92 research outputs found
Generic access to symbolic computing services
Symbolic computation is one of the computational domains that requires large computational
resources. Computer Algebra Systems (CAS), the main tools used for symbolic
computations, are mainly designed to be used as software tools installed on standalone
machines that do not provide the required resources for solving large symbolic computation
problems. In order to support symbolic computations an infrastructure built upon
massively distributed computational environments must be developed.
Building an infrastructure for symbolic computations requires a thorough analysis of
the most important requirements raised by the symbolic computation world and must
be built based on the most suitable architectural styles and technologies. The architecture
that we propose is composed of several main components: the Computer Algebra
System (CAS) Server that exposes the functionality implemented by one or more supporting
CASs through generic interfaces of Grid Services; the Architecture for Grid
Symbolic Services Orchestration (AGSSO) Server that allows seamless composition of
CAS Server capabilities; and client side libraries to assist the users in describing workflows
for symbolic computations directly within the CAS environment. We have also
designed and developed a framework for automatic data management of mathematical
content that relies on OpenMath encoding.
To support the validation and fine tuning of the system we have developed a simulation
platform that mimics the environment on which the architecture is deployed
Making Presentation Math Computable
This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book
Mathematical Services Composition
AbstractThis paper describes the definition and the use of a plan language in the context of mathematical web services. A plan is a document intended to describe how to use different mathematical web services to solve a particular problem. A plan is like a program in which most of the function calls have to be handled by web services. A plan is a multiple-state choreography document which could be either abstract, unresolved or resolved, depending on how much of the web services involved in the choreography is known. Such a plan can be instantiated into a composition language such as BPEL or to a mathematical routine (like a Maple routine) for execution
Making Presentation Math Computable
This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
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