Pocket -| Partition

Pocket Partition Documentation

Pocket Partition is a Python package designed for handling numerical sets and partitions.

For more detailed information, refer to the full documentation available at Read the Docs.

Installation

To install Pocket Partition, run the following command:

pip install git+https://github.com/blackgauss/pocketpartition.git

To update Pocket Partition run the following command:

pip install --upgrade git+https://github.com/blackgauss/pocketpartition.git

Basic Usage

Here's a simple example to get you started:

from pocketpartition import NumericalSet, NumericalSemigroup, get_atom_monoid, get_partition

# Make a numerical set
T = NumericalSet(gaps=[1,2,3,9,11,15])

# Get its atom monoid
S = get_atom_monoid(T)

# Minimal Generating Set
print(S.minimal_generating_set())

# Get its partition
P = get_partition(T)

# Display Partition with hooks
P.display(show_hooks=True)

# Get help on all methods of a certain class
help(S)

WARNING

This package can work alongside SageMath and the numericalsgps package. However, there are a few important points to note:

1. Namespace Conflicts: To avoid conflicts with the numericalsgps package, import pocketpartition using an alias, such as pp or another name.

   import pocketpartition as pp

2. Type Conversion: SageMath uses its own Integer() type, which is different from Python's int(). You may need to convert Integer() types to int() before using them with pocketpartition.

   n = int(Integer(5))  # Convert SageMath Integer to Python int

Frequently Asked Questions

Q: I already have SageMath and the numericalsgps package. Why do I need this?

A: This package is particularly useful for working with the correspondences between numerical sets, partitions, numerical semigroups, and posets.

Theory References

W.I.P.

Code References

Some functions/classes inspired by

• Sagemath SageMath GitHub repository.
• Numerical Semigroups package for GAP numericalsgps GitHub repository