PyTree

A fast implementation of trees from the mathematical theory of graphs

Inspired and applied in condensed matter physics, cellular biology and the World Wide Web.

Mathematical Introduction

Graphs

Mathematical objects of the theory of graphs have one-to-one matrix representations, as described by the theory of linear algebra. In general, a graph is a network structure, whose off-diagonal terms in the matrix representation are known to Condensed Matter Physicists as hopping or interaction terms.

Trees

A particular graph, known as a tree, is a network with a hierarchical structure, which we use to index objects in their matrix representation.

Python implementation

The Tree is a Python subclass of a List, which adds the following attributes and methods:

Attributes

• parent : Tree or none (default) children : Tree or none (default)
• ancestors : list of Trees lineage upwards
• root: root of the tree (parent without parent)
• descendants : lists lineage downwards (list of list of Trees)
• buds : lists descendants without descendants

Methods

• set_ids : add an index (id) to the buds of this Tree
• get_ids : get the indices (ids) of the buds of this Tree .attribute : attributes are inherited down the linage

Summary

A graph structure defines a matrix; a tree structure indexes the matrix.

The tree structure adds parents, children, ancestors, descendants and inheritance of attributes.

Installation

Development environment

pip install --editable . --break-system-packages

Build and upload

python3 -m build
twine upload dist/*