Hyperelliptic Integrals to Elliptic Integrals
International audience 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...
Published in: | Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation |
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Main Author: | |
Other Authors: | , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2023
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Subjects: | |
Online Access: | https://hal.science/hal-04335021 https://doi.org/10.1145/3597066.3597111 |
Summary: | International audience 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. |
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