See: Description
Class | Description |
---|---|
AbelianDifferentialAnalysisFunctionFactory | |
AbelianIntegralAnalysisFunctionFactory | |
AbelMap |
This support class performs the numerical integration of the
normalized differentials which is needed for abel's map.
|
FixPointsOfInvolution | |
HyperElliptic | |
Schottky | |
SchottkyAnalysis | |
SchottkyAnalysisFunction | |
SchottkyAnalysisFunction.ForIndexedProperty | |
SchottkyAnalysisFunction.ForProperty | |
SchottkyData | |
SchottkyDomain | |
SchottkyDomainSampler | |
SigmaAnalysisFunctionFactory |
This package implements the numerical methods and algorithms for the evaluation of certain automorphic functions and forms in the context of Schottky uniformization. A classical theorem states that for any Riemann surface R exists a Schottky group G such that is conformally equivalent to the quotient W/G, where W denotes the set of discontinuity of G. A Schottky group is a free, finitely generated, discontinuous group that is purely loxodromic, i.e., a Schottky group of rank N, which equals the genus of the associated Riemann surface, can always be generated by N loxodromic transformations s1,...,sN. Further a loxodromic transformation si can be defined by its fixed points Ai and Bi and the loxodromic factor mi, with |mi|<1.
Thus all Schottky groups of rank N can be associated to a list of 3N complex
values
S = { A1, B1, m1, ... , AN, BN, mN }
which is called the Schottky data.