Factoring bivariate lacunary polynomials without heights

Arkadev Chattopadhyay (1) , Bruno Grenet (2) , Pascal Koiran (2) , Natacha Portier (2) , Yann Strozecki (3)

1 DCS - Department of Computer Science [University of Toronto]
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 LRI - Laboratoire de Recherche en Informatique

We present an algorithm which computes the multilinear factors of a bivariate polynomials. It is based on a new Gap theorem which allows to test whether a polynomial of the form P(X,X+1) is identically zero in time polynomial in the number of terms of P(X,Y). The algorithm we obtain is more elementary than the one by Kaltofen and Koiran (ISSAC'05) since it relies on the valuation of polynomials of the previous form instead of the height of the coefficients. As a result, it can be used to find some linear factors of polynomials over a field of large finite characteristic in probabilistic polynomial time.

Domains: Computer Science [cs]; Computational Complexity [cs.CC]; Computer Science [cs]; Symbolic Computation [cs.SC]

Arkadev Chattopadhyay, Bruno Grenet, Pascal Koiran, Natacha Portier, Yann Strozecki. Factoring bivariate lacunary polynomials without heights. 38th International Symposium on Symbolic and Algebraic Computation, ACM, Boston, United States. p 141-148, ⟨10.1145/2465506.2465932⟩. ⟨ensl-00738542⟩