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Mathematical Sciences
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Department of Mathematics
University of California Davis
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ArithmeticalCongruenceMonoid is a Python class for use with the computer algebra system Sage that adds functionality for working with Arithmetical Congruence Monoids. The package was developed as a semester project with Jacob Hartzer, an undergraduate student at Texas A&M University.
  • Autocomplete is supported in the Sage web interface, i.e. typing
    will give a list of available functions. See the sample code below.
  • Currently the package can factor monoid elements and compute several combinatorial factorization invariants. More functionality will continue to be added, and feature requests are encouraged, just send me an email!
Please note that this is an alpha version and subject to change without notice.
Given below is a current version (0.1a) of ArithmeticalCongruenceMonoid.sage. You can also email me for a cutting-edge version. ArithmeticalCongruenceMonoid.sage is released under the terms of the MIT license. The MIT License is simple and easy to understand and it places almost no restrictions on what you can do with this software.
To set up your machine to use ArithmeticalCongruenceMonoid.sage, do the following.
  • First, install Sage on your machine. Instructions for doing so can be found here.
  • Next, download ArithmeticalCongruenceMonoid.sage at the link above, and place it in your favorite folder.
The following code fragment gives an overview of how to use the ArithmeticalCongruenceMonoid class from within Sage, and more complete documentation will be added in the near future.
			hilbert = ArithmeticalCongruenceMonoid(1,4)
			print hilbert.Factorizations(441)
			print hilbert.DeltaSet(441)