PyEVSpace User Guide

What is PyEVSpace?

PyEVSpace is a Python Euclidean vector space package containing types and methods for representing vector quantites and facilitating rotations between reference frames. PyEVSpace is designed for 3-dimensional space only, which allows for optimum speed since size checks to not occur.

Vector Space

A vector space is a set whose elements (vectors) obey certain axioms like addition and scaling. The components of vectors are usually elements of a field, namely the complex or real numbers. Vector spaces can be varrying dimensions, which generally is the number of directions associated with the vector space.

Euclidean Vector Space

A Euclidean vector space is a vector space intended to represent physical space. Mathematically it is essentially identical to general vector spaces, they only differ conceptually. For example, the infinte dimensional vector space of polynomials is used to solve linear systems of equations, whereas a Euclidean vector space is a finite vector space used to model physical space with Euclidean vectors, whose length and direction are meant to represent physical quantities with magnitude and direction like a velocity or force.

A Python Euclidean Vector Space

PyEVSpace is simply a Euclidean vector space implemented for Python. Its 3-dimensions are meant to represent physical quantites of our world that have both a length and a direction. These can be as simple as a position of something or a more nuanced value like angular momentum. Only 3-dimensional vectors are supported because PyEVSpace is designed with real world physical principles in mind. By limiting the dimensionality of the vector space, a significant performance can be gained by eliminating size checking for every single operation.

Why Use PyEVSpace?

PyEVSpace is a compiled library written in C, and is optimized with performance in mind. This in combination with the fixed dimension of the vector space means the library performs extremely fast. This makes PyEVSpace the perfect package to provide the framework for your Python project, or a simple tool to glue together an existing project with its small footprint. The interface is simple enough for the basic user to understand, but also offers more advanced functionality like providing memory buffers to the underlying blocks of memory for the vectors and matrices.

To learn more checkout the API documentation and the examples section for relavent examples.