2020/05/08 by Simon Abelard, Abelard, Simon
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC) #cs.SC #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.2005.03964
Preliminary version
arxiv created 2020/05/08 · arxiv updated 2020/05/11
Let C be a plane curve given by an equation f(x,y)=0 with f∈ K[x][y] a monic squarefree polynomial. We study the problem of computing an integral basis of the algebraic function field K(C) and give new complexity bounds for three known algorithms dealing with this problem. For each algorithm, we study its subroutines and, when it is possible, we modify or replace them so as to take advantage of faster primitives. Then, we combine complexity results to derive an overall complexity estimate for each algorithm. In particular, we modify an algorithm due to Böhm et al. and achieve a quasi-optimal runtime.