2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114276Let E_G be a family of hyperelliptic curves over F2^(alg cl) with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function of E_g for g in a degree n extension field of F, which has as time complexity O(n^3) and memory requirements O(n^2). With a slightly different algorithm we can get time O(n^2,667) and memory O(n^2,5), and the computation of O(n) curves of the family can be done in time and space O(n^3). All these algorithms are polynomial in the genus.23 pagesNumber TheoryAlgebraic Geometry14Q05, 11G20 (Primary) 12H25, 14F30, 14G50 (Secondary)text