Related papers: MathPartner Computer Algebra
In this paper we present efficient computational and symbolic algorithms for solving a nearly pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS)such as MAPLE, MACSYMA, MATHEMATICA, and…
GNU TeXmacs is a free wysiwyg word processor providing an excellent typesetting quality of texts and formulae. It can also be used as an interface to Computer Algebra Systems (CASs). In the present work, interfaces to three general-purpose…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
We present a system, called CASS, for the analysis of functional logic programs. The system is generic so that various kinds of analyses (e.g., groundness, non-determinism, demanded arguments) can be easily integrated. In order to analyze…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
A unified mathematical language for medicine and science will be presented. Using this language, models for DNA replication, protein synthesis, chemical reactions, neurons and a cardiac cycle of a heart have been built. Models for Turing…
It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…
This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
The emergence of ChatGPT has been rapid, and although it has demonstrated positive impacts in certain domains, its influence is not universally advantageous. Our analysis focuses on ChatGPT's capabilities in Mathematics Education,…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system…
As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the…
A novel approach is presented to teach the parallel and distributed computing concepts of synchronization and remote memory access. The single program multiple data (SPMD) partitioned global address space (PGAS) model presented in this…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale…
The standardization of an interface for dense linear algebra operations in the BLAS standard has enabled interoperability between different linear algebra libraries, thereby boosting the success of scientific computing, in particular in…
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit…