Related papers: MathPartner Computer Algebra
AI-powered education technologies can support students and teachers in computer science education. However, with the recent developments in generative AI, and especially the increasingly emerging popularity of ChatGPT, the effectiveness of…
High performance computing has been used in various fields of astrophysical research. But most of it is implemented on massively parallel systems (supercomputers) or graphical processing unit clusters. With the advent of multicore…
We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…
\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Procedural material graphs are a compact, parameteric, and resolution-independent representation that are a popular choice for material authoring. However, designing procedural materials requires significant expertise and publicly…
We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a…
This article covers how a computer algebra system (CAS) wxMaxima can be explored for teaching and learning Single-Variable and Multivariable Calculus for Korean digital natives. We present several examples where \emph{wxMaxima} can handle…
Looking back at the history of calculators, one can see that they become less functional and more computationally expensive over time. A modern calculator runs on a personal computer and is drawn at 60 fps only to help us click a few digits…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive…
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…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
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…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…