Identifying Knots within a List

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IdentifyWithin[L,H], whose code is available here, returns those elements from the list of knots , whose invariant matches that of the knot . It can also recognize mirrors and connected sums of the knots in the list. Its options include turning off (on) the search for connected sums with ConnectedSum->False (True) and choosing the invariants to be used in identification by selecting, for example, Invariants->{Jones[#][q]&, HOMFLYPT[#][a,z]&}. IdentifyWithin can be used together with SubLink to determine the components of a link. For the second component of link L11n150, for instance, we get:

(For In[1] see Setup)

In[2]:= Import[""];
In[3]:= Import[""];
In[4]:= IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]
Out[4]= {Knot[5, 2]}
5 2.gif

Unfortunately, the program does not provide absolute identification when all the used invariants cannot distinguish between two or more different knots. In that case, a list of possible candidates for is returned.