Fundamental domains for Shimura curves

README: Description of the algorithms and how to use the program.

Update on July 2007: Description of the changes and additions made on July 2007.

QuatAlg.gap: The GAP program file. (More information about the GAP language can be found in the GAP home page)

Grp100: Summary of results for discriminants under 100, including generators, relations and fundamental regions for the corresponding Shimura curves.

CompRegion100.gap: A GAP script that was used to create the Grp100.txt file.

QuatRegionViewer.pl: A viewer in perl that can display the fundamental regions computed by the GAP functions. Below are a few screen shots for the case of discriminant 35.

The initial fundamental region:

Neighbouring regions:

Zooming in on a vertex: