✦ LIBER ✦
Computing Riemann–Roch Spaces in Algebraic Function Fields and Related Topics
✍ Scribed by F. Hess
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 389 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0747-7171
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✦ Synopsis
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.