First attempt at getting origami into Oscar

experimental/Origami/README.md

@@ -0,0 +1,13 @@
+# An example template for the experimental section
+
+## Aims
+
+This is an example for a file structure to set up a new package 
+in the experimental section. All files you find here are part of the 
+minimum requirements. See also the official Oscar documentation.
+
+## Status
+
+We plan to also provide a function to automatically copy this template 
+for you to start your own package. 
+

experimental/Origami/cylinder_diagrams/h11.dat

@@ -0,0 +1 @@
+[(0,3,1,2)-(0,3,1,2), (0)-(1) (1,2,3)-(0,2,3), (0,3)-(1,3) (1,2)-(0,2), (0,1)-(2,3) (2)-(1) (3)-(0)]

experimental/Origami/cylinder_diagrams/h1111.dat

@@ -0,0 +1 @@
+[(0,3,7,4,1,2,6,5)-(0,3,6,4,1,2,7,5), (0,7,2,1,6,4,5,3)-(0,6,7,5,2,1,4,3), (0,7,5,1,3,2,4,6)-(0,1,4,7,3,6,5,2), (0,7,5,2,3,4,6,1)-(0,2,4,7,6,5,3,1), (0,1,3,4,2)-(0,6,1,5,2,3,7) (5,7,6)-(4), (0,1,4,3,5)-(0,1,7,3,6) (2,7,6)-(2,4,5), (0,1,4,5,6,3,2)-(0,1,3,5,7,4,2) (7)-(6), (0,1,5,3,7,4)-(3,6) (2,6)-(0,1,7,2,5,4), (0,1,5,6,3,2)-(0,1,3,7,5,2) (4,7)-(4,6), (0,2,6)-(0,5,7,2,4,1) (1,5,3,7,4)-(3,6), (0,2,6,7,4)-(5) (1,3,5)-(0,2,7,1,3,6,4), (0,3,4,1,2,5)-(0,3,6,1,2,7) (6,7)-(4,5), (0,3,4,5,2,1)-(0,7,3,2,4,6,1) (6,7)-(5), (0,3,5,6)-(1,3,5,7) (1,2,4,7)-(0,2,4,6), (0,4,1,2,5,6,3)-(0,1,7,4,2,3,5) (7)-(6), (0,4,2,5,6,3,1)-(0,2,7,4,3,5,1) (7)-(6), (0,4,5,2,1)-(0,7,4,2,6,1) (3,7,6)-(3,5), (0,4,6,3,5)-(3,7,4) (1,2,7)-(0,1,6,2,5), (0,4,7,1)-(0,5,3,1,4,6,2) (2,5,3,6)-(7), (0,7)-(0,4,5,6) (1,5,3,6,2,4)-(1,7,3,2), (0,7,1,2)-(3,6,4,5) (3,6,4,5)-(0,7,1,2), (0,7,3,4)-(0,5,3,6) (1,5,2,6)-(1,7,2,4), (0,1,2)-(0,1,4,5,6,7) (3,4,7,5)-(2) (6)-(3), (0,1,3)-(0,1,6,7,4) (2,6,4)-(2,5) (5,7)-(3), (0,1,3,2,4)-(0,2,1,5,6,7) (5,7)-(4) (6)-(3), (0,1,3,4,2)-(0,1,5,7,6) (5,6)-(4) (7)-(2,3), (0,1,3,5)-(0,3,4,2,1,7) (2,6,4)-(5) (7)-(6), (0,1,3,5)-(1,3,4,2) (2,6,4)-(0,7,5) (7)-(6), (0,1,4)-(0,1,6,3,7) (2,3)-(2,5) (5,6,7)-(4), (0,1,4,2,3)-(0,6,2,1,7) (5,6)-(4) (7)-(3,5), (0,1,4,3,2)-(0,1,5,6,7) (5,7)-(2,4) (6)-(3), (0,1,6,5,2)-(7) (3,7)-(0,1,5,4,6,2) (4)-(3), (0,2,1)-(7) (3,4,5)-(6) (6,7)-(0,5,2,3,1,4), (0,2,4)-(0,2,6,3,1,7) (1,5,3)-(4) (6,7)-(5), (0,2,4)-(0,5,2,3,1) (1,6,3)-(4,7) (5,7)-(6), (0,2,4,3,5)-(0,6,3,2,7) (1,6)-(1,5) (7)-(4), (0,2,4,5)-(2,4,7) (1,3,6)-(0,1,3,5) (7)-(6), (0,2,6)-(0,5,2,7) (1,4,3,5)-(1,6,3) (7)-(4), (0,3)-(0,4,6,2) (1,4,5,2)-(1,7) (6,7)-(3,5), (0,3)-(0,2,6,4) (1,6,5,2)-(1,3,7) (4,7)-(5), (0,3)-(0,2,6,5,7) (1,7,6,4,2)-(1,3) (5)-(4), (0,3,1,2)-(5,7) (4,5)-(4,6) (6,7)-(0,3,1,2), (0,3,1,2)-(7) (4,5)-(6) (6,7)-(0,5,3,1,4,2), (0,3,1,2)-(6) (4,5,6)-(4,5,7) (7)-(0,3,1,2), (0,3,1,2)-(0,6,1,7) (4,6)-(3,5) (5,7)-(2,4), (0,3,1,2)-(4,7,5) (4,6,5)-(0,3,1,2) (7)-(6), (0,3,1,2)-(0,5,7,6,1) (4,6,5)-(3) (7)-(2,4), (0,3,4,1,2,5)-(0,2,6,1,3,7) (6)-(5) (7)-(4), (0,3,4,2,5,1)-(0,6,1,2,3,7) (6)-(4) (7)-(5), (0,3,4,2,5,1)-(0,6,1,2,3,7) (6)-(5) (7)-(4), (0,3,5,1)-(0,4,7,6) (2,6,4)-(5) (7)-(1,3,2), (0,4)-(0,6) (1,5)-(1,3,4,7) (2,7,6,3)-(2,5), (0,5)-(0,6,4) (1,3,2,4)-(1,7,5,2) (6,7)-(3), (0,5)-(0,4,6,7) (1,3,2,7,4)-(1,5,2) (6)-(3), (0,5)-(0,6,7) (1,6,3)-(1,4) (2,7,4)-(2,3,5), (0,5,2,3)-(7) (1,7,4)-(2,6,5) (6)-(0,4,1,3), (0,5,3)-(0,4,7) (1,4,2)-(1,5,6) (6,7)-(2,3), (0,7)-(0,5) (1,6)-(1,4) (2,4,3,5)-(2,7,3,6), (0,7,2)-(3,6) (1,3)-(0,5,1,4,2) (4,6,5)-(7), (0,7,3)-(0,2,5) (1,5,4,2)-(1,3,6,7) (6)-(4), (0,7,5)-(0,4) (1,3,2,4)-(1,5,6,7,2) (6)-(3), (0)-(4) (1,4,3,2,5)-(6,7) (6)-(5) (7)-(0,3,1,2), (0,1)-(0,2,5) (2,3)-(7) (4,5)-(6) (6,7)-(1,4,3), (0,1)-(5) (2,3,5,4)-(6,7) (6)-(0,2) (7)-(1,4,3), (0,1)-(0,4,5) (2,4,3,5)-(6,7) (6)-(2) (7)-(1,3), (0,1)-(0,2,5,6) (2,4,6)-(7) (3,7)-(1,4) (5)-(3), (0,1)-(0,2) (2,5,6)-(7) (3,7)-(1,6,4,5) (4)-(3), (0,1,2)-(0,1,5,6,7) (3,4)-(2) (5,7)-(4) (6)-(3), (0,1,2)-(0,5,1,6) (3,7)-(2,4) (4,5)-(7) (6)-(3), (0,1,4)-(0,1,7) (2,3)-(2,6) (5,6)-(4) (7)-(3,5), (0,2,1)-(7) (3)-(2) (4,5)-(6) (6,7)-(0,5,3,4,1), (0,2,1,3)-(4,5,7,6) (4)-(2) (5,6)-(3) (7)-(0,1), (0,2,3,1)-(0,6,1,2,7) (4,5)-(3) (6)-(4) (7)-(5), (0,2,4)-(0,2,3,1) (1,5,3)-(6,7) (6)-(5) (7)-(4), (0,2,4)-(0,2,7) (1,6,3)-(4) (5)-(6) (7)-(1,5,3), (0,3)-(0,5) (1,2)-(1,4) (4,6)-(3,7) (5,7)-(2,6), (0,3,1,2)-(4,6,5,7) (4)-(1) (5)-(0) (6,7)-(2,3), (0,3,1,2)-(6,7) (4,5)-(0,3,1,2) (6)-(5) (7)-(4), (0,3,1,2)-(7) (4,7)-(5,6) (5)-(4) (6)-(0,3,1,2), (0,3,5)-(0,3,7) (1,2,4)-(1,2,6) (6)-(5) (7)-(4), (0,4,2)-(3,7) (1,3)-(1,5) (5,7)-(0,6,2) (6)-(4), (0,4,2)-(6) (1,6,3)-(5,7) (5)-(4) (7)-(0,3,1,2), (0,5,1)-(6,7) (2,6)-(5) (3,7)-(0,4,1) (4)-(2,3), (0,5,2)-(1,7,3) (1,4,3)-(0,6,2) (6)-(4) (7)-(5), (0,5,2)-(1,7,3) (1,4,3)-(0,6,2) (6)-(5) (7)-(4), (0,6,1)-(7) (2,7)-(0,5,3,4,1) (3)-(2) (4,5)-(6), (0,7)-(5,6) (1,5)-(2,7) (2,4)-(1,3) (3,6)-(0,4), (0,7,2)-(1,6,3) (1,4,3)-(7) (5)-(4) (6)-(0,5,2), (0)-(3) (1)-(2) (2,4,3,5)-(6,7) (6)-(0,1) (7)-(4,5), (0)-(4) (1)-(2,3) (2,5,3,4)-(6,7) (6)-(5) (7)-(0,1), (0,1)-(0,3) (2,3)-(6) (4,6)-(5,7) (5)-(4) (7)-(1,2), (0,1)-(0,4) (2,3)-(1,7) (4,7)-(5,6) (5)-(3) (6)-(2), (0,1,2)-(0,1,7) (3)-(6) (4)-(5) (5,6)-(2) (7)-(3,4), (0,1,2)-(0,1,7) (3,4)-(5,6) (5)-(4) (6)-(2) (7)-(3), (0,2,1)-(6,7) (3,4)-(0,5,1) (5)-(2) (6)-(4) (7)-(3), (0,2,1)-(6,7) (3,4)-(0,5,1) (5)-(4) (6)-(2) (7)-(3), (0,3)-(7) (1,2)-(6) (4)-(2,3) (5)-(0,1) (6,7)-(4,5), (0,3,1)-(7) (2)-(3) (4,7)-(5,6) (5)-(4) (6)-(0,2,1), (0,3,1)-(7) (2)-(4) (4,7)-(5,6) (5)-(3) (6)-(0,2,1), (0,4)-(6) (1,6)-(4,7) (2,7)-(3,5) (3)-(1) (5)-(0,2), (0,4,1)-(7) (2)-(4) (3)-(5) (5,7)-(0,6,1) (6)-(2,3), (0,1)-(7) (2)-(0) (3)-(4) (4,7)-(5,6) (5)-(1) (6)-(2,3), (0,1)-(7) (2)-(1) (3)-(0) (4,7)-(5,6) (5)-(4) (6)-(2,3), (0,3)-(6,7) (1,2)-(4,5) (4)-(1) (5)-(3) (6)-(2) (7)-(0), (0,3)-(6,7) (1,2)-(4,5) (4)-(3) (5)-(0) (6)-(2) (7)-(1)]

experimental/Origami/cylinder_diagrams/h112.dat

@@ -0,0 +1 @@
+[(0,2,1,6,4,5,3)-(0,6,5,2,1,4,3), (0,2,5,1,3,6,4)-(0,2,6,5,1,3,4), (0,2,5,3,1,6,4)-(0,2,6,3,1,5,4), (0,6,2,3,4,5,1)-(0,2,4,6,5,3,1), (0,6,4,1,2,3,5)-(0,1,3,6,5,4,2), (0,1,2,3,4)-(0,3,6,1,5,2) (5,6)-(4), (0,1,3,4)-(0,5,1,6,3) (2,6,5)-(2,4), (0,1,3,4,5,2)-(0,1,4,6,3,2) (6)-(5), (0,1,3,5)-(0,3,4,2,1,6) (2,6,4)-(5), (0,1,3,6,4)-(3,5) (2,5)-(0,1,6,2,4), (0,1,4,2,3)-(0,1,6,2,5) (5,6)-(3,4), (0,1,4,5,2)-(0,1,6,4,2) (3,6)-(3,5), (0,1,4,5,2,3)-(0,6,3,1,2,4) (6)-(5), (0,1,4,5,3,2)-(0,1,3,6,4,2) (6)-(5), (0,1,5,6,3)-(4) (2,4)-(0,1,6,2,5,3), (0,2,3,1)-(0,4,2,6,1,5) (4,6,5)-(3), (0,2,3,4,1)-(0,6,2,3,5,1) (5,6)-(4), (0,2,3,5)-(1,2,3,6) (1,4,6)-(0,4,5), (0,2,4)-(0,2,5,3,1,6) (1,5,6,3)-(4), (0,2,4,1)-(0,2,6,1,5) (3,6,5)-(3,4), (0,2,4,5)-(2,4,6) (1,3,6)-(0,1,3,5), (0,2,6)-(0,5,2,4) (1,4,3,5)-(1,6,3), (0,2,6)-(0,5,2,4,1) (1,5,3,4)-(3,6), (0,3,1,2)-(4,6,5) (4,6,5)-(0,3,1,2), (0,3,4,2,1)-(0,6,2,3,5,1) (5,6)-(4), (0,3,4,2,1)-(0,6,3,2,5,1) (5,6)-(4), (0,3,4,5,2,1)-(0,2,4,6,3,1) (6)-(5), (0,3,4,5,2,1)-(0,6,3,2,4,1) (6)-(5), (0,3,5,1)-(6) (2,4,6)-(0,3,2,4,5,1), (0,3,6)-(0,4,1,3,5,2) (1,5,2,4)-(6), (0,4,2,6,3)-(2,5) (1,5)-(0,6,1,4,3), (0,4,5,2,1)-(0,2,6,4,1) (3,6)-(3,5), (0,5)-(0,3,4,6) (1,4,2,6,3)-(1,5,2), (0,6,4)-(0,3,5) (1,3,2,5)-(1,6,2,4), (0,1)-(0,2,5,4) (2,3,4)-(6) (5,6)-(1,3), (0,1)-(0,3,4,5,6) (2,3,6,4)-(1) (5)-(2), (0,1,2)-(0,4,1,6) (3,4)-(5) (5,6)-(2,3), (0,1,2)-(0,1,4,5,6) (3,4,6)-(2) (5)-(3), (0,1,2)-(0,1,4,5,6) (3,5)-(2) (4,6)-(3), (0,1,2)-(0,1,4,5,6) (3,6,4)-(2) (5)-(3), (0,1,3)-(0,1,6,4) (2,4)-(2,5) (5,6)-(3), (0,1,3,2)-(0,1,4,5,6) (4,6)-(2) (5)-(3), (0,1,3,2,4)-(0,2,1,5,6) (5)-(3) (6)-(4), (0,1,3,2,4)-(0,2,1,5,6) (5)-(4) (6)-(3), (0,1,4,2)-(0,5,1,6) (3,5)-(2) (6)-(3,4), (0,1,4,2,3)-(0,5,2,1,6) (5)-(3) (6)-(4), (0,1,4,2,3)-(0,5,2,1,6) (5)-(4) (6)-(3), (0,2)-(0,5) (1,3)-(1,4,2,6) (4,6,5)-(3), (0,2,1)-(4,6) (3,4)-(3,5) (5,6)-(0,2,1), (0,2,1)-(5) (3,4,5)-(3,4,6) (6)-(0,2,1), (0,2,1)-(3,6,4) (3,5,4)-(0,2,1) (6)-(5), (0,2,1,3)-(0,4,6,5,1) (4,5)-(3) (6)-(2), (0,2,1,3)-(0,6,1,5) (4,5)-(3) (6)-(2,4), (0,2,3,1)-(0,4,6,5) (4,5)-(3) (6)-(1,2), (0,2,3,1)-(0,5,1,2,6) (4,5)-(3) (6)-(4), (0,2,3,1)-(6) (4,6)-(0,2,5,3,1) (5)-(4), (0,2,4)-(0,2,3,1) (1,5,3)-(4,6) (6)-(5), (0,2,4)-(0,2,6,3,1) (1,5,3)-(4) (6)-(5), (0,2,4)-(0,3,1,2,6) (1,5,3)-(4) (6)-(5), (0,2,4)-(0,6,2,3,1) (1,5,3)-(4) (6)-(5), (0,2,4)-(1,2,3) (1,5,3)-(0,6,4) (6)-(5), (0,2,5)-(0,2,6) (1,3,4)-(1,3,5) (6)-(4), (0,3)-(0,4,5) (1,4,2)-(1,3,6) (5,6)-(2), (0,3)-(0,4,5) (1,4,2)-(1,6) (5,6)-(2,3), (0,3)-(0,