arctans

arctans is a library for manipulating arctans to generate Machin-like formulae and other formulae involving arctans.

Installing arctans

Installing from PyPI using pip

The latest release of arctans can be installed by running:

pip3 install arctans

Installing from source using pip

arctans can be installed by running:

pip3 install git+https://github.com/mscroggs/arctans.git

Testing arctans

To run the arctans unit tests, clone the repository and run:

python3 -m pytest test/

Using arctans

arctans can be used to represent arctans and sums of arctans symbolically and generate arctan sums equivalent to a given set of sums.

For example, Machin's formula for pi (pi = 16arctan(1/5) - 4arctan(1/239)) can be created with:

from arctans import arctan, Rational

pi = 16 * arctan(Rational(1, 5)) - 4 * arctan(Rational(1, 239))
print(pi)
print(float(pi))

Or equivalently:

from arctans import arccotan

pi = 16 * arccotan(5) - 4 * arccotan(239)
print(pi)
print(float(pi))

As arccotangents of integers commonly appear in formulae for pi, when printing formulae represented using arctans, the shorthand notation [n] will be used to represent arccotan(n).

Once a formulae is expressed, new formulae that have the same value can be generated using the generate function, for example:

from arctans import arccotan, generate

pi = 16 * arccotan(5) - 4 * arccotan(239)

formulae = generate([pi])

for f in formulae:
    print(f)

This will print a number of different arctan sum formulae, including 16*[4] + -16*[21] + -4*[239] (ie pi = 16arctan(1/4) - 16arctan(1/21) - 4arctan(1/239)).

Further documentation

More detailed documentation of the latest release version of arctans can be found on Read the Docs. A series of example uses of arctans can be found in the demo folder or viewed on Read the Docs.

Getting help

You can ask questions about using arctans by using GitHub Discussions. Bugs can be reported using the GitHub issue tracker.

Contributing to arctans

Reporting bugs and suggesting enhancements

If you find a bug in arctans and want to report it, or if you want to suggest a new feature or an improvement of a current feature, please open an issue on the issue tracker.

Submitting a pull request

If you want to directly submit code to arctans, you can do this by forking the arctans repo, then submitting a pull request. If you want to contribute, but are unsure where to start, have a look at the issues labelled "good first issue".

On opening a pull request, unit tests and ruff and mypy style checks will run. You can click on these in the pull request to see where (if anywhere) there are errors in your code.

Code of conduct

We expect all our contributors to follow the Contributor Covenant. Any unacceptable behaviour can be reported to Matthew (arctans@mscroggs.co.uk).