# Identifying Knots within a List

`IdentifyWithin[L,H]`, whose code is available here, returns those elements from the list of knots $H$, whose invariant matches that of the knot $L$. 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["http://katlas.org/w/index.php?title=IdentifyWithin.m&action=raw"];`
 `In[3]:=` `Import["http://katlas.org/w/index.php?title=SubLink.m&action=raw"];`
 `In[4]:=` `IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]` `Out[4]=` `{Knot[5, 2]}`

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 $L$ is returned.