Elementary Integration of Superelliptic Integrals - Archive ouverte HAL
Communication Dans Un Congrès Année : 2021

Elementary Integration of Superelliptic Integrals

Résumé

Consider a superelliptic integral $I=\int P/(Q S^1/k ) dx$ with $\mathbbK =\mathbbQ (ξ)$, ξ a primitive kth root of unity, $P,Q,S\in\mathbbK [x]$ and S has simple roots and degree coprime with k. Note d the maximum of the degree of $P,Q,S$, h the logarithmic height of the coefficients and g the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of I generically in $O((kd)^ømega+2g+1 h^g+1 )$ operations.

Dates et versions

hal-03510201 , version 1 (04-01-2022)

Identifiants

Citer

Thierry Combot. Elementary Integration of Superelliptic Integrals. ISSAC '21: International Symposium on Symbolic and Algebraic Computation, Jul 2021, Virtual Event Russian Federation, Russia. pp.99-106, ⟨10.1145/3452143.3465540⟩. ⟨hal-03510201⟩
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