Related papers: Digital Collections of Examples in Mathematical Sc…

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…

As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…

These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…

Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\ldots,a_n)$ where the extensions numbers $a_k$ may be…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…

In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…

This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…

I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational…

Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…

As of 2005, sampling has been incorporated in all major database systems. While efficient sampling techniques are realizable, determining the accuracy of an estimate obtained from the sample is still an unresolved problem. In this paper, we…

Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…

This paper presents a selective review of statistical computation methods for massive data analysis. A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades. In this work, we focus…

In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…

Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Computer science has experienced dramatic growth and diversification over the last twenty years. Towards a current understanding of the structure of this discipline, we analyze a cohort of the computer science literature using the DBLP…