|The LinKnot function
fDowfromPD (webMathematica fDowfromPD)
produces Dowker code of a KL from P-data.
For every KL you can compute its writhe by using the function WritheKnotFromPdata (webMathematica WritheKnotFromPdata), and calculate the P-data of its mirror image by using the function GetMirrorImageKnot (webMathematica GetMirrorImageKnot). For example, for the knot K = "2 3 4 5" the writhe of K is -10, and its mirror image is given by the following P-data:
Every notation has its advantages and disadvantages. A minimal Dowker code uniquely defines a KL. Dowker codes or P-data are indispensable in any communication with a computer, where an input is always a code given by some number sequences. That information is almost unusable for us: we need some richer information having geometrical-topological contents almost directly visible from it, as in the case of the Conway notation. We designed the program LinKnot in an attempt to use KLs in the Conway notation as an input and to be able to work with classes of KLs: with families or worlds. This is crucial for understanding general properties of KLs extendable to these classes (families, worlds), calculated in a general form, and even expressed by general formulas.
The LinKnot function Dow (webMathematica Dow) calculates a Dowker code with signs for every KL given by its Conway symbol. For example, for the link K="111*2.2.2.-2 0.2 0.-2 0" it calculates its Dowker code
In order to translate one notation to another, in addition to the already mentioned LinKnot function fCreatePData converting Conway symbols into P-data, K2K function KnotbyDT (webMathematica KnotbyDT) converts DT-notation of knots (in Knotscape format) into P-data. Because these functions work only with knots, LinKnot includes the conversion function fPDataFromDow (webMathematica fPDataFromDow) that calculates P-data for KLs as well, given in DT-notation (in Knotscape format), and function fPDataFromDowker (webMathematica fPDataFromDowker) calculates P-data for KL given by Dowker code with signs. The LinKnot function fKnotscapeDow (webMathematica fKnotscapeDow) calculates a DT-code for any KL given by its Conway symbol.