ProjSym

ProjSym is an open‑source software library designed for symbolic computation and dimensional reduction of mathematical structures. It was created in 2015 by a team of researchers at the Institute for Computational Geometry and is released under the MIT license. The primary goal of ProjSym is to provide a flexible framework for manipulating symbolic expressions, projecting them between different coordinate systems, and visualizing the results, especially in the context of geometry, algebraic topology, and theoretical physics.

The core of ProjSym consists of several modules. The Symbolic Engine handles parsing, simplification, and differentiation of algebraic expressions, while the Projection Module implements a variety of algorithms to map high‑dimensional data onto lower‑dimensional manifolds. Users can choose between linear, non‑linear, and manifold‑specific projection techniques such as principal component analysis, manifold learning, and toric embeddings. A dedicated Visualization Engine renders the projected data in 2‑ and 3‑dimensional plots, supporting interactive exploration through zooming and rotating.

ProjSym is written in Python and interfaces easily with NumPy, SciPy, and matplotlib. It also offers bindings to the Julia language for performance-critical operations. The library is installed via pip and can be used as a command‑line tool or imported as a Python module. Documentation is generated automatically from docstrings and includes tutorials, API references, and sample notebooks.

Academic researchers employ ProjSym for visualizing solutions of partial differential equations, studying the geometry of complex manifolds, and exploring symmetry groups in particle physics. In industry, it is used for dimensionality reduction in data‑analysis pipelines and to generate synthetic datasets with controlled geometric properties. The community around ProjSym has grown through contributions on GitHub, where issues, pull requests, and feature suggestions are actively managed. Continual updates deliver new projection algorithms, performance improvements, and expanded support for symbolic algebra systems. Overall, ProjSym offers a versatile platform for anyone requiring precise symbolic manipulation combined with robust dimensional reduction and visualization capabilities.