To install the "foliar" module into SageMath+SnapPy do the following in this directory:
sage -pip install .
You can test to make sure all is well by doing:
sage -python -m foliar.test
which should conclude with a message such as:
All doctests: 0 failures out of 73 tests.
Example of searching for a foliar orientation on various triangulations of a closed manifold:
sage: import snappy, foliar sage: M = snappy.Manifold('m004(1,2)') sage: eo = foliar.first_foliation(M, 5, 25) sage: eo.gives_foliation() True sage: eo.euler_class_vanishes() True
Example of searching for a persistently foliar orientation on a 1-cusped manifold:
sage: m004 = snappy.Manifold('m004') sage: foliar.degeneracy_slopes(m004) [(1, 0)] sage: m003 = snappy.Manifold('m003') sage: foliar.degeneracy_slopes_with_search(m003) ([], [])
Note here that m003 is Floer simple and hence nothing is found.
For many more useful examples, see the docstrings the files "src/main.py" and "src/edge_orient.py".
The file "foliar_tris/persistent_knots.csv.bz2" contains the persistent foliar orientations for some 1.2 million knot exteriors.
It would not be hard to merge the code here into SnapPy proper, and so this should be done.