Talking with SnapPy

Since Regina 4.95, a default installation of Regina can talk directly with a default installation of SnapPy on many platforms. This includes macOS 10.7 or greater (if you installed the SnapPy app bundle in the usual Applications folder), and GNU/Linux (if your SnapPy uses the default system Python installation).

Simply type import snappy from within any of Regina's Python environments. To send information back and forth between Regina and SnapPy:

Regarding fillings and peripheral curves: Regina does not store fillings or peripheral curves for its own native triangulation packets, as represented by the Triangulation3 class. However, it does store fillings and peripheral curves for its hybrid SnapPea triangulation packets, as represented by the SnapPeaTriangulation class. The trade-off is that the native Triangulation3 class offers Regina's full fine-grained control over the triangulation, whereas the hybrid SnapPeaTriangulation class has a more limited (largely read-only) interface.

If you wish to send the complement of a native Regina Link to SnapPy, you can pass your link directly to the SnapPeaTriangulation constructor, which will preserve the peripheral curves from the link diagram; then you can pass this to SnapPy via SnapPeaTriangulation.snapPea() as above.

Regarding the interface: the SnapPeaTriangulation class inherits from Triangulation3, and so you can use it anywhere that a read-only triangulation is expected (in particular, you can use it for enumerating vertex normal surfaces or angle structures). However, because SnapPeaTriangulation must maintain two synchronised copies of the triangulation (Regina's and SnapPea's), it is essentially read-only: any attempt to modify the triangulation using Regina's native routines (e.g., pachner() or barycentricSubdivision()) will cause the SnapPea triangulation to delete itself and become a “null triangulation” instead.

The following Python session illustrates several of the concepts discussed above.

bab@ember:~$ regina-python 
Regina 7.0
Software for low-dimensional topology
Copyright (c) 1999-2021, The Regina development team
>>> import snappy
>>> m = snappy.Manifold('m001')
>>> t = SnapPeaTriangulation(m._to_string())
>>> print t.detail()
Size of the skeleton:
  Tetrahedra: 2
  Triangles: 4
  Edges: 2
  Vertices: 1

Tetrahedron gluing:
  Tet  |  glued to:      (012)      (013)      (023)      (123)
  -----+-------------------------------------------------------
    0  |               1 (103)    1 (320)    1 (210)    1 (132)
    1  |               0 (320)    0 (102)    0 (310)    0 (132)

Vertices:
  Tet  |  vertex:    0   1   2   3
  -----+--------------------------
    0  |             0   0   0   0
    1  |             0   0   0   0

Edges:
  Tet  |  edge:   01  02  03  12  13  23
  -----+--------------------------------
    0  |           0   1   1   1   1   0
    1  |           0   1   1   1   1   0

Triangles:
  Tet  |  face:  012 013 023 123
  -----+------------------------
    0  |           0   1   2   3
    1  |           2   0   1   3

Tetrahedron shapes:
  0: ( -1.60812e-16, 1 )
  1: ( -1.60812e-16, 1 )

Cusps:
  0: Vertex 0, complete

>>> print t.hasStrictAngleStructure()
True
>>> print AngleStructures(t).detail()
4 vertex angle structures (no restrictions):
0 1 0 ; 1 0 0
0 0 1 ; 1 0 0
1 0 0 ; 0 1 0
1 0 0 ; 0 0 1

>>> t2 = Example3.figureEight()
>>> m2 = snappy.Manifold(t2.snapPea())
>>> print m2.volume()
2.02988321282
>>>