Elementary Integration of Superelliptic Integrals
Thierry Combot

TL;DR
This paper introduces an algorithm for elementary integration of superelliptic integrals, capable of solving a broad class of such integrals efficiently under generic conditions.
Contribution
It presents a novel algorithm that solves the elementary integration problem for superelliptic integrals with specific algebraic conditions, improving computational efficiency.
Findings
Algorithm solves the integration problem in polynomial time for generic cases.
Complexity depends on degree, genus, and coefficient height of the polynomial.
Provides a theoretical foundation for symbolic integration of superelliptic functions.
Abstract
Consider a superelliptic integral with , a primitive th root of unity, and has simple roots and degree coprime with . Note the maximum of the degree of , the logarithmic height of the coefficients and the genus of . We present an algorithm which solves the elementary integration problem of generically in operations.
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