Linear Transformation Finder

LTF is a Ruby program that generates Maxima code to find linear transformations between vectors given input/output constraints.

Platform

LTF should work on any platform that supports both Ruby and Maxima, namely Linux, Mac OS X, and Windows. However, as of this writing it has only been tested on a Gentoo Linux system.

Download

The latest version of LTF can be found at:

www.jessemerriman.com/project/ltf

Installation

You can choose to install either through RubyGems, which I highly recommend, or manually. First make sure you have the required prerequisites.

Prerequisites

Install Ruby if not already installed.
Install Maxima if not already installed.

Installation using RubyGems

Install RubyGems if not already installed.
Open up a command line, and change to the directory in which you downloaded LTF‘s Gem file.
Run:
```
  $ gem install ltf
```

Installation without RubyGems

If you don‘t want to use RubyGems, you can download the LTF Zip file instead of the Gem, and unzip that to the location of your choice. You‘ll have to make sure the lib/ directory is in Ruby‘s $LOAD_PATH. You can either run LTF like this:

  $ ruby -Ipath/to/LTF/lib/dir path/to/ltf

or insert the following as the second line of the ltf executable (and any other Ruby program that uses the LTF library):

  $LOAD_PATH << '/path/to/LTF/lib/dir'

Failure to do either of these will result in a LoadError upon attempting to run the program.

Usage

The executable ltf will appear under the bin/ directory where LTF was installed (if you used RubyGems on Linux, this may be something like /usr/lib/ruby/gems/1.8/gems/ltf-0.0.1/bin/ltf).

LTF can be run from the command line like so:

  $ ltf [-h|--help]

Vector input-output constraints will be read from STDIN, one line at a time, in the following format:

  [a,b,c,...,n] [A,B,C,...,N]

Where each letter is a value. Values may begin with whitespace, followed by a number, which is either an integer, a decimal, or a fraction. Here are some example constraints:

  [0,0] [0,0]
  [1, 45, -2] [3, -65, 54]
  [6.4] [100.1]
  [1/2, 5.4] [-55.01, -33/34]

Comments can be entered if they start with whitespace followed by a #, either on lines of their own or after a constraint:

  # this is a comment
  [0] [1] # this is another comment

Example

  $ ltf
  Enter constraints, one per line. Enter a blank line when done.
  # Find a "spin-push-down" transformation.
  [0,0,0] [0,0,0]
  [1,1,1] [1/2,1/2,1/2]
  [0,1,1] [1,0,0]
  [1,0,1] [0,1,0]
  [1,1,0] [0,0,1]

  Solution:
  (x3+x2-x1)/2
  (x3-x2+x1)/2
  -(x3-x2-x1)/2

Each part of the output is the next part of the transformation. So in this case, the result is:

  [ x1 ]    [ (x3+x2-x1)/2  ]   [ (-x1 + x2 + x3)/2 ]
  [ x2 ] -> [ (x3-x2+x1)/2  ] = [ ( x1 - x2 + x3)/2 ]
  [ x3 ]    [ -(x3-x2-x1)/2 ]   [ ( x1 + x2 - x3)/2 ]

Other examples may be found in the examples/ directory where LTF was installed.

Bugs

Please send bug reports or patches to jessemerriman@warpmail.net

README.rdoc