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example$ regina-python
Regina 7.0
Software for low-dimensional topology
Copyright (c) 1999-2021, The Regina development team
>>> ################################
>>> #
>>> # Sample Python Script
>>> #
>>> # Illustrates different queries and actions on a 3-manifold triangulation
>>> # and its normal surfaces.
>>> #
>>> # See the file "triangulation.session" for the results of running this
>>> # script.
>>> #
>>> ################################
>>>
>>> # Create a new (3,4,7) layered solid torus. This is a 3-tetrahedron
>>> # triangulation of a solid torus.
>>> t = Example3.lst(3, 4)
>>> print(t)
Bounded orientable 3-D triangulation, f = ( 1 5 7 3 )
>>>
>>> # Print the full skeleton of the triangulation.
>>> print(t.detail())
Size of the skeleton:
Tetrahedra: 3
Triangles: 7
Edges: 5
Vertices: 1
Tetrahedron gluing:
Tet | glued to: (012) (013) (023) (123)
-----+-------------------------------------------------------
0 | boundary boundary 1 (012) 1 (130)
1 | 0 (023) 0 (312) 2 (013) 2 (120)
2 | 1 (312) 1 (023) 2 (312) 2 (230)
Vertices:
Tet | vertex: 0 1 2 3
-----+--------------------------
0 | 0 0 0 0
1 | 0 0 0 0
2 | 0 0 0 0
Edges:
Tet | edge: 01 02 03 12 13 23
-----+--------------------------------
0 | 0 1 2 2 1 3
1 | 1 2 3 3 2 4
2 | 2 4 3 3 4 3
Triangles:
Tet | face: 012 013 023 123
-----+------------------------
0 | 0 1 2 3
1 | 2 3 4 5
2 | 5 4 6 6
>>>
>>> # Calculate some algebraic properties of the triangulation.
>>> print(t.homology())
Z
>>> print(t.homologyBdry())
2 Z
>>>
>>> # Test for 0-efficiency, which asks Regina to search for certain types
>>> # of normal surfaces.
>>> print(t.isZeroEfficient())
False
>>>
>>> # Make our own list of vertex normal surfaces in standard coordinates.
>>> surfaces = NormalSurfaces(t, NormalCoords.Standard)
>>>
>>> # Print the full list of vertex normal surfaces.
>>> print(surfaces.detail())
Embedded, vertex surfaces
Coordinates: Standard normal (tri-quad)
Number of surfaces is 9
1 1 1 1 ; 0 0 0 || 1 1 0 0 ; 1 0 0 || 0 0 0 0 ; 0 2 0
0 0 1 1 ; 1 0 0 || 1 1 1 1 ; 0 0 0 || 1 1 1 1 ; 0 0 0
0 0 0 0 ; 0 2 0 || 0 0 1 1 ; 1 0 0 || 1 1 1 1 ; 0 0 0
0 0 0 0 ; 0 0 2 || 0 0 0 0 ; 0 2 0 || 0 0 1 1 ; 1 0 0
1 1 0 0 ; 0 0 1 || 1 1 0 0 ; 0 0 0 || 0 0 0 0 ; 0 1 0
3 3 0 0 ; 0 0 1 || 1 1 0 0 ; 0 0 2 || 1 1 0 0 ; 0 0 1
0 0 1 1 ; 1 0 0 || 1 1 0 0 ; 1 0 0 || 0 0 0 0 ; 0 2 0
0 0 0 0 ; 0 1 0 || 0 0 0 0 ; 1 0 0 || 0 0 0 0 ; 0 1 0
1 1 1 1 ; 0 0 0 || 1 1 1 1 ; 0 0 0 || 1 1 1 1 ; 0 0 0
>>>
>>> # Print the Euler characteristic and orientability of each surface.
>>> for s in surfaces:
... print("Chi =", s.eulerChar(), "; Or =", s.isOrientable())
...
Chi = -1 ; Or = True
Chi = 0 ; Or = True
Chi = 0 ; Or = True
Chi = 0 ; Or = True
Chi = 0 ; Or = False
Chi = 1 ; Or = True
Chi = -2 ; Or = True
Chi = -1 ; Or = False
Chi = 1 ; Or = True
>>>
>>> # List all surfaces with more than one quad in the first tetrahedron.
>>> for s in surfaces:
... if s.quads(0,0) + s.quads(0,1) + s.quads(0,2) > 1:
... print(s)
...
0 0 0 0 ; 0 2 0 || 0 0 1 1 ; 1 0 0 || 1 1 1 1 ; 0 0 0
0 0 0 0 ; 0 0 2 || 0 0 0 0 ; 0 2 0 || 0 0 1 1 ; 1 0 0
>>>
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