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

Using uv (recommended):

uv add git+https://github.com/blackgauss/pocketpartition.git

Using pip:

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

To update with pip:

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