snappy-16-knots 1.21

Database of 16 crossing knots

This repository stores the manifold databases for 16 crossing knots, and includes the source code for the Python module snappy_16_knots which packages them up for use in SnapPy and Spherogram.

To install this package, do:

python -m pip install --upgrade snappy_16_knots

or, if you are using SageMath:

sage -pip install --upgrade snappy_16_knots

A prerequisite for using snappy_16_knots is snappy_15_knots; the above command should be able to automatically install snappy_15_knots, if it is not readily installed.

To use this module with SnapPy, you need to have SnapPy version 3.3.2 or later installed. You can check your SnapPy version with:

>>> import snappy
>>> snappy.__version__
'3.3.2'

If you have an older version of SnapPy, you can upgrade it with:

python -m pip install --upgrade snappy

or, if you are using SageMath:

sage -pip install --upgrade snappy

With the above setup, simply importing snappy will automatically import snappy_16_knots and make the extended census available in SnapPy. The extended census can then be accessed via SnapPy’s Manifold class. For example:

>>> m = snappy.Manifold('K16a101')
>>> m.triangulation_isosig()
'yLLLPLLAwMLzwQQLQcbehfiljimnonrqrsstuvwxxxdjqdgtehqxqajhfuajoffaacv_bacB'

>>> m = snappy.Manifold('K16a101(2,3)')
>>> m.triangulation_isosig()
''yLLLPLLAwMLzwQQLQcbehfiljimnonrqrsstuvwxxxdjqdgtehqxqajhfuajoffaacv_bacB(2,3)''

The iterator for all manifolds in this module, along with those in snappy_15_knots, is snappy.HTLinkExteriors. For example:

>>> len(snappy.HTLinkExteriors)
1822509

>>> for M in snappy.HTLinkExteriors[-9:-6]: print(M, M.volume())
K16n1008898(0,0) 22.8613896980723
K16n1008899(0,0) 17.0540820108716
K16n1008900(0,0) 16.9295548661239

>>> for M in snappy.HTLinkExteriors(num_cusps=2)[-3:]: print(M, M.volume(), M.num_cusps())
L14n40046(0,0)(0,0) 18.6813172532672 2
L14n40047(0,0)(0,0) 14.8257607028697 2
L14n40048(0,0)(0,0) 23.2884335333958 2

The raw source for the tables are in:

manifold_src/original_manifold_sources

stored as plain text CSV files for the potential convenience of other users. The triangulations themselves are stored in the “isosig” format of Burton, as described in the appendix to this paper with an added “decoration” suffix that describes the peripheral framing.