Sample Python Sessions

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) 1999-2016, 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) 1999-2016, 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) 1999-2016, 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
>>>