Hyperelliptic Integrals to Elliptic Integrals - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2023

Hyperelliptic Integrals to Elliptic Integrals

Résumé

Consider a hyperelliptic integral , , with . When S is of degree ≤ 4, such integral can be calculated in terms of elementary functions and elliptic integrals of three kinds . When S is of higher degree, it is typically non elementary, but it is sometimes possible to obtain an expression of I using also elliptic integrals when the Jacobian of y2 = S(x) has elliptic factors. We present an algorithm searching for elliptic factors and a modular criterion for their existence. Then, we present an algorithm for computing an expression of I using elliptic integrals, which always succeed in the completely decomposable Jacobian case.

Dates et versions

hal-04335021 , version 1 (11-12-2023)

Identifiants

Citer

Thierry Combot. Hyperelliptic Integrals to Elliptic Integrals. ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023, Jul 2023, Tromsø Norway, France. pp.191-198, ⟨10.1145/3597066.3597111⟩. ⟨hal-04335021⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More