Braid Representatives: Difference between revisions
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
| Line 4: | Line 4: | ||
<!--$$?BR$$--> |
<!--$$?BR$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
|||
{| width=70% border=1 align=center |
|||
| |
|||
<font color=blue><tt>In[2]:=</tt></font><font color=red><code> ?BR</code></font> |
|||
<tt>BR stands for Braid Representative. BR[k,l] represents a braid on k strands with crossings l={i1,i2,...}, where a positive index i within the list l indicates a right-handed crossing between strand number i and strand number i+1 and a negative i indicates a left handed crossing between strands numbers |i| and |i|+1. Each ij can also be a list of non-adjacent (i.e., commuting) indices. BR also acts as a "type caster": BR[K] will return a braid whose closure is K if K is given in any format that KnotTheory` understands. BR[K] where K is is a named knot with up to 10 crossings returns a minimum braid representative for that knot.</tt> |
|||
| |
|||
<font color=blue><tt>In[3]:=</tt></font><font color=red><code> BR::about</code></font> |
|||
<tt>The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See his article on the subject at arXiv:math.GT/0401051. Vogel's algorithm was implemented by Dan Carney in the summer of 2005 at the University of Toronto.</tt> |
|||
|} |
|||
<!--END--> |
<!--END--> |
||
Revision as of 10:02, 24 August 2005
Every knot and every link is the closure of a braid. KnotTheory` can also represent knots and links as braid closures:
(For In[1] see Setup)
|
In[2]:= BR stands for Braid Representative. BR[k,l] represents a braid on k strands with crossings l={i1,i2,...}, where a positive index i within the list l indicates a right-handed crossing between strand number i and strand number i+1 and a negative i indicates a left handed crossing between strands numbers |i| and |i|+1. Each ij can also be a list of non-adjacent (i.e., commuting) indices. BR also acts as a "type caster": BR[K] will return a braid whose closure is K if K is given in any format that KnotTheory` understands. BR[K] where K is is a named knot with up to 10 crossings returns a minimum braid representative for that knot. |
In[3]:= The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See his article on the subject at arXiv:math.GT/0401051. Vogel's algorithm was implemented by Dan Carney in the summer of 2005 at the University of Toronto. |