4,5,2) (1,4,2)-(1,6) (5,6)-(3), (0,3)-(0,2,5,6) (1,4,6,2)-(1,3) (5)-(4), (0,3)-(0,2,4) (1,5,2)-(1,3,6) (4,6)-(5), (0,3)-(0,2,5) (1,5,4,2)-(1,3,6) (6)-(4), (0,3)-(0,2,5,6) (1,6,4,2)-(1,3) (5)-(4), (0,3,1)-(0,4,6,5) (2,5,4)-(1) (6)-(2,3), (0,3,1,2)-(5) (4,5)-(4,6) (6)-(0,3,1,2), (0,3,1,2)-(0,4,6,5,1) (4,5)-(3) (6)-(2), (0,3,1,2)-(5,6) (4,6)-(0,3,1,2) (5)-(4), (0,3,2,1)-(0,4,5,6) (4,6)-(1,3) (5)-(2), (0,3,4)-(3,6) (1,2,5)-(0,1,2,4) (6)-(5), (0,4)-(0,3) (1,5)-(1,4,6) (2,6,3)-(2,5), (0,4)-(0,3) (1,5)-(1,6) (2,6,3)-(2,4,5), (0,4,1)-(6) (2,3)-(5) (5,6)-(0,3,4,2,1), (0,4,2)-(5) (1,5,3)-(4,6) (6)-(0,3,1,2), (0,5)-(0,4) (1,3,2,4)-(1,5,6,2) (6)-(3), (0,5)-(0,4,6) (1,3,2,4)-(1,5,2) (6)-(3), (0,5)-(0,4) (1,4,2,3)-(1,6,2,5) (6)-(3), (0,5,1)-(0,4,6) (2,6)-(1,3) (3,4)-(2,5), (0,5,2)-(3,6) (1,3)-(0,1,4,2) (4,6)-(5), (0,5,4,1)-(6) (2,6)-(0,4,3,5,1) (3)-(2), (0,6,2)-(3) (1,3)-(0,5,1,4,2) (4,5)-(6), (0,6,2)-(1,5,3) (1,4,3)-(6) (5)-(0,4,2), (0)-(3) (1,3,2,4)-(5,6) (5)-(4) (6)-(0,2,1), (0)-(1) (1,3,4,2)-(5,6) (5)-(0,4) (6)-(2,3), (0)-(3) (1,4,2,3)-(5,6) (5)-(4) (6)-(0,2,1), (0)-(1,2) (1,4,2,3)-(5,6) (5)-(4) (6)-(0,3), (0,1)-(0,2,5) (2)-(3) (3,6)-(1,4) (4,5)-(6), (0,1)-(0,2) (2,4)-(6) (3,6)-(1,5,4) (5)-(3), (0,1)-(0,3,5,6) (2,4)-(1) (3,6)-(4) (5)-(2), (0,1)-(0,3) (2,5)-(1,6) (3,6)-(4,5) (4)-(2), (0,1,2)-(0,1,6) (3)-(5) (4,5)-(2) (6)-(3,4), (0,1,2)-(3,6,4,5) (3,4)-(2) (5)-(0) (6)-(1), (0,1,2)-(0,1,5,6) (3,4)-(2) (5)-(4) (6)-(3), (0,1,2)-(0,5,1,6) (3,4)-(2) (5)-(3) (6)-(4), (0,1,2)-(0,1,6) (3,6)-(4,5) (4)-(3) (5)-(2), (0,1,4)-(0,1,6) (2,3)-(2,5) (5)-(4) (6)-(3), (0,2)-(5) (1,3)-(6) (4)-(0,1) (5,6)-(2,4,3), (0,2)-(0,5) (1,3)-(1,6) (4,5)-(3) (6)-(2,4), (0,2)-(6) (1,4)-(3,5) (3,6)-(2,4) (5)-(0,1), (0,2,1)-(5,6) (3,4)-(0,2,1) (5)-(4) (6)-(3), (0,2,1)-(6) (3,6)-(4,5) (4)-(3) (5)-(0,2,1), (0,2,1)-(5,6) (3,6)-(0,4,1) (4)-(2) (5)-(3), (0,2,1)-(5,6) (3,6)-(0,4,1) (4)-(3) (5)-(2), (0,2,1)-(6) (3,6)-(0,5,4,1) (4)-(3) (5)-(2), (0,3,1)-(6) (2)-(4) (4,6)-(0,5,1) (5)-(2,3), (0,3,1)-(6) (2)-(3) (4,6)-(0,5,1) (5)-(2,4), (0,4,1)-(6) (2)-(3) (3,6)-(4,5) (5)-(0,2,1), (0,4,2)-(5,6) (1,3)-(0,1,2) (5)-(4) (6)-(3), (0,5,2)-(3) (1,3)-(1,6) (4)-(5) (6)-(0,4,2), (0)-(2) (1)-(3) (2,4,3)-(5,6) (5)-(4) (6)-(0,1), (0,1)-(0,6) (2)-(5) (3)-(4) (4,5)-(1) (6)-(2,3), (0,1)-(0,2) (2)-(3) (3,4)-(5,6) (5)-(4) (6)-(1), (0,2)-(6) (1)-(0) (3,6)-(4,5) (4)-(3) (5)-(1,2), (0,2)-(6) (1)-(3) (3,6)-(4,5) (4)-(0) (5)-(1,2), (0,4)-(6) (1)-(0) (2)-(3) (3,6)-(4,5) (5)-(1,2), (0,6)-(4,5) (1,2)-(3,6) (3)-(0) (4)-(2) (5)-(1), (0,6)-(4,5) (1,2)-(3,6) (3)-(2) (4)-(1) (5)-(0)]

