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 nor 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.
|Translated title of the contribution||Computing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics|
|Pages (from-to)||425 - 445|
|Number of pages||20|
|Journal||Journal of Symbolic Computation|
|Publication status||Published - Apr 2002|