Identifying Knots within a List
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]:=
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Import["http://katlas.org/wiki/IdentifyWithin.m&action=raw"];
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In[3]:=
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Import["http://katlas.org/wiki/SubLink.m&action=raw"];
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In[4]:=
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IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]
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Out[4]=
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{Knot[5, 2]}
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![]() L11n150 |
![]() 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 is returned.