On the complexity of computing integral bases of function fields
Simon Abelard
Abstract: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 algorit… Show more
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