78,085 research outputs found
Periodic solutions for systems of coupled nonlinear Schrödinger equations with five and six components
Systems of coupled nonlinear Schrödinger (CNLS) equations arise in several branches of physics, e.g., optics and plasma physics. Systems with two or three components have been studied intensively. Recently periodic solutions for CNLS systems with four components are derived. The present work extends the search of periodic solutions for CNLS systems to those with five and six components. The Hirota bilinear method, theta and elliptic functions are employed in the process. The long wave limit is studied, and known results of solitary waves are recovered. The validity of these periodic solutions is verified independently by direct differentiation with computer algebra software. ©2002 The American Physical Society.published_or_final_versio
Toric Geometry in OSCAR
We report on the computer implementation for toric geometry in the computer
algebra system .
The main architectural feature of is that its four
fundamental tools (Hecke, Nemo), ,
and are ,
rather than external software. Toric geometry benefits greatly from this
architecture.
is a high-performance programming language designed for
numerical and scientific computing. The growing ecosystem of
packages ensures its continued viability for scientific computing and data
analysis. Indeed, is written in . This implies
that the performance of should be comparable or even better
than many other implementations.Comment: 6 pages, prepared for the ComputerAlgebraRundbrief (March 2023
A Process Algebra Software Engineering Environment
In previous work we described how the process algebra based language PSF can
be used in software engineering, using the ToolBus, a coordination architecture
also based on process algebra, as implementation model. In this article we
summarize that work and describe the software development process more formally
by presenting the tools we use in this process in a CASE setting, leading to
the PSF-ToolBus software engineering environment. We generalize the refine step
in this environment towards a process algebra based software engineering
workbench of which several instances can be combined to form an environment
Robust Computer Algebra, Theorem Proving, and Oracle AI
In the context of superintelligent AI systems, the term "oracle" has two
meanings. One refers to modular systems queried for domain-specific tasks.
Another usage, referring to a class of systems which may be useful for
addressing the value alignment and AI control problems, is a superintelligent
AI system that only answers questions. The aim of this manuscript is to survey
contemporary research problems related to oracles which align with long-term
research goals of AI safety. We examine existing question answering systems and
argue that their high degree of architectural heterogeneity makes them poor
candidates for rigorous analysis as oracles. On the other hand, we identify
computer algebra systems (CASs) as being primitive examples of domain-specific
oracles for mathematics and argue that efforts to integrate computer algebra
systems with theorem provers, systems which have largely been developed
independent of one another, provide a concrete set of problems related to the
notion of provable safety that has emerged in the AI safety community. We
review approaches to interfacing CASs with theorem provers, describe
well-defined architectural deficiencies that have been identified with CASs,
and suggest possible lines of research and practical software projects for
scientists interested in AI safety.Comment: 15 pages, 3 figure
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A general theory of action languages
We present a general theory of action-based languages as a paradigm, for the description, of those computational
systems which include elements of concurrency and networking, and extend this approach
to describe dist.ributed systems and also t,o describe the interaction of a system, with an environment.
As part of this approach we introduce the Action Language as a common model for the class of nondeterministic
concurrent programming languages and define its intensional and interaction semantics
in terrors of continuous transformation of environment behavior. This semantics i.s specialized for
programs with stores, and extended to describe distributed computations
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