Related papers: Software Portability for Computer Algebra
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The aim of this paper is to propose a strategy to implement the Minimal Model Program in modern computer algebra systems.
The mid-1990s saw the design of programming languages for software architectures, which define the high-level aspects of software systems including how code components were composed to form full systems. Our paper "Abstractions for Software…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
The software patterns provide building blocks to the design and implementation of a software system, and try to make the software engineering to progress from experience to science. The software patterns were made famous because of the…
Computer Science education has been evolving over the years to reflect applied realities. Until about a decade ago, theory of computation, algorithm design and system software dominated the curricula. Most courses were considered core and…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Know a days Computer system become essential and it is most commonly used in every field of life. The computer saves time and use to solve complex and extensive problem quickly in an efficient way. For this purpose software programs are…
In the last 15 years, software architecture has emerged as an important software engineering field for managing the development and maintenance of large, software- intensive systems. Software architecture community has developed numerous…
A key mission of computer science is to enable people realize their creative ideas as naturally and painlessly as possible. Software engineering is at the center of this mission -- software technologies enable reification of ideas into…
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…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
Modern software systems are built to be used in dynamic environments using configuration capabilities to adapt to changes and external uncertainties. In a self-adaptation context, we are often interested in reasoning about the performance…
Software development projects management is a complex endeavor because it requires dealing with numerous unforeseen events that constantly arise along the way and that go against the expectations that had been established at the beginning.…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
Software systems impact society at different levels as they pervasively solve real-world problems. Modern software systems are often so sophisticated that their complexity exceeds the limits of human comprehension. These systems must…
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
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…