Drorbn - User contributions [en]

VasCalc Documentation - vectorSpace

2006-05-25T13:58:32Z

142.150.137.199:

The vectorSpace package is a small package used to set up quotients of finite dimensional vector spaces. The source files for this package are

*[http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/Coefficient.java Coefficient.java],
*[http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/QuotientSpace.java QuotientSpace.java],
*[http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/AlgebraVector.java AlgebraVector.java].

The class contained in [http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/BigRational.java BigRational.java] contains Eric Laroche's implementation of arithemetic involving arbitrarily large rationals (see [[VasCalc - Bibliography]]), which is used as the default base field in vectorSpace. Additionally, there are two small test programs:[http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/testQuotSp.java testQuotSp.java] and [http://katlas.math.toronto.edu/svn/VasCalc/trunk/vectorSpace/testAlgVect.java testAlgVect.java].
==Usage==

VasCalc - Progress Log

2006-05-24T21:42:44Z

142.150.137.199:

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

====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]]
 
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".
 

====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]]

VasCalc - A Vassiliev Invariants Calculator

2006-05-24T18:45:51Z

142.150.137.199:

These pages document our work on VasCalc. Let us start with the project description as appeared in our NSERC proposal:

<blockquote>
Finite type (Vassiliev) invariants stand in the centre of knot theory.
They are known to encompass very many of the invariants pivotal to knot
theory and to low dimensional topology, and thus hundreds of papers
were written about them. Finite type invariants are in principle
algorithmic and computable, yet the computations are a complicated
many-step procedure and there aren't yet coherent computer programs to
carry them out.

After 15 years of progress regarding finite type invariants, I feel
that finally our understanding of the mathematics is stable enough to
justify and guide a computational effort. I propose that this work be
carried out as a joint NSERC summer research internship by Zavosh
Amir-Khosravi and Siddarth Sankaran, where Zavosh will be writing the
java- or C++-based "inner most loop" while Siddarth will be working on
all the surrounding logic. We will make sure that every piece of the
work will be well documented and will have some "stand alone" value, so
overall, I expect the project to have significant impact on the subject
of finite type invariants.
</blockquote>

* [http://www.third-bit.com/swc2/lec/version.html A bit about subversion] and [http://katlas.math.toronto.edu/svn/VasCalc/ our subversion repository].

* [[VasCalc - Documentation]].

* [[VasCalc - Progress Log]].

* [[VasCalc - To Do List]].