10 165 - Revision history

ScottTestRobot at 21:57, 1 September 2005

2005-09-01T21:57:12Z

DrorsRobot at 22:40, 31 August 2005

2005-08-31T22:40:28Z

← Older revision		Revision as of 18:40, 31 August 2005
Line 3:		Line 3:
	<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)		<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
	<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->		<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
	<!-- -->		<!-- <math>\text{Null}</math> -->
	<!-- -->		<!-- <math>\text{Null}</math> -->
	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
Line 43:		Line 43:
	coloured_jones_4 = <math>q^{84}-3 q^{83}-q^{82}+5 q^{81}+3 q^{80}+8 q^{79}-17 q^{78}-18 q^{77}+2 q^{76}+13 q^{75}+59 q^{74}-8 q^{73}-50 q^{72}-54 q^{71}-39 q^{70}+121 q^{69}+77 q^{68}+13 q^{67}-93 q^{66}-197 q^{65}+51 q^{64}+120 q^{63}+188 q^{62}+44 q^{61}-285 q^{60}-142 q^{59}-47 q^{58}+278 q^{57}+315 q^{56}-148 q^{55}-250 q^{54}-348 q^{53}+148 q^{52}+508 q^{51}+131 q^{50}-166 q^{49}-595 q^{48}-113 q^{47}+541 q^{46}+392 q^{45}+14 q^{44}-723 q^{43}-366 q^{42}+490 q^{41}+589 q^{40}+183 q^{39}-787 q^{38}-570 q^{37}+416 q^{36}+745 q^{35}+339 q^{34}-798 q^{33}-748 q^{32}+284 q^{31}+830 q^{30}+506 q^{29}-674 q^{28}-839 q^{27}+56 q^{26}+718 q^{25}+614 q^{24}-372 q^{23}-718 q^{22}-161 q^{21}+405 q^{20}+520 q^{19}-67 q^{18}-401 q^{17}-194 q^{16}+104 q^{15}+266 q^{14}+48 q^{13}-124 q^{12}-87 q^{11}-7 q^{10}+71 q^9+25 q^8-20 q^7-14 q^6-6 q^5+10 q^4+3 q^3-4 q^2+1</math> \|		coloured_jones_4 = <math>q^{84}-3 q^{83}-q^{82}+5 q^{81}+3 q^{80}+8 q^{79}-17 q^{78}-18 q^{77}+2 q^{76}+13 q^{75}+59 q^{74}-8 q^{73}-50 q^{72}-54 q^{71}-39 q^{70}+121 q^{69}+77 q^{68}+13 q^{67}-93 q^{66}-197 q^{65}+51 q^{64}+120 q^{63}+188 q^{62}+44 q^{61}-285 q^{60}-142 q^{59}-47 q^{58}+278 q^{57}+315 q^{56}-148 q^{55}-250 q^{54}-348 q^{53}+148 q^{52}+508 q^{51}+131 q^{50}-166 q^{49}-595 q^{48}-113 q^{47}+541 q^{46}+392 q^{45}+14 q^{44}-723 q^{43}-366 q^{42}+490 q^{41}+589 q^{40}+183 q^{39}-787 q^{38}-570 q^{37}+416 q^{36}+745 q^{35}+339 q^{34}-798 q^{33}-748 q^{32}+284 q^{31}+830 q^{30}+506 q^{29}-674 q^{28}-839 q^{27}+56 q^{26}+718 q^{25}+614 q^{24}-372 q^{23}-718 q^{22}-161 q^{21}+405 q^{20}+520 q^{19}-67 q^{18}-401 q^{17}-194 q^{16}+104 q^{15}+266 q^{14}+48 q^{13}-124 q^{12}-87 q^{11}-7 q^{10}+71 q^9+25 q^8-20 q^7-14 q^6-6 q^5+10 q^4+3 q^3-4 q^2+1</math> \|
	coloured_jones_5 = <math>q^{125}-3 q^{124}-q^{123}+5 q^{122}+3 q^{121}+3 q^{120}-2 q^{119}-15 q^{118}-21 q^{117}+4 q^{116}+26 q^{115}+40 q^{114}+33 q^{113}-15 q^{112}-80 q^{111}-96 q^{110}-27 q^{109}+73 q^{108}+158 q^{107}+151 q^{106}+6 q^{105}-192 q^{104}-275 q^{103}-173 q^{102}+75 q^{101}+346 q^{100}+413 q^{99}+160 q^{98}-253 q^{97}-560 q^{96}-514 q^{95}-63 q^{94}+539 q^{93}+825 q^{92}+539 q^{91}-223 q^{90}-957 q^{89}-1063 q^{88}-330 q^{87}+778 q^{86}+1449 q^{85}+1050 q^{84}-299 q^{83}-1581 q^{82}-1711 q^{81}-446 q^{80}+1362 q^{79}+2252 q^{78}+1279 q^{77}-889 q^{76}-2484 q^{75}-2089 q^{74}+174 q^{73}+2499 q^{72}+2766 q^{71}+583 q^{70}-2277 q^{69}-3252 q^{68}-1346 q^{67}+1931 q^{66}+3600 q^{65}+2000 q^{64}-1551 q^{63}-3798 q^{62}-2558 q^{61}+1174 q^{60}+3955 q^{59}+3029 q^{58}-886 q^{57}-4073 q^{56}-3419 q^{55}+602 q^{54}+4218 q^{53}+3816 q^{52}-378 q^{51}-4337 q^{50}-4181 q^{49}+51 q^{48}+4412 q^{47}+4581 q^{46}+314 q^{45}-4307 q^{44}-4896 q^{43}-871 q^{42}+4012 q^{41}+5094 q^{40}+1437 q^{39}-3408 q^{38}-4997 q^{37}-2047 q^{36}+2587 q^{35}+4613 q^{34}+2427 q^{33}-1630 q^{32}-3865 q^{31}-2566 q^{30}+734 q^{29}+2924 q^{28}+2353 q^{27}-36 q^{26}-1947 q^{25}-1898 q^{24}-339 q^{23}+1100 q^{22}+1313 q^{21}+467 q^{20}-511 q^{19}-806 q^{18}-368 q^{17}+182 q^{16}+389 q^{15}+246 q^{14}-25 q^{13}-191 