The Determinant and the Signature: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
DrorsRobot (talk | contribs) No edit summary |
No edit summary |
||
Line 19: | Line 19: | ||
{| align=center |
{| align=center |
||
|[[Image:5_1.gif|frame|none|<center>[[5_1]]</center>| |
|[[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} |