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The Design of the CoCoA 3 System

This thesis presents the design of CoCoA, a specialpurpose computer algebra system dedicated to the Commutative Algebra. After an Introduction to the field of the Computer Algebra the system is presented from the architectural point of view. Two chapters expose the Groebner Framework, an advanced tool for doing computations Based on an Generalization of the Buchberger Algorithm, and an application of this tool to the computation of Minimal Free Resolutions. Then it is introduced EEE, an new advanced polynomial representation which exhibits both great compactness of space and good performance. A final chapter present a general approach for accessing computing systems in an interactive Web-based environment.

Mostra/Nascondi contenuto.
IntroductionThis thesis presents the design of the architecture of CoCoA, a special purpose computeralgebra system dedicated to the Commutative Algebra.Contribution of the ThesisThe major contribution of the thesis consists of the presentation of the approachIhaveusedin order to design and develop the CoCoA system. The approach consists of a combinationof methodologies and techniques, used to satisfy the needs of the typical user of the system:a matematician with few or no background on programming.In particular I have focused mycontribution on the design of the architecture of the system,which has been privileged with respect to the mathematical research. The major contri-bution on the mathematical side has been the invention of EEE, an eÆcient representationfor multivariate polynomials.The strong points of the system architecture are: CoCoAL, the high level language for the user interaction; CTL, a low level language used to abstract the system behaviour from the syntaxsugar of CoCoAL and for eÆcency reasons; the CDevices, which consist of an abstraction of the phisical devices, and are usedto ensure a high portability to the system; the Grobner Framework, an advanced technique designed to solve di erent Grobner-related problems using a single, parametric Buchberger Algorithm; the Session ManagementFramework, a general approach for writing distributed web-based applications which interact with Computation Systems.4

Tesi di Dottorato

Dipartimento: DISI: Dip. Informatica e Scienze dell'Informazione

Autore: Antonio Capani Contatta »

Composta da 105 pagine.


Questa tesi ha raggiunto 1022 click dal 20/03/2004.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.