Several sample Python sessions are reproduced below.
Each session was started by running
regina-python
from the command line.
Working with a triangulation
example$ regina-python
Regina 5.1
Software for low-dimensional topology
Copyright (c) 1999-2017, 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 = Triangulation3()
>>> t.insertLayeredSolidTorus(3,4)
<regina.engine.Simplex3 object at 0x11396e6e0>
>>> print t
Triangulation with 3 tetrahedra
>>>
>>> # 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.enumerate(t, NS_STANDARD)
>>>
>>> # Verify that the normal surface list is already a child packet of the
... # triangulation. This happens automatically whenever you enumerate
... # normal surfaces (or angle structures).
... if surfaces.parent() == t:
... print "OK: Parent-child relationship is correct."
... else:
... print "ERROR: Parent-child relationship is incorrect."
...
OK: Parent-child relationship is correct.
>>>
>>> # 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 i in range(surfaces.size()):
... s = surfaces.surface(i)
... 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 i in range(surfaces.size()):
... s = surfaces.surface(i)
... 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
>>>
>>> # Tidy up.
... # Delete the triangulation. This will automatically delete the surface
... # list, which is a child of the triangulation in the packet tree.
... t = None
>>>
Working with a packet tree
example$ regina-python
Regina 5.1
Software for low-dimensional topology
Copyright (c) 1999-2017, The Regina development team
>>> ################################
... #
... # Sample Python Script
... #
... # Illustrates the traversal and manipulation of an entire packet tree.
... #
... # See the file "tree.session" for the results of running this script.
... #
... ################################
...
>>> # Recreate the original SnapPea census of cusped hyperbolic manifolds
... # triangulated by at most 5 tetrahedra.
... census = Container()
>>> for i in range(415):
... mfd = SnapPeaCensusManifold(SnapPeaCensusManifold.SEC_5, i)
... tri = mfd.construct()
... tri.setLabel(mfd.name())
... census.insertChildLast(tri)
...
>>> # The triangulations are now all children of the "census" container.
... # Remove all triangulations with more than two tetrahedra.
... tri = census.firstChild()
>>> while tri != None:
... next = tri.nextSibling()
... if tri.size() > 2:
... tri.makeOrphan()
... tri = next
...
>>> # Print the homology of each remaining triangulation.
... tri = census.firstChild()
>>> while tri != None:
... print tri.label() + ":", tri.homology()
... tri = tri.nextSibling()
...
Gieseking manifold: Z
SnapPea m001: Z + Z_2
SnapPea m002: Z + Z_2
SnapPea m003: Z + Z_5
Figure eight knot complement: Z
>>>
Reporting progress of long operations
example$ regina-python
Regina 5.1
Software for low-dimensional topology
Copyright (c) 1999-2017, The Regina development team
>>> ################################
... #
... # Sample Python Script
... #
... # Illustrates progress reporting during long operations.
... #
... # See the file "progress.session" for the results of running this script.
... #
... ################################
...
>>> import time
>>>
>>> # Create an 18-tetrahedron triangulation of a knot complement with real
... # boundary faces (not an ideal vertex). The knot is L106003 from the
... # knot/link census. We used Regina to truncate the ideal vertex, and
... # then copied the isomorphism signature so that we can reconstruct the
... # triangulation here.
... sig = 'sfLfvQvwwMQQQccjghjkmqlonrnrqpqrnsnksaisnrobocksks'
>>> tri = Triangulation3(sig)
>>> print tri.size(), 'tetrahedra'
18 tetrahedra
>>>
>>> # Create a progress tracker to use during the normal surface enumeration.
... # This will report the state of progress while the enumeration runs in
... # the background.
... tracker = ProgressTracker()
>>>
>>> # Start the normal surface enumeration.
... # Because we are passing a progress tracker to enumerate(), the
... # enumeration will start in the background and control will return
... # immediately to the python console.
... surfaces = NormalSurfaces.enumerate(tri, NS_STANDARD, NS_VERTEX,
... NS_ALG_DEFAULT, tracker)
>>>
>>> # At this point the enumeration is up and running.
... # Output a progress report every half-second until it finishes.
... while not tracker.isFinished():
... print 'Progress:', tracker.percent(), '%'
... time.sleep(0.5)
...
Progress: 0.774536132812 %
Progress: 51.85546875 %
Progress: 89.0057373047 %
>>>
>>> # The surface enumeration is now complete.
... print surfaces.size(), 'normal surfaces'
2319 normal surfaces
>>>