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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.
In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient method for a particular problem. To solve a Cauchy problem for a system of
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an algebraic pattern, bywhich we mean an $infty$-category equipped with a factorization system and a collection of elementary objects. Examples
The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of the homotopy
We study the mod-$ell$ homotopy type of classifying spaces for commutativity, $B(mathbb{Z}, G)$, at a prime $ell$. We show that the mod-$ell$ homology of $B(mathbb{Z}, G)$ depends on the mod-$ell$ homotopy type of $BG$ when $G$ is a compact connected
The commutative differential graded algebra $A_{mathrm{PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{mathcal{I}}(X)$ of $A_{mathrm{PL}}(X)$. Our