Together with the classical ones, Conway symbols are used for the first time as an alternative notation in the book Knots and Links by D. Rolfsen, and after that by some other authors (e.g., C.C. Adams, 1994). However, if you try to draw some KLs from their Conway symbols, you will sometimes be surprised: the projection obtained will not be isomorphic with that given by D. Rolfsen. For example, in the case of the knot 9_{15}, it is clear that from its Conway symbol 2 3 2 2 we obtain the projection with 5, and not with 4 digons. It is interesting to notice that in Conway symbols of all nonalternating polyhedral KLs with n £ 10 crossings the symbol .1, i.e., a single vertex with a changed sign never appears, except in the case of the 4component link "103*1.1.1.1::.1" (or 10^{***} according to Conway's paper). The first polyhedral nonalternating knots that cannot be expressed by Conway symbols without .1s will be the 12crossing knots
In the program Knot 2000 (K2K), to get started by using the function GetPdatabyTracking (webMathematica GetPdatabyTracking), you need to draw a KL diagram on the mousetracking window, and then get its Pdata. Thanks to the LinKnot function fCreatePData (webMathematica fCreatePData), instead of the graphical input, you can use the Conway notation of KLs represented as a Mathematica string. For example, the figureeight knot 4_{1} is denoted by "2 2", knot 9_{5} by "5 1 3", link 5_{1}^{2} is denoted by "2 1 2", link 9_{21}^{2} by "3 1,3,2" (for all of them a space between tangles denotes a product of tangles), etc. A sequence of k pluses at the end of the Conway symbol is denoted by +k, and a sequence of k minuses by +k (e.g., knot 10_{76} given in Conway notation as 3,3,2++ is denoted by "3,3,2+2", and the link 9_{17}^{3} given in Conway notation as 3,2,2,2 by "3,2,2,2+2"). The space denoting a product of tangles is used in the same way in all other symbols. For example, the knot 10_{133} is denoted by "2, 2 1,2+1", and the knot 10_{154} by "(2 1,2) (2 1,2)" (with spaces).
