Computations of Knot Invariants
                          Thomas Wolf
                          23 Feb 2023

https://cariboutests.com/games/knots/uk3-15.txt
has 2 lines for each knot. The first line shows the name of the knot.
The second line shows 3 numbers:
- the unknotting number,
- the minimal number of simplifying crossings of all minimal crossing diagrams
- the maximal number of simplifying crossings of all minimal crossing diagrams
Method of computation: A database holds for every knot with
crossing number <= 15 all diagrams or most diagrams with the
minimal number of crossing. That can be up to several 1000
diagrams for a single knot. For all of them all crossings are
switched individually and the resulting diagram is maximally
simplified. If the diagram is not recognized then all crossings
are switched individually and so on. A database holds all already
computed unknotting numbers. This is used and extended in the
computation.
 
https://cariboutests.com/games/knots/colour3-15-N.txt
has 1 line for each knot. The knot name is followed by | which is
followed by a sequence of numbers separated by |. These numbers
are the non-trivial diagonal elements of the Smith Normal form of
the coefficient matrix of the colouring conditions a+b = 2c. Each
number is a multiple of all numbers to its right. All these
numbers are the n in the colouring conditions a+b=2c mod n such
that non-trivial solutions (colourings) exist. The multiplicity
of n is given by how many of these numbers have n as a factor.

https://cariboutests.com/games/knots/HOMFLY3-15.txt
includes for each knot with crossing number <=15
the HOMFLY polynomial defined through aP(L+) - a⁻¹P(L-) = zP(L0).
The first line contains the knot name. The second line contains
the number of terms. Each further line gives 3 numbers describing
the term: the coefficient and the exponents of a and z in the term.
A 278 MB file containing HOMFLY polynomials of all knots with
up to 16 crossings is available.