Related papers: simpcomp -- A GAP toolbox for simplicial complexes
The central problem in computational algebraic topology is the computation of the homotopy groups of a given space, represented as a simplicial set. Algorithms have been found which achieve this, but the running times depend on the size of…
The automated assembly of complex products requires a system that can automatically plan a physically feasible sequence of actions for assembling many parts together. In this paper, we present ASAP, a physics-based planning approach for…
Galaxy morphological classification is a fundamental aspect of galaxy formation and evolution studies. Various machine learning tools have been developed for automated pipeline analysis of large-scale surveys, enabling a fast search for…
We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP
These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph ${\tt G}$ is the simplicial complex whose faces are the multipaths of ${\tt G}$. We compute the Euler characteristic, and associated…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
"GRAMA" is a Mathematica package for doing symbolic tensor computations and complicated algebraic manipulations in 10-dimensional (D=10) simple (N=1) supergravity. The main new ingredients of this package inside the general Mathematica…
The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is called discretization map. Using the geometry of the tangent and…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally…
The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require…
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…
scida is a Python package for reading and analyzing large scientific data sets with support for various cosmological and galaxy formation simulations out-of-the-box. Data access is provided through a hierarchical dictionary-like data…
We introduce a new Macaulay 2 package, SimplicialDecomposability, which works in conjunction with the extant package SimplicialComplexes in order to compute a shelling order, if one exists, of a specified simplicial complex. Further,…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
In this short note we count the finite semirings up to isomorphism, and up to isomorphism and anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.
In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative…
A club structure is defined on the category of simplicial sets. This club generalizes the operad of associative rings by adding "amalgamated" products.
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…