ReductionKnotLink
To minimize number of crossings of a KL you can
use the function ReductionKnotLink. As the input,
write P-data of the KL. The result is P-data of the minimized KL
and images of the original and minimized KL.
Remark: the reduction to a KL with a minimum number
of crossings produced by ReductionKnotLink sometimes is not complete (e.g., in
the case of "(3,-2) (3,-2)"= ".2.2"), so this can produce non-correct
results.
As the input you can also use non-minimal Conway
symbol of the KL in order to obtain obtain P-data of the minimized KL.
Please write Conway symbol of (non-minimal) KL as a Mathematica string, e.g., "2 -3 2 3 2"
The third posible input is Dowker code (with
signs) of KL,
giving
as the result P-data of the minimized KL.
The fourth input is Dowker code of KL (in
the Knotscape format),
giving
as the result P-data of the minimized KL.
  
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