Changes in this Release
- Automatically generated Release according to changes in the original databases
- See the web-sites of KnotInfo and LinkInfo for more information
This version introduces 2 new properties:
* `geometric_type`: There are three possible types: `hyperbolic`, `torus knot T(k,l)`, `satellite T(k,l)_(m,n)`. Where `k, l, m, n` are integers describing the winding numbers of the corresponding torus and cable constructions.
* `cosmetic_crossing`: A knot `K` supports a cosmetic crossing change if some nontrivial crossing change converts `K` into `K`. It is conjectured that no knot has a cosmetic crossing change. The new property indicates all the knots which satisfy the cosmetic crossing change conjecture.
In addition, this version includes a revision of the `braid_notation`. This was necessary because there were cases where the `braid_notation` corresponded to the reverse knot compared to the `pd_notation`. This revision also forces the `braid_notation` to start with $\pm 1$.
Note, that there are 16 knots for which two braid notations are recorded. These are:
K10_136 K11n_8 K11n_121 K11n_131 K12n_17 K12n_20 K12n_24 K12n_65 K12n_119 K12n_284 K12n_311 K12n_314 K12n_358 K12n_362 K12n_403 K12n_482
For example, the knot `K10_136` has braid index 4, and the first braid is of width 4 (and length 11). It has braid length 10, and the second braid has length 10 (and width 5). The listed knots are the only ones in the table for which the minimum length is not realized by a braid of minimal width.
Warning
These pairs of braid notation have been in the database before, but now their syntax has changed. Therefore, the `braid_notation` of these 16 knots is incompatible with the `braid` and `braid_notation` methods of the SageMath interface for all versions of SageMath, including the current version 10.4. If you want avoid this, you should not install this version of `database_knotinfo` in SageMath. A compatible SageMath interface is being worked on (see https://github.com/sagemath/sage/pull/38822).