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Computing Riemann-Roch spaces in algebraic function fields and related topics. (English) Zbl 1058.14071

Summary: 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.

MSC:

14Q05 Computational aspects of algebraic curves
14H05 Algebraic functions and function fields in algebraic geometry
14C40 Riemann-Roch theorems
14-04 Software, source code, etc. for problems pertaining to algebraic geometry

Software:

Magma; KANT/KASH
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References:

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