Sigmatools

Sigmatools is an open‑source software library designed for symbolic and numeric analysis of mathematical expressions involving the Greek letter sigma as a variable or operator. The project was initiated in 2017 by a team of researchers from the University of Hamburg and the Institute of Applied Mathematics in Prague. It has grown into a modular framework that supports both symbolic manipulation in a high‑level language and efficient numeric evaluation through compiled extensions in C++.

The core of Sigmatools is a lightweight parser that translates user expressions into an abstract syntax tree. From this tree the library can perform algebraic simplification, differentiation, integration, and series expansion. Users can also define custom sigmas—typically representing summation indices or aggregate operators—and treat them like normal mathematical symbols, allowing complex sums to be expressed and simplified without manual index handling.

Sigmatools offers an API for Python, Rust, and JavaScript, making it accessible to a broad range of developers. Its numeric engine uses SIMD instructions to accelerate evaluation of large symbolic expressions, and it can interface with popular numerical libraries such as NumPy and Eigen. Additional features include automatic differentiation for machine‑learning workloads, and a command‑line interface that can be used in shell scripts for batch processing.

The library is distributed under the MIT license and is maintained on GitHub. Documentation is available in the form of a read‑the‑docs site, with tutorials that cover basic usage, advanced symbolic techniques, and performance optimization. Community support is provided through a dedicated GitHub Discussions forum and a weekly IRC channel.

Because of its blend of symbolic power and high‑performance execution, Sigmatools is commonly used in research projects dealing with combinatorial sums, financial mathematics, and physics simulations where sigma‐style notation is prevalent.