q^{12}-111 q^{11}+8 q^{10}+49 q^9+49 q^8+11 q^7-29 q^6-10 q^5+4 q^4+q^3+2 q^2+2 q-4+2 q^{-1} </math> \|		coloured_jones_5 = <math>q^{125}-3 q^{124}-q^{123}+5 q^{122}+3 q^{121}+3 q^{120}-2 q^{119}-15 q^{118}-21 q^{117}+4 q^{116}+26 q^{115}+40 q^{114}+33 q^{113}-15 q^{112}-80 q^{111}-96 q^{110}-27 q^{109}+73 q^{108}+158 q^{107}+151 q^{106}+6 q^{105}-192 q^{104}-275 q^{103}-173 q^{102}+75 q^{101}+346 q^{100}+413 q^{99}+160 q^{98}-253 q^{97}-560 q^{96}-514 q^{95}-63 q^{94}+539 q^{93}+825 q^{92}+539 q^{91}-223 q^{90}-957 q^{89}-1063 q^{88}-330 q^{87}+778 q^{86}+1449 q^{85}+1050 q^{84}-299 q^{83}-1581 q^{82}-1711 q^{81}-446 q^{80}+1362 q^{79}+2252 q^{78}+1279 q^{77}-889 q^{76}-2484 q^{75}-2089 q^{74}+174 q^{73}+2499 q^{72}+2766 q^{71}+583 q^{70}-2277 q^{69}-3252 q^{68}-1346 q^{67}+1931 q^{66}+3600 q^{65}+2000 q^{64}-1551 q^{63}-3798 q^{62}-2558 q^{61}+1174 q^{60}+3955 q^{59}+3029 q^{58}-886 q^{57}-4073 q^{56}-3419 q^{55}+602 q^{54}+4218 q^{53}+3816 q^{52}-378 q^{51}-4337 q^{50}-4181 q^{49}+51 q^{48}+4412 q^{47}+4581 q^{46}+314 q^{45}-4307 q^{44}-4896 q^{43}-871 q^{42}+4012 q^{41}+5094 q^{40}+1437 q^{39}-3408 q^{38}-4997 q^{37}-2047 q^{36}+2587 q^{35}+4613 q^{34}+2427 q^{33}-1630 q^{32}-3865 q^{31}-2566 q^{30}+734 q^{29}+2924 q^{28}+2353 q^{27}-36 q^{26}-1947 q^{25}-1898 q^{24}-339 q^{23}+1100 q^{22}+1313 q^{21}+467 q^{20}-511 q^{19}-806 q^{18}-368 q^{17}+182 q^{16}+389 q^{15}+246 q^{14}-25 q^{13}-191 q^{12}-111 q^{11}+8 q^{10}+49 q^9+49 q^8+11 q^7-29 q^6-10 q^5+4 q^4+q^3+2 q^2+2 q-4+2 q^{-1} </math> \|
	coloured_jones_6 = \|		coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_7 = \|		coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> \|
	computer_talk =		computer_talk =
	<table>		<table>
Line 51:		Line 51:
	<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>		<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
	</tr>		</tr>
	<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 165]]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 165]]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 6, 2, 7], X[7, 18, 8, 19], X[3, 9, 4, 8], X[17, 3, 18, 2],		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 6, 2, 7], X[7, 18, 8, 19], X[3, 9, 4, 8], X[17, 3, 18, 2],
Line 71:		Line 71:
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 165]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_165_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 165]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_165_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 165]]&) /@ {~~SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>~~		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki> (#[Knot[10, 165]]&) /@ {
			SymmetryType, UnknottingNumber, ThreeGenus,
			BridgeIndex, SuperBridgeIndex, NakanishiIndex
			}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 2, 3, NotAvailable, 1}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 2, 3, NotAvailable, 1}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 165]][t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 165]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 01:23, 31 August 2005

2005-08-31T01:23:14Z

Show changes

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:13Z

Show changes

DrorsRobot at 00:59, 30 August 2005

2005-08-30T00:59:57Z

← Older revision		Revision as of 20:59, 29 August 2005
Line 1:		Line 1:
			<!-- This page was generated from the splice template "Rolfsen_Splice_Template". Please do not edit! -->
	<!-- -->		<!-- -->
	<!-- -->		<!-- -->
Line 135:		Line 136:
	</table>		</table>

			{\| width=100%
	See/edit the [[Rolfsen_Splice_Template]].		\|align=left\|See/edit the [[Rolfsen_Splice_Template]].

