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dc.contributor.advisorVerschelde, Janen_US
dc.contributor.authorAdrovic, Dankoen_US
dc.date.accessioned2013-02-21T21:14:52Z
dc.date.available2013-02-21T21:14:52Z
dc.date.created2012-12en_US
dc.date.issued2013-02-21
dc.date.submitted2012-12en_US
dc.identifier.urihttp://hdl.handle.net/10027/9735
dc.description.abstractIn this thesis, we develop a polyhedral method to solve polynomial systems. We are primarily interested in obtaining the Puiseux series representations of positive dimensional solution sets for square polynomial systems and systems, which consist of more equations than unknowns. By developing our polyhedral method, we aim to generalize polyhedral homotopies. Our polyhedral method can be seen as the symbolic-numeric version of the fundamental theorem of tropical algebraic geometry. We illustrate our polyhedral method on the cyclic n-roots problems and offer a tropical perspective on the lemma of Backelin.en_US
dc.language.isoenen_US
dc.subjectNewton-Puiseux methoden_US
dc.subjectpolyhedral homotopiesen_US
dc.subjectPuiseux seriesen_US
dc.subjecttropismen_US
dc.subjectinitial formsen_US
dc.subjectunimodular coordinate transformationsen_US
dc.subjectcyclic n-roots problemen_US
dc.titleSolving Polynomial Systems With Tropical Methodsen_US
thesis.degree.departmentMathematics, Statistics, and Computer Scienceen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberCuller, Marcen_US
dc.contributor.committeeMemberDumas, Daviden_US
dc.contributor.committeeMemberGreenblatt, Michaelen_US
dc.contributor.committeeMemberHampton, Marshallen_US
dc.type.materialtexten_US


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