The Determinant and the Signature: Difference between revisions

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{| align=center
{| align=center
|[[Image:5_1.gif|frame|none|<center>[[5_1]]</center>|120px]]
|[[Image:5_1.gif|frame|none|<center>[[5_1]]</center>|80px]]
|[[Image:10_132.gif|frame|none|<center>[[10_132]]</center>|120px]]
|[[Image:10_132.gif|frame|none|<center>[[10_132]]</center>|120px]]
|}
|}

Revision as of 22:26, 25 August 2005


(For In[1] see Setup)

In[2]:= ?KnotDet

KnotDet[K] returns the determinant of a knot K.

In[3]:= ?KnotSignature

KnotSignature[K] returns the signature of a knot K.

Thus, for example, the knots 5_1 and 10_132 have the same determinant (and even the same Alexander and Jones polynomials), but different signatures:

In[4]:=

KnotDet /@ {Knot[5, 1], Knot[10, 132]}

Out[4]=
{5, 5}
In[5]:=

{Equal @@ (Jones[#][q]& /@ {Knot[5, 1], Knot[10, 132]}), Equal @@ (Alexander[#][t]& /@ {Knot[5, 1], Knot[10, 132]})}

Out[5]=
{True, True}
In[6]:=

KnotSignature /@ {Knot[5, 1], Knot[10, 132]}

Out[6]=
{-4, 0}