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Mathematical Sciences
Building, Room 3149
Department of Mathematics
University of California Davis
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Davis, CA 95616
NumericalSemigroup is a Python class for use with the computer algebra system Sage that adds functionality for working with Numerical Semigroups. Internally, it uses the GAP package numericalsgps, and is intended to help ease the interface between Sage and the GAP package.
  • All types returned are true Sage types, not just wrappers around GAP types.
  • Autocomplete is supported in the Sage web interface, i.e. typing
    will give a list of available functions. See the sample code below.
  • Most factorization invariants supported by GAP are implemented, and more functionality will continue to be added. In fact, feature requests are encouraged, just send me an email!
Please note that this is an alpha version and subject to change without notice.
You can find an action shot here.
Given below is a current version of NumericalSemigroup.sage. You can also email me for a cutting-edge version. NumericalSemigroup.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 NumericalSemigroup.sage, do the following.
  • First, install Sage on your machine. Instructions for doing so can be found here.
  • Next, install the GAP package numericalsgps into your Sage installation. Instructions for installing GAP packages in Sage can be found here, and the URL for the numericalsgps package can be found here.
  • Finally, download NumericalSemigroup.sage at the link above, and place it in your favorite folder.
The following code fragment gives an overview of how to use the NumericalSemigroup class from within Sage, and more complete documentation will be added in the near future.
			McNuggets = NumericalSemigroup([6,9,20])
			print McNuggets.frob
			print McNuggets.LengthSet(400)
			print McNuggets.DeltaSet(400)
			print McNuggets.OmegaPrimality(400)
			print McNuggets.CatenaryDegree(400)