Drorbn - User contributions [en]

VasCalc - Progress Log

2006-07-07T20:37:35Z

70.29.23.152:

This is the [[VasCalc - A Vassiliev Invariants Calculator|VasCalc Project]] Progress Log.

====Friday July 7 2006====
So the little bug in ChordsMod4T appears to be resolved. The [[VasCalc- Results| results]] pages no longer directly disprove the consistency of mathematics. Also the program is a fair bit faster than the previous incarnation, but coefficient arithmetic is still by far the biggest resource thief.

====Friday June 23 2006====
Success! Our program is now complete - we can generate the relations, and compute the quotient . What remains is the interface to Mathematica, which should be easy, and optimizing the program, which may be a little harder. A little example will be up soon.

====Tuesday June 20 2006====
Now we are able to generate all chord diagrams on a given number of lines and circles, as well as all the diagrams with a T added! Almost done is the piece that puts the two together - the ChordsMod4T class, which mods out the first space with the relations generated by the second. There are still many things to be done with this part of the program before we're truly finished: I've listed these on the [[VasCalc - To Do List]] page. Fun fact: there are 902 chord diagrams on one circle with 6 chords, 9749 diagrams with 7 chords, and 127072 diagrams with 8 chords. Evidently, we'll have to make some improvements to the program - generating one circle with 9 chords runs out of memory.
====Saturday June 17 2006====
The [http://katlas.math.toronto.edu/svn/VasCalc/trunk/ChordDiagram.java ChordDiagram class] is now up and running. As explained in the [[VasCalc Documentation - ChordDiagram| documentation]], this class is used to store information about individual chord diagrams. Because of the way we've set up labelling the diagrams, the task of generating all diagrams becomes very easy - this part of the program is almost done as well.
====Tuesday May 30 2006====
A new file [http://katlas.math.toronto.edu/svn/VasCalc/trunk/ChordDiagram.java ChordDiagram.java] was committed to the repository. This is a class that holds information describing one chord diagram and contains methods that will help in constructing chord diagrams systematically. It is not yet complete, though not far from it.
====Monday May 29 2006====
I've updated the vectorSpace package, and added a Mathematica interface, as well an almost complete [[VasCalc Documentation - vectorSpace|document]] on the wiki. Can someone check that the instructions for installation work?
Also, does the simulated Mathematica session work on this wiki?
====Wednesday May 24 2006====
A new package [http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace vectorSpace] has been committed to the repository, to handle quotients of finite-dimensional vector spaces. See the [[VasCalc - Documentation|documentation]] for usage details.
====Saturday May 20 2006====
Our first task is to write a program to construct and manipulate the (formal) quotient vector space A(m,n,l), consisting of diagrams with m chords between n lines and l circles, modulo the four-T relations. Here's a rough sketch of the structure of this program:

[[Image:Dmod4T.jpg|thumb|120px|left]]
<br>
Java things are in orange, Mathematica things are in blue. Red arrows are helper functions that need to be written, and black arrows denote "natural class heirarchy".
<br clear="all">

====Monday May 15 2006====
Another slightly different HelloWorld test has been added to the [http://katlas.math.toronto.edu/svn/VasCalc/trunk/ SVN repository]. This time, one can use the default Java runtime bundled with Mathematica/Windows (so the user does not need to know anything about where Java lives on their system) by telling the Java compiler to produce code for Java 1.4. This is accomplished by issuing the command:
:<code>javac -source 1.4 -target 1.4 file_to_be_compiled.java </code>

I suppose this prevents us from using the new features of Java 1.5, but I don't know what they are.

As for the test program, download [http://katlas.math.toronto.edu/svn/VasCalc/trunk/javatest.m javatest.m] and [http://katlas.math.toronto.edu/svn/VasCalc/trunk/test1.class test1.class], and issue the following commands in Mathematica (replacing the '/path_to_files' with the location you downloaded the files to, and don't forget the quotes in the second line):

:<code> << /path_to_files/javatest.m </code>

:<code> HelloWorld[VasCalcPath -> "/path_to_files"] </code>

and read your mystery message!

==== Sunday May 14 2006====
J/Link passed the Hello World test. The java class and Mathematica
notebook were commited to the repository trunk. Note the Mathematica file
must be edited in order to specify the path to java and the class.
In order to get it to work I had to tweak a few things:
* The JRE bin directory had to be added to the PATH. The JDK path is not enough because J/Link looks for files like jawt.dll and awt.dll that don't come with JDK.
* HelloWorld.class had to be in one of the dirs in CLASSPATH, because J/Link loads classes only through their full class name.
* In Mathematica, when running InstallJava[], it was necessary to specify the path name for a newer version of java.exe. By default it runs the Windows java, which didn't run what was compiled with a new JDK.