experimental/Origami/cylinder_diagrams/h2.dat

@@ -0,0 +1 @@
+[(0,2,1)-(0,2,1), (0)-(1) (1,2)-(0,2)]

experimental/Origami/cylinder_diagrams/h22.dat

@@ -0,0 +1 @@
+[(0,5,3,1,2,4)-(0,5,3,1,2,4), (0)-(1) (1,2,5,4,3)-(0,2,5,4,3), (0,3,5)-(1,3,5) (1,2,4)-(0,2,4), (0,3,5,4)-(1,3,5,4) (1,2)-(0,2), (0)-(3) (1)-(2) (2,4,3,5)-(0,5,1,4), (0,1)-(2,3) (2,4)-(1,4) (3,5)-(0,5), (0,2)-(1,3) (1)-(0) (3,4,5)-(2,4,5), (0,3,4,5)-(1,4,5,2) (1)-(3) (2)-(0), (0,3,5)-(1,2,5) (1)-(0) (2,4)-(3,4), (0,2,1)-(3,5,4) (3)-(1) (4)-(2) (5)-(0), (0,5)-(3,4) (1,4)-(2,5) (2)-(1) (3)-(0), (0,5,2,1,4,3)-(0,4,2,1,5,3), (0,5,2,3,1,4)-(0,3,1,5,2,4), (0,5,3,2,1,4)-(0,1,3,4,5,2), (0,1,2,3)-(0,4,1,5,2) (4,5)-(3), (0,1,3,4)-(3,5) (2,5)-(0,1,2,4), (0,2,3,4,1)-(0,5,2,3,1) (5)-(4), (0,2,4)-(0,3,1,2,5) (1,5,3)-(4), (0,3,1,2)-(0,4,1,5) (4,5)-(2,3), (0,3,4)-(1,3,5) (1,2,5)-(0,2,4), (0,3,4,2,1)-(0,2,5,3,1) (5)-(4), (0,4,5,2)-(3) (1,3)-(0,5,1,4,2), (0,5,1)-(2,4,3) (2,4,3)-(0,5,1), (0,1)-(0,3,4,5) (2,3,5)-(1) (4)-(2), (0,1)-(0,2,4,5) (2,5)-(3) (3,4)-(1), (0,1,2)-(0,4,1,5) (3,5)-(2) (4)-(3), (0,1,3,2)-(0,1,4,5) (4)-(2) (5)-(3), (0,2,1)-(4) (3,4)-(3,5) (5)-(0,2,1), (0,2,1)-(4,5) (3,5)-(0,2,1) (4)-(3), (0,2,3)-(2,5) (1,4)-(0,1,3) (5)-(4), (0,3)-(0,4,5) (1,4,2)-(1,3) (5)-(2), (0,3,1)-(0,4,5) (2,4)-(1) (5)-(2,3), (0,3,1)-(5) (2,5)-(3,4) (4)-(0,2,1), (0,3,1,2)-(0,4,1,5) (4)-(2) (5)-(3), (0,5)-(3,4) (1,4)-(0,2) (2,3)-(1,5), (0,5)-(0,4) (1,4)-(1,3) (2,3)-(2,5), (0,1)-(0,5) (2)-(4) (3,4)-(1) (5)-(2,3), (0,2,1)-(3,4,5) (3)-(1) (4)-(2) (5)-(0), (0,3)-(5) (1)-(0) (2,5)-(3,4) (4)-(1,2), (0,3)-(0,5) (1,2)-(1,4) (4)-(3) (5)-(2), (0,5)-(3,4) (1,4)-(2,5) (2)-(0) (3)-(1)]

experimental/Origami/cylinder_diagrams/h4.dat

@@ -0,0 +1 @@
+[(0,4,2,1,3)-(0,4,2,1,3), (0)-(1) (1,2,4,3)-(0,2,4,3), (0,3,4)-(1,3,4) (1,2)-(0,2), (0,2)-(1,3) (1)-(0) (3,4)-(2,4), (0,3,4)-(1,4,2) (1)-(3) (2)-(0)]

experimental/Origami/docs/doc.main

@@ -0,0 +1,8 @@
+# An example documentation
+
+This is a sample text to outline the structure of the packages in the `Experimental` folder.
+You can show docstrings like this:
+```@docs
+    my_access_func(S::ExampleStruct)
+```
+