			Back to the [[#top\|top]].
			\|align=right\|{{Knot Navigation Links\|ext=gif}}
			\|}

	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 21:57, 29 August 2005

2005-08-29T21:57:56Z

Show changes

ScottTestRobot at 00:05, 29 August 2005

2005-08-29T00:05:33Z

← Older revision		Revision as of 20:05, 28 August 2005
Line 1:		Line 1:
	<!-- -->		<!-- -->
			<!-- -->

			<!-- -->
			<!-- -->
	<!-- provide an anchor so we can return to the top of the page -->		<!-- provide an anchor so we can return to the top of the page -->
	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	<!-- this relies on transclusion for next and previous links -->		<!-- this relies on transclusion for next and previous links -->
	{{Knot Navigation Links\|ext=gif}}		{{Knot Navigation Links\|ext=gif}}

		⚫	{{Rolfsen Knot Page Header\|n=0\|k=1\|KnotilusURL=<math>\textrm{KnotilusURL}(\textrm{GaussCode}())</math>}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=0\|k=1\|KnotilusURL=<math>\textrm{KnotilusURL}(\textrm{GaussCode}())</math>}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
Line 24:		Line 21:
	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
	<tr align=center>		<tr align=center>
	<td width=40.%><table cellpadding=0 cellspacing=0>		<td width=40.%><table cellpadding=0 cellspacing=0>
Line 38:		Line 31:
	<tr align=center><td>1</td><td bgcolor=yellow>1</td><td>1</td></tr>		<tr align=center><td>1</td><td bgcolor=yellow>1</td><td>1</td></tr>
	<tr align=center><td>-1</td><td bgcolor=yellow>1</td><td>1</td></tr>		<tr align=center><td>-1</td><td bgcolor=yellow>1</td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

Line 81:		Line 73:
	q</nowiki></pre></td></tr>		q</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:27Z

← Older revision		Revision as of 21:44, 27 August 2005
Line 1:		Line 1:
			<!-- -->
	{{Template:Basic Knot Invariants\|name=10_165}}

			<!-- provide an anchor so we can return to the top of the page -->
			<span id="top"></span>

			<!-- this relies on transclusion for next and previous links -->
			{{Knot Navigation Links\|ext=gif}}

			{\| align=left
			\|- valign=top
			\|[[Image:{{PAGENAME}}.gif]]
			\|{{Rolfsen Knot Site Links\|n=0\|k=1\|KnotilusURL=<math>\textrm{KnotilusURL}(\textrm{GaussCode}())</math>}}
			\|{{:{{PAGENAME}} Quick Notes}}
			\|}

			<br style="clear:both" />

			{{:{{PAGENAME}} Further Notes and Views}}

			{{Knot Presentations}}
			{{3D Invariants}}
			{{4D Invariants}}
			{{Polynomial Invariants}}
			{{Vassiliev Invariants}}

			===[[Khovanov Homology]]===

			The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

			<center><table border=1>
			<tr align=center>
			<td width=40.%><table cellpadding=0 cellspacing=0>
			<tr><td>\</td><td> </td><td>r</td></tr>
			<tr><td> </td><td> \ </td><td> </td></tr>
			<tr><td>j</td><td> </td><td>\</td></tr>
			</table></td>
			<td width=20.%>0</td ><td width=40.%>χ</td></tr>
			<tr align=center><td>1</td><td bgcolor=yellow>1</td><td>1</td></tr>
			<tr align=center><td>-1</td><td bgcolor=yellow>1</td><td>1</td></tr>
			</table></center>

			{{Computer Talk Header}}

			<table>
			<tr valign=top>
			<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=    </pre></td>
			<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
			</tr>
			<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[0, 1]]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>0</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[0, 1]]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[Loop[1]]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[0, 1]]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[0, 1]]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[1, {}]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[0, 1]][t]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[0, 1]][z]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[0, 1], Knot[11, NonAlternating, 34], Knot[11, NonAlternating, 42]}</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[0, 1]], KnotSignature[Knot[0, 1]]}</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{1, 0}</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Knot[0, 1]][q]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] \|\| (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[0, 1]}</nowiki></pre></td></tr>
			<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[0, 1]][q]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -2 2
			1 + q + q</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[0, 1]][a, z]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[0, 1]], Vassiliev[3][Knot[0, 1]]}</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 0}</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[0, 1]][q, t]</nowiki></pre></td></tr>
			<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>1
			- + q
			q</nowiki></pre></td></tr>
			</table>

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:50Z

Resetting knot page to basic template.

New page