On the complexity of skew arithmetic

Joris van der Hoeven (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

In this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients. As in the case of ordinary polynomials, we show that these complexities can be expressed in terms of the cost of multiplication.

Mots clés: Linear differential equations; algorithm; complexity; multiplication; local solution; gcd; lcm

Domaines: Calcul formel [cs.SC]; Complexité [cs.CC]; Logiciel mathématique [cs.MS]

Joris van der Hoeven. On the complexity of skew arithmetic. 2011. ⟨hal-00557750v4⟩