Related papers: A modular extension for a computer algebra system
Rigged modules over an operator algebra are a generalization of Hilbert modules over a $C^{\star}$-algebra. We characterize the rigged modules over an operator algebra $\mathcal A$ which are orthogonally complemented in $C_\infty(\mathcal…
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
In this work, we describe a self-replication-based mechanism for designing agents of increasing complexity. We demonstrate the validity of this approach by solving simple, standard evolutionary computation problems in simulation. In the…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
This paper describes a way to improve the scalability of program synthesis by exploiting modularity: larger programs are synthesized from smaller programs. The key issue is to make each "larger-created-from-smaller" synthesis sub-problem be…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Reconfigurable computing refers to the use of processors, such as Field Programmable Gate Arrays (FPGAs), that can be modified at the hardware level to take on different processing tasks. A reconfigurable computing platform describes the…
ABCpy is a highly modular scientific library for Approximate Bayesian Computation (ABC) written in Python. The main contribution of this paper is to document a software engineering effort that enables domain scientists to easily apply ABC…
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…
We present discrete models of special biserial (SB) algebras and their string modules, drawing inspiration from cellular automata, and cast new light on patterns among syzygies. We explore applications of our models to open questions in…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
Simulations with high accuracy are an essential part of scientific research to accelerate the innovation process. They are especially useful for finding novel approaches or optimizing existing methods. Today, powerful software tools are…
A range of methodologies and techniques are available to guide the design and implementation of language extensions and domain-specific languages. A simple yet powerful technique is based on source-to-source transformations interleaved…