06-1350/Syzygies in Asymptote - Revision history

Andy: /* Installation */

2008-12-01T16:28:59Z

Installation

← Older revision		Revision as of 12:28, 1 December 2008
Line 7:		Line 7:

	===Installation===		===Installation===
	To use the syzygy script, ~~first~~ install [http://asymptote.sourceforge.net Asymptote]. Instructions for installing the program on several OSes is given in the documentation at the Asymptote website. The documentation also gives helpful instructions on how to run a script in Asymptote to produce a picture~~. Once installed, download [http://katlas.math.toronto.edu/svn/06-1350/syzygy/trunk/syzygy/syzygy.asy syzygy.asy] and put it in a directory where Asymptote can find it~~. You should also have (or install) a variant of TeX on your system, such as MiKTeX, so that Asymptote can typeset labels.		To use the syzygy script, you need to have a working version of Asymptote. Asymptote is installed on coxeter. To install on another computer, see [http://asymptote.sourceforge.net Asymptote]. Instructions for installing the program on several OSes is given in the documentation at the Asymptote website. The documentation also gives helpful instructions on how to run a script in Asymptote to produce a picture. You should also have (or install) a variant of TeX on your system, such as MiKTeX, so that Asymptote can typeset labels. The <tt>syzygy</tt> package is now part of the standard Asymptote distribution.

	===Braids===		===Braids===

Drorbn: Reverted edit of 205.234.69.161, changed back to last version by Drorbn

2007-06-07T13:27:47Z

Reverted edit of 205.234.69.161, changed back to last version by Drorbn

← Older revision		Revision as of 09:27, 7 June 2007
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</pre>		</pre>

Line 62:		Line 62:

	<math>		<math>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</math>		</math>

Line 69:		Line 69:

	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)
	</math>		</math>

Line 75:		Line 75:

	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]
	- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]		- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]
	</pre>		</pre>

Line 162:		Line 162:
	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>
	\|}		\|}

Line 174:		Line 174:

	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]
	rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]		+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]
	</pre>		</pre>

205.234.69.161 at 11:22, 7 June 2007

2007-06-07T11:22:47Z

← Older revision		Revision as of 07:22, 7 June 2007
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</pre>		</pre>

Line 62:		Line 62:

	<math>		<math>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</math>		</math>

Line 69:		Line 69:

	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)
	</math>		</math>

Line 75:		Line 75:

	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]
	- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]		- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]
	</pre>		</pre>

Line 162:		Line 162:
	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>
	\|}		\|}

Line 174:		Line 174:

	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]
	+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]		rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]
	</pre>		</pre>

Drorbn at 08:21, 10 May 2007

2007-05-10T08:21:44Z

Show changes

211.160.179.81 at 07:40, 10 May 2007

2007-05-10T07:40:59Z

Show changes

Drorbn: Reverted edit of 61.132.90.174, changed back to last version by Drorbn

2007-05-08T16:41:06Z

Reverted edit of 61.132.90.174, changed back to last version by Drorbn

← Older revision		Revision as of 12:41, 8 May 2007
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			{{06-1350/Navigation}}
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	For a condensed version of this page, check [[06-1350/Syzygies in Asymptote in Brief]].		For a condensed version of this page, check [[06-1350/Syzygies in Asymptote in Brief]].
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</pre>		</pre>

Line 62:		Line 62:

	<math>		<math>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</math>		</math>

Line 69:		Line 69:

	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)
	</math>		</math>

Line 75:		Line 75:

	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]
	- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]		- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]
	</pre>		</pre>

Line 162:		Line 162:
	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>
	\|}		\|}

Line 174:		Line 174:

	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]
	rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]		+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]
	</pre>		</pre>

61.132.90.174 at 16:38, 8 May 2007

2007-05-08T16:38:13Z

← Older revision		Revision as of 12:38, 8 May 2007
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	{{06-1350/Navigation}}

	For a condensed version of this page, check [[06-1350/Syzygies in Asymptote in Brief]].		For a condensed version of this page, check [[06-1350/Syzygies in Asymptote in Brief]].
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</pre>		</pre>

Line 62:		Line 62:

	<math>		<math>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</math>		</math>

Line 69:		Line 69:

	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)
	</math>		</math>

Line 75:		Line 75:

	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]
	- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]		- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]
	</pre>		</pre>

Line 162:		Line 162:
	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>
	\|}		\|}

Line 174:		Line 174:

	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]
	+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]		rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]
	</pre>		</pre>

Drorbn: Reverted edit of 200.238.102.162, changed back to last version by Drorbn

2007-04-11T00:26:21Z

Reverted edit of 200.238.102.162, changed back to last version by Drorbn

← Older revision		Revision as of 20:26, 10 April 2007
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</pre>		</pre>

Line 62:		Line 62:

	<math>		<math>
	(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =		(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =
	(1123)^\star B^ (1203)^\star B^ (1231)^\star B^		(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+
	</math>		</math>

Line 69:		Line 69:

	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)
	</math>		</math>

Line 75:		Line 75:

	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]
	- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]		- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]
	</pre>		</pre>

Line 162:		Line 162:
	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>
	\|}		\|}

Line 174:		Line 174:

	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]
	rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]		+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]
	</pre>		</pre>

200.238.102.162 at 21:23, 10 April 2007

2007-04-10T21:23:54Z

← Older revision		Revision as of 17:23, 10 April 2007
Line 55:		Line 55:

	<pre>		<pre>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</pre>		</pre>

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	<math>		<math>
	(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ =		(1230)^\star B^ (1213)^\star B^ (1023)^\star B^ =
	(1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+		(1123)^\star B^ (1203)^\star B^ (1231)^\star B^
	</math>		</math>

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	<math>		<math>
	\rho_3(x_1,x_2,x_3,x_4) = b^+(x_1,x_2,x_3) + b^+(x_1+x_3,x_2,x_4) + b^+(x_1,x_3,x_4) - b^+(x_1+x_2,x_3,x_4) - b^+(x_1,x_2,x_4) - b^+(x_1+x_4,x_2,x_3)		\rho_3(x_1,x_2,x_3,x_4) = b^ (x_1,x_2,x_3) b^ (x_1 x_3,x_2,x_4) b^ (x_1,x_3,x_4) - b^ (x_1 x_2,x_3,x_4) - b^ (x_1,x_2,x_4) - b^ (x_1 x_4,x_2,x_3)
	</math>		</math>

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	<pre>		<pre>
	rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] + bp[x1 + x3, x2, x4] + bp[x1, x3, x4]		rho3[x1_, x2_, x3_, x4_] :> bp[x1, x2, x3] bp[x1 x3, x2, x4] bp[x1, x3, x4]
	- bp[x1 + x2, x3, x4] - bp[x1, x2, x4] - bp[x1 + x4, x2, x3]		- bp[x1 x2, x3, x4] - bp[x1, x2, x4] - bp[x1 x4, x2, x3]
	</pre>		</pre>

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	\|-		\|-
	\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>		\|<math>\Phi B(x_1,x_2,x_3,x_4,x_5) = </math>
	\|<math>\rho_3(x_1,x_2,x_3,x_5) + \rho_{4a}(x_1+x_5,x_2,x_3,x_4) + \rho_{4b}(x_1+x_2,x_3,x_4,x_5)</math>		\|<math>\rho_3(x_1,x_2,x_3,x_5) \rho_{4a}(x_1 x_5,x_2,x_3,x_4) \rho_{4b}(x_1 x_2,x_3,x_4,x_5)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_3(x_1,x_2,x_3+x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>		\|<math>- \rho_3(x_1,x_2,x_3 x_4,x_5) - \rho_{4a}(x_1,x_2,x_3,x_4)</math>
	\|-		\|-
	\|		\|
	\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) + \rho_3(x_1+x_3,x_2,x_4,x_5).</math>		\|<math>- \rho_{4b}(x_1,x_3,x_4,x_5) \rho_3(x_1 x_3,x_2,x_4,x_5).</math>
	\|}		\|}

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	<pre>		<pre>
	PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] + rho4a[x1 + x5, x2, x3, x4]		PhiAroundB[x1_, x2_, x3_, x4_, x5_] :> rho3[x1, x2, x3, x5] rho4a[x1 x5, x2, x3, x4]
	+ rho4b[x1 + x2, x3, x4, x5] - rho3[x1, x2, x3 + x4, x5] - rho4a[x1, x2, x3, x4]		rho4b[x1 x2, x3, x4, x5] - rho3[x1, x2, x3 x4, x5] - rho4a[x1, x2, x3, x4]
	- rho4b[x1, x3, x4, x5] + rho3[x1 + x3, x2, x4, x5]		- rho4b[x1, x3, x4, x5] rho3[x1 x3, x2, x4, x5]
	</pre>		</pre>

Drorbn: /* Conclusion */

2006-12-12T15:49:43Z

Conclusion

← Older revision		Revision as of 11:49, 12 December 2006
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	===Conclusion===		===Conclusion===
	Example syzygyies and the latest version of the script can be found in the syzygy directory on the course Subversion repository [[http://katlas.math.toronto.edu/svn/06-1350/syzygy/trunk/syzygy/]]. Please contact me if you have any questions or suggestions. Good luck and happy syzyging!		Example syzygyies and the latest version of the script can be found in the syzygy directory on the course Subversion repository [http://katlas.math.toronto.edu/svn/06-1350/syzygy/trunk/syzygy/]. Please contact me if you have any questions or suggestions. Good luck and happy syzyging!