Please use this identifier to cite or link to this item: `https://hdl.handle.net/10316/103132`
DC FieldValueLanguage
dc.contributor.authorCruz, Ana Maria Marques-
dc.date.accessioned2022-10-17T22:04:44Z-
dc.date.available2022-10-17T22:04:44Z-
dc.date.issued2022-09-30-
dc.date.submitted2022-10-17-
dc.identifier.urihttps://hdl.handle.net/10316/103132-
dc.description.abstractGröbner bases are a fundamental concept in computational algebra. Since the creation of the theory behind them in 1949, by Wolfgang Gröbner, they became an important tool in any area where polynomial computations play a part, both in theory and in practice. Although they have proved to be very useful, their calculation is very expensive in certain cases. The first algorithm ever developed to compute these bases is the so-called Buchberger’s Algorithm and is still one of the most commonly used algorithms for this purpose. As a preliminary step in improving the efficiency of the algorithm, one would like to be able to predict, given an ideal, how complicated it is to compute its Gröbner basis using Buchberger’s Algorithm. In this dissertation, we address precisely this issue, following the work of Mojsilovic, Peifer and Petrovic. We create a dataset consisting of some binomial and toric distributions. Some of their properties were studied in order to seek the relationship between these characteristics and the number of polynomial additions. Then we introduce linear regression and a simple neural network model to try to predict the number of iterations using the ideals properties. Then, it is used a recurrent neural network to study the relationship between the exponents of ideals and that of polynomial additions is studied. The performance of the three models is compared and we show that there is a considerable improvement when using a recurrent neural network model and conclude that we are able to predict the number of polynomial additions, in some cases.eng
dc.language.isoeng-
dc.rightsopenAccess-
dc.subjectBases de Gröbnerpor
dc.subjectAlgoritmo Buchbergerpor
dc.subjectRegressão Linearpor
dc.subjectRedes Neuronaispor
dc.subjectIdeaispor
dc.subjectGröbner Basiseng
dc.subjectBuchberger's Algorithmeng
dc.subjectLinear Regressioneng
dc.subjectNeural Networkseng
dc.subjectIdealseng
dc.titlePredicting the perfomance of Buchberger`s algorithmeng
dc.title.alternativePrever o desempenho do algoritmo de Buchbergerpor
dc.typemasterThesis-
degois.publication.locationDepartamento de Matemática da Universidade de Coimbra-
degois.publication.titlePredicting the perfomance of Buchberger`s algorithmeng
dc.peerreviewedyes-
dc.identifier.tid203079973-
thesis.degree.disciplineMatemática-
thesis.degree.level1-
uc.degree.grantorUnitFaculdade de Ciências e Tecnologia - Departamento de Matemática-
uc.degree.grantorID0500-
uc.contributor.authorCruz, Ana Maria Marques::0000-0001-8995-1299-
uc.degree.classification16-
uc.degree.presidentejuriSantos, José Luís Esteves dos-
uc.degree.elementojuriYudin, Ivan-
uc.degree.elementojuriGouveia, João Eduardo da Silveira-
item.languageiso639-1en-
item.fulltextCom Texto completo-
item.openairetypemasterThesis-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.grantfulltextopen-
Appears in Collections:UC - Dissertações de Mestrado
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