Related papers: Introducing Geometric Algebra to Geometric Computi…
Abstraction is one of the fundamental concepts of software design. Consequently, the determination of an appropriate abstraction level for the multitude of artefacts that form a software system is an integral part of software engineering.…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
This paper presents a concept of a domain-specific framework for software analytics by enabling querying, modeling, and integration of heterogeneous software repositories. The framework adheres to a multi-layered abstraction mechanism that…
Over the past years there has been quite a lot of activity in the algebraic community about using algebraic methods for providing support to model-driven software engineering. The aim of this workshop is to gather researchers working on the…
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
The use of statistical software in academia and enterprises has been evolving over the last years. More often than not, students, professors, workers, and users, in general, have all had, at some point, exposure to statistical software.…
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…
This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
We present graph-based modeling abstractions to represent cyber-physical dependencies arising in complex systems. Specifically, we propose an algebraic graph abstraction to capture physical connectivity in complex optimization models and a…
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
Reasoning about functions that operate over algebraic data types is an important problem for a large variety of applications. One application of particular interest is network applications that manipulate or reason about complex message…
Geometric Deep Learning techniques have become a transformative force in the field of Computer-Aided Design (CAD), and have the potential to revolutionize how designers and engineers approach and enhance the design process. By harnessing…