The Determinant and the Signature: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
| Line 3: | Line 3: | ||
{{Startup Note}} |
{{Startup Note}} |
||
<!--$$?KnotDet$$--> |
<!--$$?KnotDet$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{{Help1|n=2|s=KnotDet}} |
|||
KnotDet[K] returns the determinant of a knot K. |
|||
{{Help2}} |
|||
<!--END--> |
<!--END--> |
||
<!--$$?KnotSignature$$--> |
<!--$$?KnotSignature$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{{Help1|n=3|s=KnotSignature}} |
|||
KnotSignature[K] returns the signature of a knot K. |
|||
{{Help2}} |
|||
<!--END--> |
<!--END--> |
||
| Line 16: | Line 24: | ||
<!--$$KnotDet /@ {Knot[5, 1], Knot[10, 132]}$$--> |
<!--$$KnotDet /@ {Knot[5, 1], Knot[10, 132]}$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{{InOut1|n=4}} |
|||
KnotDet /@ {Knot[5, 1], Knot[10, 132]} |
|||
{{InOut2|n=4}}<pre style="border: 0px; padding: 0em"><nowiki>{5, 5}</nowiki></pre> |
|||
{{InOut3}} |
|||
<!--END--> |
<!--END--> |
||
<!--$${Equal @@ (Jones[#][q]& /@ {Knot[5, 1], Knot[10, 132]}), Equal @@ (Alexander[#][t]& /@ {Knot[5, 1], Knot[10, 132]})}$$ |
<!--$${Equal @@ (Jones[#][q]& /@ {Knot[5, 1], Knot[10, 132]}), Equal @@ (Alexander[#][t]& /@ {Knot[5, 1], Knot[10, 132]})}$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{{InOut1|n=5}} |
|||
{Equal @@ (Jones[#][q]& /@ {Knot[5, 1], Knot[10, 132]}), Equal @@ (Alexander[#][t]& /@ {Knot[5, 1], Knot[10, 132]})} |
|||
{{InOut2|n=5}}<pre style="border: 0px; padding: 0em"><nowiki>{True, True}</nowiki></pre> |
|||
{{InOut3}} |
|||
<!--END--> |
|||
<!--$$KnotSignature /@ {Knot[5, 1], Knot[10, 132]}$$--> |
<!--$$KnotSignature /@ {Knot[5, 1], Knot[10, 132]}$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{{InOut1|n=6}} |
|||
KnotSignature /@ {Knot[5, 1], Knot[10, 132]} |
|||
{{InOut2|n=6}}<pre style="border: 0px; padding: 0em"><nowiki>{-4, 0}</nowiki></pre> |
|||
{{InOut3}} |
|||
<!--END--> |
<!--END--> |
||
Revision as of 22:25, 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}
|
