Related papers: MathPartner Computer Algebra
Multi-agent systems (MAS) utilizing multiple Large Language Model agents with Retrieval Augmented Generation and that can execute code locally may become beneficial in cosmological data analysis. Here, we illustrate a first small step…
Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
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…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
Parametric Computer-aided design (CAD) enables the creation of reusable models by integrating variables into geometric properties, facilitating customization without a complete redesign. However, creating parametric designs in…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
Matlab is one of the most widely used mathematical computing environments in technical computing. It has an interactive environment which provides high performance computing (HPC) procedures and easy to use. Parallel computing with Matlab…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
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…
When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large…
In this paper, we provide an overview of the SAT+CAS method that combines satisfiability checkers (SAT solvers) and computer algebra systems (CAS) to resolve combinatorial conjectures, and present new results vis-\`a-vis best matrices. The…
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 present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…