Getting Started¶

Installation¶

1. Python interpreter.

This program is written in Python and needs a Python interpreter to run; to be specific, Python 3.3 or above is required. If you don’t have this already installed on your system, your best bet is to download the latest version (currently 3.5) from the Python website. For Linux users, Python may be available from your distribution’s repositories; take care to install version 3.x rather than 2.x!

2. Source code.

If you have git available on your system, the easiest way to obtain the program is to simply clone the repository:

git clone https://github.com/DMRobertson/thompsons_v.git

If this is not possible, a ZIPped version can be downloaded from the project page on GitHub.

3. Package requirements.

The de-facto package management tool for Python is the pip program, which is installed as part of Python 3.4 and higher. Python 3.3 users should consult the pip documentation for instructions on how to install pip directly. Some Linux distributions may also provide pip as a package (make sure it’s for Python 3—it may be listed as pip3).

Once pip is installed, navigate to the project directory and run

pip install -r requirements.txt

(possibly you may need to use pip3). This should do all the hard work for you.

Direct installation:

If you would prefer not to install pip, you may install the prerequisites directly. There is only one major Python package required to run the program: NetworkX, a library for working with graphs in Python. This may be available in Linux repositories, e.g. Ubuntu.

This documentation is built using Sphinx. If you wish to build it yourself, or run the test suite, you must install Sphinx also. Again, consider checking Linux repositories e.g. in Ubuntu.

First steps¶

Navigate to the root folder (thompsons_v) in a terminal and start up Python using the python command. Once the python prompt (>>>) is available, try to import thompson:

\$ python
Python 3.3.3 (v3.3.3:c3896275c0f6, Nov 18 2013, 21:19:30) [MSC v.1600 64 bit (AMD64)] on win32
>>> import thompson
>>>


If this fails, check that you’re using Python 3.3 or above. If python started up Python 2.x, try using the command python3 instead.

We can now use the python REPL as a sort of calculator for these groups.

>>> from thompson import *
>>> sig = (2, 1) #signature of the algebra we work in
>>> domain = Generators.standard_basis(sig).expand(0).expand(0)
>>> range  = Generators.standard_basis(sig).expand(0).expand(1)
>>> print(domain)
[x1 a1 a1, x1 a1 a2, x1 a2]
>>> print(range)
[x1 a1, x1 a2 a1, x1 a2 a2]
>>> phi = Automorphism(domain, range)
>>> print(phi)
InfiniteAut: V(2, 1) -> V(2, 1) specified by 3 generators (after expansion and reduction).
x1 a1 a1 -> x1 a1
x1 a1 a2 -> x1 a2 a1
x1 a2    -> x1 a2 a2

>>> phi.image('x a2 a1 a2 a2 a1')
Word('x1 a2 a2 a1 a2 a2 a1', (2, 1))
>>> phi.order
inf
>>> phi.print_characteristics()
(-1, a1)
(1, a2)
>>> phi.dump_QNB()
x1 a1 Left semi-infinite component with characteristic (-1, a1)
x1 a2 Right semi-infinite component with characteristic (1, a2)

>>> print(phi ** 2)
InfiniteAut: V(2, 1) -> V(2, 1) specified by 4 generators (after expansion and reduction).
x1 a1 a1 a1 -> x1 a1
x1 a1 a1 a2 -> x1 a2 a1
x1 a1 a2    -> x1 a2 a2 a1
x1 a2       -> x1 a2 a2 a2
>>> print(~phi) #inverse
InfiniteAut: V(2, 1) -> V(2, 1) specified by 3 generators (after expansion and reduction).
x1 a1    -> x1 a1 a1
x1 a2 a1 -> x1 a1 a2
x1 a2 a2 -> x1 a2
>>> print(~phi * phi) # == identity
PeriodicAut: V(2, 1) -> V(2, 1) specified by 1 generators (after expansion and reduction).
x1 -> x1


Locating examples¶

A number of examples are included in this package, some of which are used in [BDR] . To access them, use the load_example() function:

>>> from thompson import *
>>> print(phi)
InfiniteAut: V(2, 1) -> V(2, 1) specified by 7 generators (after expansion and reduction).
x1 a1 a1 a1 a1 -> x1 a1 a1
x1 a1 a1 a1 a2 -> x1 a1 a2 a1 a1
x1 a1 a1 a2 a1 -> x1 a2 a2
x1 a1 a1 a2 a2 -> x1 a2 a1
x1 a1 a2       -> x1 a1 a2 a1 a2
x1 a2 a1       -> x1 a1 a2 a2 a2
x1 a2 a2       -> x1 a1 a2 a2 a1


Note

Previously, one would access this example by using from thompson.examples import nathan_pond_example. I changed this, because it meant that every example was loaded (and the quasinormal bases etc. computed) whenever thompson.examples was imported.

To see the list of available examples, consult the documentation for the examples module. You might also like to consult the demo notebook on GitHub.

Running the test suite¶

Make sure Sphinx is installed (see the installation section). Then navigate to the docs folder and run make doctest. This should look through the source code for short tests and alert you if any of them fail. You can also run make html to build this documentation. Reset with make clean.