Hyperelliptic Integrals to Elliptic Integrals
Pages 191 - 198
Abstract
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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Index Terms
- Hyperelliptic Integrals to Elliptic Integrals
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Publication History
Published: 24 July 2023
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ISSAC 2023
ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023
July 24 - 27, 2023
Tromsø, Norway
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