experimental/Origami/src/Origami.jl

@@ -0,0 +1,309 @@
+# Add your new types, functions, and methods here.
+
+module OrigamiHelper
+
+using ..GAP
+
+function __init__()
+  mod_p = "https://ag-weitze-schmithusen.github.io/ModularGroup/PackageInfo.g"
+  ori_p = "https://ag-weitze-schmithusen.github.io/Origami/PackageInfo.g"
+  GAP.Packages.install(mod_p)
+  GAP.Packages.install(ori_p)
+  GAP.Packages.load("Origami")
+end
+
+end
+
+include("exports.jl")
+include("types.jl")
+include("canonical.jl")
+include("deck_group.jl")
+include("action.jl")
+include("special_origami.jl")
+include("generate.jl")
+include("homology_action.jl")
+include("cyclic_torus_covers.jl")
+include("homology.jl")
+include("normal_origami.jl")
+include("systoles.jl")
+
+@doc raw"""
+    origami(h::PermGroupElem, v::PermGroupElem)
+
+This function constructs an Origami object from two given permutations h and v . A test is
+performed to check whether the surface described by the given permutations is connected, i.e.
+whether the group generated by the two permutations acts transitively.
+
+# Examples
+```jldoctest
+julia> h = @perm (1,2)
+(1,2)
+
+julia> v = @perm (2,3)
+(1,2)
+
+julia> o = origami(h,v)
+Origami ((1,2),(2,3), 3)
+```
+"""
+function origami(h::PermGroupElem, v::PermGroupElem)
+  d = max(degree(h), degree(v))
+  G = symmetric_group(d)
+  obj = GAP.Globals.Origami(GapObj(h), GapObj(v))
+  return Origami(obj, G(h), G(v), d)
+end
+
+# ugly workaround
+function from_GAP_origami(o::GapObj)
+  d = GAP.Globals.DegreeOrigami(o)::Int
+  G = symmetric_group(d)
+  h = PermGroupElem(G, GAP.Globals.HorizontalPerm(o))
+  v = PermGroupElem(G, GAP.Globals.VerticalPerm(o))
+  return origami(h, v)
+end
+
+function origami_disconnected(h::PermGroupElem, v::PermGroupElem, d::Integer)
+  return Origami(GAP.Globals.OrigamiNC(GapObj(h), GapObj(v), d), h, v, d)
+end
+
+function Base.:(==)(a::Origami, b::Origami)
+  # TODO rewrite this? for now use Gap equality
+  return (a.h == b.h) && (a.v == b.v)
+end
+
+function Base.hash(o::Origami, h::UInt=0x000000000)
+  return hash(o.h, hash(o.v, hash(o.d, h)))
+end
+
+function horizontal_perm(o::Origami)
+  return o.h
+end
+
+function vertical_perm(o::Origami)
+  return o.v
+end
+
+function degree(o::Origami)
+  return o.d
+end
+
+function Base.show(io::IO, o::Origami)
+  h = horizontal_perm(o)
+  v = vertical_perm(o)
+  d = degree(o)
+  print(io, "Origami ($(h),$(v), $(d))")
+end
+
+GapObj(O::Origami) = O.o
+
+@doc raw"""
+    stratum(o::Origami)
+
+This function calculates the stratum of an origami, i.e. the list of the (non-ascendingly
+ordered) non-zero degrees of the singularities. For a singularity of cone angle 2kπ the
+degree of the singularity is k-1.
+
+# Examples
+```jldoctest
+julia> o = origami(cperm([1,2],[3,4]), cperm([2,5,3,6],[4,7]))
+Origami ((1,2)(3,4),(2,5,3,6)(4,7), 7)
+
+julia> stratum(o)
+3-element Vector{Int64}:
+ 2
+ 1
+ 1
+```
+"""
+function stratum(o::Origami)
+  h = horizontal_perm(o)
+  v = vertical_perm(o)
+  commutator = comm(h, v)
+  cycs = cycles(commutator)
+  unsorted_stratum = [length(c) - 1 for c in cycs if length(c) > 1]
+  return sort!(unsorted_stratum; rev=true)
+end
+
+@doc raw"""
+    genus(o::Origami)
+
+Calculates the genus of an origami.
+
+# Examples
+```jldoctest
+julia> o = origami(cperm([1,2]), cperm([2,3]))
+Origami ((1,2),(2,3), 3)
+
+julia> genus(o)
+2
+```
+"""
+function genus(o::Origami)
+  return ZZ((sum(stratum(o)) + 2) / 2)
+end
+
+function veech_group(O::Origami)
+  # TODO use hashtables or not? Implement modular subgroup?
+  GAP.Globals.ComputeVeechGroupWithHashTables(GapObj(O))
+end
+
+function index_monodromy_group(o::Origami)
+  return GAP.Globals.IndexOfMonodromyGroup(GapObj(o))::Int
+end
+
+function sum_of_lyapunov_exponents(o::Origami)
