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example$ regina-python
Regina 4.1.3
A Normal Surface Theory Calculator
Copyright (c) 1999-2004, Ben Burton
>>> ################################
... #
... # Sample Python Script
... #
... # Illustrates various queries and actions that can be performed upon 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 = regina.NTriangulation()
>>> t.insertLayeredSolidTorus(3,4)
<regina.NTetrahedron object at 0x401f3ed4>
>>> print t
Triangulation with 3 tetrahedra.
>>>
>>> # Dump skeletal information for the triangulation.
... print t.toStringLong()
Size of the skeleton:
Tetrahedra: 3
Faces: 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
Faces:
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.getHomologyH1()
Z
>>> print t.getHomologyH1Bdry()
2 Z
>>>
>>> # Test for 0-efficiency, which involves searching for particular types
... # of normal surface.
... print t.isZeroEfficient()
0
>>>
>>> # Get a list of normal surfaces in standard tri-quad coordinates.
... from regina import NNormalSurfaceList
>>> surfaces = NNormalSurfaceList.enumerate(t, NNormalSurfaceList.STANDARD)
>>>
>>> # Verify that the normal surface list has been made a child packet of the
... # triangulation. This happens automatically whenever the normal
... # surfaces (or angle structures) of a triangulation are enumerated.
... if surfaces.getTreeParent() == t:
... print "OK: Parent-child relationship is correct."
... else:
... print "ERROR: Parent-child relationship is incorrect."
...
OK: Parent-child relationship is correct.
>>>
>>> # Dump the entire list of vertex normal surfaces.
... print surfaces.toStringLong()
Embedded vertex normal surfaces
Coordinates: Standard normal (tri-quad)
Number of surfaces is 9
0 0 0 0 ; 0 1 0 || 0 0 0 0 ; 1 0 0 || 0 0 0 0 ; 0 1 0
0 0 1 1 ; 1 0 0 || 1 1 0 0 ; 1 0 0 || 0 0 0 0 ; 0 2 0
1 1 0 0 ; 0 0 1 || 1 1 0 0 ; 0 0 0 || 0 0 0 0 ; 0 1 0
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
1 1 1 1 ; 0 0 0 || 1 1 1 1 ; 0 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
3 3 0 0 ; 0 0 1 || 1 1 0 0 ; 0 0 2 || 1 1 0 0 ; 0 0 1
>>>
>>> # Print the Euler characteristic and orientability of each surface.
... for i in range(surfaces.getNumberOfSurfaces()):
... s = surfaces.getSurface(i)
... print "Chi =", s.getEulerCharacteristic(), "; Or =", s.isOrientable()
...
Chi = -1 ; Or = false
Chi = -2 ; Or = true
Chi = 0 ; Or = false
Chi = -1 ; Or = true
Chi = 0 ; Or = true
Chi = 0 ; Or = true
Chi = 1 ; Or = true
Chi = 0 ; Or = true
Chi = 1 ; Or = true
>>>
>>> # List all the surfaces with more than one quad in the first tetrahedron.
... for i in range(surfaces.getNumberOfSurfaces()):
... s = surfaces.getSurface(i)
... if s.getQuadCoord(0,0) + s.getQuadCoord(0,1) + s.getQuadCoord(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
>>>
>>> # Tidy up.
... # Delete the triangulation; this will automatically delete the surface
... # list since the surface list is a child packet of the triangulation.
... t = None
>>>
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