Homology Computation by Reduction of Chain Complexes

master
dc.abstract.enHomology is a fundemental part of algebraical topology. It is a sound tool used for classifying topological spaces by assigning a sequence of abelian groups to a space. Its main advantage is that we can discover global properties of a space only by performing local computations. In computational homology it is very common that the space to be analyzed is given as a set of numerical (experimental) data.This work deals with computing homology of a chain complex. Not only it contains the classical approach (based on Smith Normal Form) but also an efficient reduction algorithm (CCR) along with its implementation, analysis and experimental results is described.pl
dc.abstract.plHomology is a fundemental part of algebraical topology. It is a sound tool used for classifying topological spaces by assigning a sequence of abelian groups to a space. Its main advantage is that we can discover global properties of a space only by performing local computations. In computational homology it is very common that the space to be analyzed is given as a set of numerical (experimental) data.This work deals with computing homology of a chain complex. Not only it contains the classical approach (based on Smith Normal Form) but also an efficient reduction algorithm (CCR) along with its implementation, analysis and experimental results is described.pl
dc.affiliationWydział Matematyki i Informatykipl
dc.contributor.advisorMrozek, Marian - 130783 pl
dc.contributor.authorWitek, Przemysławpl
dc.contributor.departmentbycodeUJK/WMI2pl
dc.contributor.reviewerŚlusarek, Maciej - 132329 pl
dc.contributor.reviewerMrozek, Marian - 130783 pl
dc.date.accessioned2020-07-14T18:16:27Z
dc.date.available2020-07-14T18:16:27Z
dc.date.submitted2011-09-15pl
dc.fieldofstudyinformatyka teoretycznapl
dc.identifier.apddiploma-54840-62950pl
dc.identifier.projectAPD / Opl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/169797
dc.languagepolpl
dc.subject.enhomology, algebraical topology, cubical sets, data structures, smith formpl
dc.subject.plhomology, algebraical topology, cubical sets, data structures, smith formpl
dc.titleHomology Computation by Reduction of Chain Complexespl
dc.typemasterpl
dspace.entity.typePublication
dc.abstract.enpl
Homology is a fundemental part of algebraical topology. It is a sound tool used for classifying topological spaces by assigning a sequence of abelian groups to a space. Its main advantage is that we can discover global properties of a space only by performing local computations. In computational homology it is very common that the space to be analyzed is given as a set of numerical (experimental) data.This work deals with computing homology of a chain complex. Not only it contains the classical approach (based on Smith Normal Form) but also an efficient reduction algorithm (CCR) along with its implementation, analysis and experimental results is described.
dc.abstract.plpl
Homology is a fundemental part of algebraical topology. It is a sound tool used for classifying topological spaces by assigning a sequence of abelian groups to a space. Its main advantage is that we can discover global properties of a space only by performing local computations. In computational homology it is very common that the space to be analyzed is given as a set of numerical (experimental) data.This work deals with computing homology of a chain complex. Not only it contains the classical approach (based on Smith Normal Form) but also an efficient reduction algorithm (CCR) along with its implementation, analysis and experimental results is described.
dc.affiliationpl
Wydział Matematyki i Informatyki
dc.contributor.advisorpl
Mrozek, Marian - 130783
dc.contributor.authorpl
Witek, Przemysław
dc.contributor.departmentbycodepl
UJK/WMI2
dc.contributor.reviewerpl
Ślusarek, Maciej - 132329
dc.contributor.reviewerpl
Mrozek, Marian - 130783
dc.date.accessioned
2020-07-14T18:16:27Z
dc.date.available
2020-07-14T18:16:27Z
dc.date.submittedpl
2011-09-15
dc.fieldofstudypl
informatyka teoretyczna
dc.identifier.apdpl
diploma-54840-62950
dc.identifier.projectpl
APD / O
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/169797
dc.languagepl
pol
dc.subject.enpl
homology, algebraical topology, cubical sets, data structures, smith form
dc.subject.plpl
homology, algebraical topology, cubical sets, data structures, smith form
dc.titlepl
Homology Computation by Reduction of Chain Complexes
dc.typepl
master
dspace.entity.type
Publication
Affiliations

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