+  return QQFieldElem(GAP.Globals.SumOfLyapunovExponents(GapObj(o)))
+end
+
+function translations(o::Origami)
+  h = horizontal_perm(o)
+  v = vertical_perm(o)
+
+  function act_on_tuples_by_conj(tup::Vector{PermGroupElem}, g::PermGroupElem)
+    return [tup[1]^g, tup[2]^g]
+  end
+
+  S = stabilizer(symmetric_group(degree(o)), [h, v], act_on_tuples_by_conj)[1]
+  return elements(S)
+end
+
+function is_hyperelliptic(o::Origami)
+  # check whether -1 is in the veech group
+  if !veech_group_is_even(o)
+    return false
+  end
+
+  x = horizontal_perm(o)
+  y = vertical_perm(o)
+  g = genus(o)
+
+  L = point_reflections(o)
+  L = filter(i -> order(i) == 2, L)
+
+  isempty(L) && return false
+
+  degree_list = collect(1:degree(o))
+  for sigma in L
+    # fixpoints
+    b =
+      length(setdiff(degree_list, moved_points(sigma))) +
+      length(setdiff(degree_list, moved_points(sigma * x))) +
+      length(setdiff(degree_list, moved_points(sigma * y)))
+
+    p1 = sigma * x^-1 * y^-1
+    p2 = y * x * (x * y)^-1
+    for i in degree_list
+      if i^p1 == i^p2
+        b += 1
+      end
+    end
+
+    if 2 * g + 2 - b == 0
+      return true
+    end
+  end
+
+  return false
+end
+
+function cylinder_structure(o::Origami)
+  gap_obj = GAP.Globals.CylinderStructure(GapObj(o))
+  cyl_lists = Vector{Vector{Int}}(gap_obj)
+  cyl_tuples = [(l[1], l[2]) for l in cyl_lists]
+  return cyl_tuples
+end
+
+function veech_group_and_orbit(o::Origami)
+  return GAP.Globals.VeechGroupAndOrbit(GapObj(o))
+end
+
+function veech_group_is_even(o::Origami)
+  return GAP.Globals.VeechGroupIsEven(GapObj(o))::Bool
+end
+
+function are_equivalent(o1::Origami, o2::Origami)
+  return GAP.Globals.OrigamisEquivalent(GapObj(o1), GapObj(o2))::Bool
+end
+
+# TODO why is this not in canonical.jl?
+function normalform_conjugators(o::Origami)
+  x = horizontal_perm(o)
+  y = vertical_perm(o)
+  n = degree(o)
+  G = PermGroupElem[]
+  sym = parent(x)
+
+  # Starting from each of the vertices found above, do a breadth-first search
+  # and list the vertices in the order they appear.
+  # This defines a permutation l with which we conjugate x and y.
+  # From the resulting list of pairs of permutations (all of which are by
+  # definition simultaneously conjugated to (x,y)) we choose the
+  # lexicographically smallest one as the canonical form.
+  for i in 1:n
+    L = fill(0, n)
+    seen = fill(false, n)
+    Q = [i]
+    seen[i] = true
+    numSeen = 1
+    L[i] = 1
+    while numSeen < n
+      v = popfirst!(Q)
+      wx = v^x
+      wy = v^y
+      if !seen[wx]
+        push!(Q, wx)
+        seen[wx] = true
+        numSeen += 1
+        L[wx] = numSeen
+      end
+      if !seen[wy]
+        push!(Q, wy)
+        seen[wy] = true
+        numSeen += 1
+        L[wy] = numSeen
+      end
+    end
+    push!(G, perm(sym, L))
+  end
+
+  return G
+end
+
+function point_reflections(o::Origami)
+  if !veech_group_is_even(o)
+    throw("VeechGroup must contain -1")
+  end
+
+  h = horizontal_perm(o)
+  v = vertical_perm(o)
+  o1 = origami(h^-1, v^-1)
+  h1 = horizontal_perm(o1)
+  v1 = vertical_perm(o1)
+  G = normalform_conjugators(o)
+  G1 = normalform_conjugators(o1)
+
+  f(i) = origami(h^i, v^i)
+  f1(i) = origami(h1^i, v1^i)
+
+  # origamis derived from the permutations above
+  O = f.(G)
+  # we need to calculate these to test find k s.t.
+  # sigma_i *origami *sigma_i^-1=delta_k(i)*origami_1*delta_k(i)^-1
+  O1 = f1.(G1)
+
+  # fitting the permuations together
+  result = PermGroupElem[]
+
+  l = length(O)
+  for i in 1:l
+    index = findfirst(item -> item == O[i], O1)
+    push!(result, G[i] * (G1[index])^-1)
+  end
+
+  return unique!(result)
+end
+
+function automorphisms(o::Origami)
+  # TODO is this structure useful?
+  return (translations(o), 1), (point_reflections(o), -1)
+end