Related papers: Computer Algebra in R with caracas
This paper explores an innovative approach to teaching data wrangling skills to students through hands-on activities before transitioning to coding. Data wrangling, a critical aspect of data analysis, involves cleaning, transforming, and…
Computing makes up a large and growing component of data science and statistics courses. Many of those courses, especially when taught by faculty who are statisticians by training, teach R as the programming language. A number of…
We design the Arboretum$.$hs package for symbolic computations with algebras of trees and more general graphs in Haskell. Thanks to the declarative nature of functional programming, the package's implementation closely follows mathematical…
We introduce BayesChange, a computationally efficient R package, built on C++, for Bayesian change point detection and clustering of observations sharing common change points. While many R packages exist for change point analysis,…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We present CubicJordanMatrixAlg, a GAP package for symbolic computation in cubic Jordan matrix algebras and in related Lie-theoretic structures. As an application, we use it to compute certain (commutator) relations in $F_4$-graded groups…
This article explains the usage of R package CausalModels, which is publicly available on the Comprehensive R Archive Network. While packages are available for sufficiently estimating causal effects, there lacks a package that provides a…
R packages are the fundamental units of reproducible code in R, providing a mechanism for distributing user-developed code, documentation, and data. Docker is a virtualization technology that allows applications and their dependencies to be…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
We report on the computer implementation for toric geometry in the computer algebra system $\texttt{OSCAR}$. The main architectural feature of $\texttt{OSCAR}$ is that its four fundamental tools $\texttt{Antic}$ (Hecke, Nemo),…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian…
Retrieval-augmented generation (RAG) combines document retrieval with large language models to produce responses grounded in external evidence. While several R packages support core components of RAG workflows, integrated evaluation of RAG…
Space-filling experimental design techniques are commonly used in many computer modeling and simulation studies to explore the effects of inputs on outputs. This research presents raxpy, a Python package that leverages expressive annotation…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…