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 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, NS_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
>>>
Working with a packet tree
example$ regina-python
Regina 7.0
Software for low-dimensional topology
Copyright (c) 1999-2021, 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.
>>> #
>>> # Since we are building a packet tree, we need to use PacketOfTriangulation3,
>>> # not the plain type Triangulation3 (which is not a packet type).
>>> census = Container()
>>> for i in range(415):
... mfd = SnapPeaCensusManifold(SnapPeaCensusManifold.SEC_5, i)
... census.append(make_packet(mfd.construct(), mfd.name()))
...
>>> # The triangulations are now all children of the "census" container.
>>> # Remove all triangulations with more than two tetrahedra.
>>> #
>>> # Since we are deleting children, we step through the children manually
>>> # instead of just iterating over children().
>>> tri = census.firstChild()
>>> while tri != None:
... next = tri.nextSibling()
... if tri.size() > 2:
... tri.makeOrphan()
... tri = next
...
>>> # Print the homology of each remaining triangulation.
>>> # This time we are not adding or removing children, so we can just iterate.
>>> for tri in census.children():
... print(tri.label() + ":", tri.homology())
...
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 7.0
Software for low-dimensional topology
Copyright (c) 1999-2021, 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 threading
>>> 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)
Bounded orientable 3-D triangulation, f = ( 1 20 37 18 )
>>>
>>> # 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 in a new thread.
>>> surfaces = None
>>> def run():
... global surfaces, tracker
... surfaces = NormalSurfaces(tri, NS_STANDARD, NS_VERTEX,
... NS_ALG_DEFAULT, tracker)
...
>>> thread = threading.Thread(target = run)
>>> thread.start()
>>>
>>> # At this point the enumeration is up and running.
>>> # Output a progress report every quarter-second until it finishes.
>>> while not tracker.isFinished():
... print('Progress:', tracker.percent(), '%')
... time.sleep(0.25)
...
Progress: 0.17578125 %
Progress: 54.20654296875 %
Progress: 91.80555555555556 %
>>>
>>> # The surface enumeration is now complete.
>>> thread.join()
>>> print(surfaces)
2319 embedded, vertex surfaces (Standard normal (tri-quad))
>>>
