A computer algebra system for the study of commutativity up-to-coherent homotopies

TL;DR

ComCH is a Python package that models derived commutative algebra structures, enabling effective computations of Steenrod operations on cochain complexes of spaces.

Contribution

It introduces a specialized computer algebra system for modeling and computing with commutativity up-to-coherent homotopies, focusing on operads like surjection and Barratt-Eccles.

Findings

Provides models for key operads in derived commutative algebra.

Enables effective computation of Steenrod cohomology operations.

Facilitates study of cochain complexes of topological spaces.

Abstract

The Python package ComCH is a lightweight specialized computer algebra system that provides models for well known objects, the surjection and Barratt-Eccles operads, parameterizing the product structure of algebras that are commutative in a derived sense. The primary examples of such algebras treated by ComCH are the cochain complexes of spaces, for which it provides effective constructions of Steenrod cohomology operations at all prime.