Computing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics

F Hess

Research output: Contribution to journalArticle (Academic Journal)peer-review

70 Citations (Scopus)

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 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 contributionComputing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics
Original languageEnglish
Pages (from-to)425 - 445
Number of pages20
JournalJournal of Symbolic Computation
Volume33 (4)
Publication statusPublished - Apr 2002

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