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 4.96
Software for 3-manifold topology and normal surface theory
Copyright (c) 1999-2013, 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 = NTriangulation()
>>> t.insertLayeredSolidTorus(3,4)
<regina.engine.NTetrahedron object at 0x10c5221a0>
>>> 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.getHomologyH1()
Z
>>> print t.getHomologyH1Bdry()
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 = NNormalSurfaceList.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.getTreeParent() == 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.getNumberOfSurfaces()):
... s = surfaces.getSurface(i)
... print "Chi =", s.getEulerChar(), "; 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.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, which is a child of the triangulation in the packet tree.
... t = None
>>>
Working with a packet tree
example$ regina-python
Regina 4.95
Software for 3-manifold topology and normal surface theory
Copyright (c) 1999-2013, 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.
... #
... ################################
...
>>> # Create a new census of all closed orientable 3-manifold
... # triangulations with two tetrahedra.
... census = NContainer()
>>> NCensus.formCensus(census, 2, NBoolSet.sTrue,
... NBoolSet.sTrue, NBoolSet.sFalse, 0, 0)
16
>>>
>>> # Calculate the homology of each triangulation in the census.
... # The triangulations are all children of the "census" container.
... tri = census.getFirstTreeChild()
>>> while tri != None:
... print tri.getPacketLabel() + ":", tri.getHomologyH1()
... tri = tri.getNextTreeSibling()
...
Item 1: Z_7
Item 2: Z_5
Item 3: Z
Item 4: Z_3
Item 5: Z_8
Item 6: 0
Item 7: 0
Item 8: 0
Item 9: Z_2
Item 10: 0
Item 11: 0
Item 12: Z_3
Item 13: 0
Item 14: Z_3
Item 15: 2 Z_2
Item 16: Z_2
>>>
>>> # Remove all triangulations with trivial homology from the tree.
... tri = census.getFirstTreeChild()
>>> while tri != None:
... next = tri.getNextTreeSibling()
... hom = tri.getHomologyH1()
... if hom.isTrivial():
... tri.makeOrphan()
... tri = next
...
<regina.engine.NTriangulation object at 0x1088396e0>
<regina.engine.NTriangulation object at 0x108839670>
<regina.engine.NTriangulation object at 0x1088397c0>
<regina.engine.NTriangulation object at 0x108839520>
<regina.engine.NTriangulation object at 0x108839750>
<regina.engine.NTriangulation object at 0x108839670>
>>>
>>> # Print the homology of each remaining triangulation.
... tri = census.getFirstTreeChild()
>>> while tri != None:
... print tri.getPacketLabel() + ":", tri.getHomologyH1()
... tri = tri.getNextTreeSibling()
...
Item 1: Z_7
Item 2: Z_5
Item 3: Z
Item 4: Z_3
Item 5: Z_8
Item 9: Z_2
Item 12: Z_3
Item 14: Z_3
Item 15: 2 Z_2
Item 16: Z_2
>>>
Reporting progress of long operations
example$ regina-python
Regina 4.95
Software for 3-manifold topology and normal surface theory
Copyright (c) 1999-2013, 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 = NTriangulation(sig)
>>> print tri.getNumberOfTetrahedra(), '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 = NProgressTracker()
>>>
>>> # 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 = NNormalSurfaceList.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: 0.0 %
Progress: 31.8218994141 %
Progress: 44.7033691406 %
Progress: 59.3591308594 %
Progress: 79.1180419922 %
Progress: 90.4166666667 %
>>>
>>> # The surface enumeration is now complete.
... print surfaces.getNumberOfSurfaces(), 'normal surfaces'
2319 normal surfaces
>>>