Ideally, one would like to write a Mathematica notebook without
any hardcoded paths that others can use with no changes. Is this
possible?

==== Thursday May 11 20006====
* First day meeting's blackboard: [[Image:060511-1.jpg|thumb|160px|left]]
<br clear="all">

VasCalc Results - ChordMod4T

2006-07-01T01:16:53Z

70.29.23.152:

This page documents some computational results obtained by using the [[VasCalc Documentation - ChordsMod4T| ChordsMod4T]] software component of the [[VasCalc]] project. We denote by A(l,m,n) the formal vector space of chord diagrams with n chords on a skeleton of l lines and m circles, modulo the 4T relations.

===How A(l,m,n) is constructed===

===Some Dimensions of A(l,m,n)===

{| border="1"
|+ Dimensions of chord diagram spaces with 2 chords
!rowspan="2"|Number of Lines
!colspan="10"|Number of Circles
|-
|0||1||2||3||4||5||6||7||8||9
|-
|0||0||2||8||27||69||145||272||469||758||1164
|-
|1||2||8||26||68||145||272||469||758||1164||1715
|-
|2||9||25||66||144||272||469||758||1164||1715||2442
|-
|3||28||63||141||271||469||758||1164||1715||2442||3379
|-
|4||69||135||267||468||758||1164||1715||2442||3379||4563
|-
|5||145||257||463||757||1164||1715||2442||3379||4563||6034
|-
|6||272||448||751||1163||1715||2442||3379||4563||6034||7835
|-
|7||469||730||1156||1714||2442||3379||4563||6034||7835||10012
|}

{| border="1"
|+ Dimensions of chord diagram spaces with 3 chords
!rowspan="2"|Number of Lines
!colspan="7"|Number of Circles
|-

|0||1||2||3||4||5||6
|-
|0||0||3||19||92||370||1120||2778
|-
|1||3||19||88||351||1096||2768||6083
|-
|2||23|| 88||329||1053||2734||6073||12176
|-

|3||111||321||991||2657||6029||12166||22689
|-
|4||394||954||2524||5908||12112||22679
|-
|5||1130||2418||5664||11937||22615||39875
|-
|6||2778||5424||11533||22376||39801||66793
|}

VasCalc Results - ChordMod4T

2006-06-30T22:18:52Z

70.29.23.152:

This page documents some computational results obtained by using the [[VasCalc Documentation - ChordsMod4T| ChordsMod4T]] software component of the [[VasCalc]] project. We denote by A(l,m,n) the formal vector space of chord diagrams with n chords on a skeleton of l lines and m circles, modulo the 4T relations.

===How A(l,m,n) is constructed===

===Some Dimensions of A(l,m,n)===

{| border="1"
|+ Dimensions of chord diagram spaces with 2 chords
|Number of Lines
!colspan="10"|Number of Circles
|-
|
|0||1||2||3||4||5||6||7||8||9
|-
|0||0||2||8||27||69||145||272||469||758||1164
|-
|1||2||8||26||68||145||272||469||758||1164||1715
|-
|2||9||25||66||144||272||469||758||1164||1715||2442
|-
|3||28||63||141||271||469||758||1164||1715||2442||3379
|-
|4||69||135||267||468||758||1164||1715||2442||3379||4563
|-
|5||145||257||463||757||1164||1715||2442||3379||4563||6034
|-
|6||272||448||751||1163||1715||2442||3379||4563||6034||7835
|-
|7||469||730||1156||1714||2442||3379||4563||6034||7835||10012
|}

{| border="1"
|+ Dimensions of chord diagram spaces with 3 chords
|Number of Lines
!colspan="7"|Number of Circles
|-
|
|0||1||2||3||4||5||6
|-
|0||0||3||19||92||370||1120||2778
|-
|1||3||19||88||351||1096||2768||6083
|-
|2||23|| 88||329||1053||2734||6073||12176
|-

|3||111||321||991||2657||6029||12166||22689
|-
|4||394||954||2524||5908||12112||22679
|-
|5||1130||2418||5664||11937||22615||39875

|}

VasCalc - Documentation

2006-06-27T22:30:49Z

70.29.23.152:

This page will contain the documentation for the various parts of [[VasCalc - A Vassiliev Invariants Calculator|VasCalc]], and will be updated as work gets completed.

In the interest of modularity, we have broken down the project into independant subcomponents. Follow the links for documentation on each component:

* [[VasCalc Documentation - vectorSpace|vectorSpace]] - a small Java package to deal with finite-dimensional vector spaces.

*[[VasCalc Documentation - ChordsMod4T| ChordsMod4T]] - a program to compute and work with spaces of chord diagrams modulo 4T relations.