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   lgebra 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].
VL - 2016
IS - Volume 25
PY - 2017
SN - 1732-3916
C1 - 2083-8476
SP - 209
EP - 225
DO - 10.4467/20838476SI.16.016.6197
UR - https://ejournals.eu/en/journal/schedae-informaticae/article/complexity-of-the-inversion-algorithm-of-polynomial-mappings
KW - polynomial automorphism
KW - differential Galois theory
KW - computational complexity
KW - computer algebra system