User:Ben/KRhomology - Revision history

Drorbn: /* Calculations */

2007-04-24T21:40:15Z

Calculations

← Older revision		Revision as of 17:40, 24 April 2007
Line 2:		Line 2:
	Since calculations have now been incorporated into the normal KAtlas data structure, I don't feel like there's much point in having a table of them here.		Since calculations have now been incorporated into the normal KAtlas data structure, I don't feel like there's much point in having a table of them here.

	Look for example at pages like ~~http://katlas.math.toronto.edu/wiki/~~Data:3_1/Khovanov_Rozansky_Polynomial.		Look for example at pages like [[3_1]] and [[Data:3_1/Khovanov_Rozansky_Polynomial]].

	==Macaulay2 program==		==Macaulay2 program==

2007-04-24T19:42:15Z

← Older revision		Revision as of 15:42, 24 April 2007
Line 5:		Line 5:

	==Macaulay2 program==		==Macaulay2 program==
			WARNING: This program is obsolete... and the newer version is probably broken. Complain to Ben?

	Save this as a file (called KR.m2), open Macaulay2 (in command line or emacs), and type <code>load "KR.m2"</code>.		Save this as a file (called KR.m2), open Macaulay2 (in command line or emacs), and type <code>load "KR.m2"</code>.
	<code>KRpoly</code> is probably the command you want (but it only works for knots at the moment). It outputs <math>\frac{1-t}{qt+1}KR_K(q,s,t)</math>.		<code>KRpoly</code> is probably the command you want (but it only works for knots at the moment). It outputs <math>\frac{1-t}{qt+1}KR_K(q,s,t)</math>.

2007-04-24T19:33:39Z

Macaulay2 program

← Older revision		Revision as of 15:33, 24 April 2007
Line 6:		Line 6:
	==Macaulay2 program==		==Macaulay2 program==
	Save this as a file (called KR.m2), open Macaulay2 (in command line or emacs), and type <code>load "KR.m2"</code>.		Save this as a file (called KR.m2), open Macaulay2 (in command line or emacs), and type <code>load "KR.m2"</code>.
	<code>KRpoly</code> is ~~probabby~~ the command you want (but it only works for knots at the moment). It outputs <math>\frac{1-t}{qt+1}KR_K(q,s,t)</math>.		<code>KRpoly</code> is probably the command you want (but it only works for knots at the moment). It outputs <math>\frac{1-t}{qt+1}KR_K(q,s,t)</math>.
	Using <code>texMath</code> puts things in format for LaTeX.		Using <code>texMath</code> puts things in format for LaTeX.

2007-04-24T19:25:29Z

Calculations

← Older revision		Revision as of 15:25, 24 April 2007
Line 1:		Line 1:
	==Calculations==		==Calculations==
	Since calculations have now been incorporated into the normal KAtlas data structure, I don't feel like there's much point in having a table of them here.		Since calculations have now been incorporated into the normal KAtlas data structure, I don't feel like there's much point in having a table of them here.

			Look for example at pages like http://katlas.math.toronto.edu/wiki/Data:3_1/Khovanov_Rozansky_Polynomial.

	==Macaulay2 program==		==Macaulay2 program==

2006-01-30T23:24:52Z

Macaulay2 program

← Older revision		Revision as of 19:24, 30 January 2006
Line 8:		Line 8:

	Changes from the previous version: the important change is in the construction of the Rouquier complex. Now it works by breaking up the braid into (at the moment, very simple) patterns it recognizes, and uses simplified Rouquier complexes for those chunks. This seems to be make a big difference in computational time, indicating that a program that could simplify large Rouquier complexes could lead to very large computational savings. I've made some progress in this direction, but am still struggling to produce something truly robust.		Changes from the previous version: the important change is in the construction of the Rouquier complex. Now it works by breaking up the braid into (at the moment, very simple) patterns it recognizes, and uses simplified Rouquier complexes for those chunks. This seems to be make a big difference in computational time, indicating that a program that could simplify large Rouquier complexes could lead to very large computational savings. I've made some progress in this direction, but am still struggling to produce something truly robust.

			The program posted on Jan. 15 had a bug in it, and shouldn't be used. That bug is now fixed.

2006-01-30T23:23:24Z

Macaulay2 program

@@ Line 162: / Line 162: @@
 IImod = (H,I,J,W,n,S) -> (
      i:=ideal(S_H+S_I-S_J-S_(J+1),S_H*S_I-S_J*S_(J+1));
      if W then (
-	  M0=S^1/i;
+	  C=stmod(H,I,J,W,S)**S^{-n+1};
-	  f1=map(M0,M1,S_H-S_I-S_J+S_(J+1));
+	       if mod(j,2)==0 then L=prepend(map(S^{-n+j}/i,S^{-n+j-1}/i,S_H-S_J),L)
-	  f2=map(M1,M2,S_J-S_I);
+	       else L=prepend(map(S^{-n+j}/i,S^{-n+j-1}/i,S_I-S_J),L);
-	  C=chainComplex(f1,f2));
+	  D=chainComplex L;
-	  M0=S^{2}/j;
-	  M2=S^{1}/i;
+	  C=stmod(H,I,J,W,S)**S^{n-1};
-	  f1=map(M0,M1);
+     	  L=singleton(C.dd_0);
-     C)
+	       );
 --this produces the standard Rouquier complex for a single crossing

2006-01-15T22:34:20Z

added revised program, deleted table of computations

2005-12-08T17:34:27Z

Macaulay2 program

← Older revision		Revision as of 13:34, 8 December 2005
Line 205:		Line 205:
	--polynomial of K). THIS CURRENTLY ONLY WORKS FOR KNOTS, NOT LINKS.		--polynomial of K). THIS CURRENTLY ONLY WORKS FOR KNOTS, NOT LINKS.
	KRpoly = K -> (		KRpoly = K -> (
	-- if K#?KRpoly then return K#KRpoly;		if K#?KRpoly then return K#KRpoly;
	L:=KRHom K;		L:=KRHom K;
	R:=ring L_0;		R:=ring L_0;

2005-12-08T16:29:44Z

fixed bugs

← Older revision		Revision as of 12:29, 8 December 2005
Line 205:		Line 205:
	--polynomial of K). THIS CURRENTLY ONLY WORKS FOR KNOTS, NOT LINKS.		--polynomial of K). THIS CURRENTLY ONLY WORKS FOR KNOTS, NOT LINKS.
	KRpoly = K -> (		KRpoly = K -> (
	if K#?KRpoly then return K#KRpoly;		-- if K#?KRpoly then return K#KRpoly;
	L:=KRHom K;		L:=KRHom K;
	R:=ring L_0;		R:=ring L_0;
Line 223:		Line 223:
	)		)
	));		));
	K#KRpoly=P//(q*t+1)		K#KRpoly=P//(q*t+1);
	K#KRpoly)		K#KRpoly)

	KRdisp =K -> (
	if not K#?KRdeg then KRpoly K;
	N=K#KRdeg;
	spoM=spots K#KRHom_0;
	net P \|\| " " \|\| ( " " \|\| stack apply(spoM, net)) \| " " \| horizontalJoin between(" ", apply(
	toList (0..#M-1),i-> net i \|\| stack(
	apply(
	spoM,j->net(flatten(N_i j))
	)
	)
	)
	)
	)
	</pre>		</pre>

2005-12-08T16:04:34Z

changed program to hopefully use less memory