An ¥unknotting (unlinking) operation is defined by S. Jablan (1998) . Every selfcrossing point of a KL can be turned into an uncrossing by introducing a "mirror". This can be repeated until we obtain the unknot (link without selfcrossings). Analogously as we defined unknotting (unlinking) number, it is possible to define an ¥unknotting (unlinking) number u_{¥} (K) by the "classical" and "standard" definition, to prove that two definitions are equivalent, and make a Conjecture on u_{¥} number:
Every ¥change transforms an alternating knot to an alternating knot, so the set of all alternating knots is closed with regard to ¥changes. According to Tait's Flyping Theorem, all minimal projections of an alternating knot give the same result, so for every alternating knot it is sufficient to use only one minimal projection. The LinKnot function NoSelfCrossNo (webMathematica NoSelfCrossNo) calculates the u_{¥} number of a KL given by its Conway symbol, Dowker code, or Pdata according to this Conjecture. Again, a particular value of the u_{¥} number is a characteristic of a family : for the knot family (2k+1), (k ³ 1), u_{¥} ((2k+1)) = 1; for the knot family (2k) 2, (k ³ 1), u_{¥} ((2k) 2) = 2; for the knot family ((2k) (2l)), (k,l > 1), u_{¥} ((2k) (2l)) = 3, etc.
