Computing Riemann---Roch spaces in algebraic function fields and related topics

Authors:
F. Hess
Affiliations:
Univ. of Bristol, Woodland Road
Venue:
Journal of Symbolic Computation
Year:
2002

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Abstract

We develop a simple and efficient algorithm to compute Riemann---Roch spaces of divisors in general algebraic function fields which does not use the Brill-Noether method of adjoints or any series expansions. The basic idea also leads to an elementary proof of the Riemann-Roch theorem. We describe the connection to the geometry of numbers of algebraic function fields and develop a notion and algorithm for divisor reduction. An important application is to compute in the divisor class group of an algebraic function field.