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The constructible module provides exact representation of constructible numbers in Python.

Python 2 and Python 3 are supported.

The constructible numbers are the smallest field containing the rational numbers, where the square root of any non-negative constructible number is constructible as well. The non-negative constructible numbers are the lengths which can be constructed from the unit length using only a compass and a straightedge.

Usually the sqrt function is enough to work with constructible numbers:

>>> from constructible import sqrt
>>> x = sqrt(2) + sqrt(3)
>>> print(x)
((0 + 1 * sqrt(2)) + (1 + 0 * sqrt(2)) * sqrt((3 + 0 * sqrt(2))))
>>> y = x*x
>>> print(y)
((5 + 0 * sqrt(2)) + (0 + 2 * sqrt(2)) * sqrt((3 + 0 * sqrt(2))))
>>> z = y*y
>>> t = 10*y - z
>>> t == 1
True

To install from PYPI just type

pip install constructible

The library is a single pure python file, so it is also easy to install by hand.

There are some tests using unittest. Thanks to Travis-CI each push to github triggers a test:

The following steps are needed:

• make sure .pypirc is up to date:

  [distutils]
  index-servers =
    pypinew
    pypitest
  
  [pypinew]
  repository = https://upload.pypi.org/legacy/
  username=xxx
  password=xxx
  
  [pypitest]
  repository=https://test.pypi.org/legacy/
  username=xxx
  password=xxx
  

• Update the version in setup.py

• Tag the version in git:

  git tag 0.1 -m "Adds a tag so that we can put this on PyPI."
  git push --tags origin
  

• Test release with:

  python setup.py sdist upload -r pypitest
  

• Productive release with:

  python setup.py sdist upload -r pypinew
  

• 2016-05-23 V0.1 Initial Release
• 2016-09-30 V0.2 Fixing Issue 1 and added Tests
• 2016-10-03 V0.3 Fixing Issue 2
• 2016-10-23 V0.4 Added __hash__ and __float__, speed optimizations
• 2020-07-08 V0.5 New hash function and improvements by Arsenii A.

Thanks to Anders Kaseorg whose implementation of constructible numbers in Haskell provided inspiration and in particular the algorithm for taking square roots in quadratic extension fields.