Barry M. Trager
ABSTRACT
This paper presents a new, simple, and efficient algorithm for factoring polynomials in several variables over an algebraic number field. The algorithm is then used iteratively, to construct the splitting field of a polynomial over the integers. Finally the factorization and splitting field algorithms are applied to the problem of determining the transcendental part of the integral of a rational function. In particular, a constructive procedure is given for finding the least degree extension field in which the integral can be expressed.
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Index Terms
- Algebraic factoring and rational function integration
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