On the Local Smith Normal Form
Smith Normal Form over Local Rings and Related Problems by Mustafa Elsheikh A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Computer Science Waterloo, Ontario, Canada, 2017 c Mustafa Elsheikh 2017 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner Jean-Guillaume Dumas Professeur, Math´ematiques Appliqu´ees Universit´eGrenoble Alpes, France Supervisor Mark Giesbrecht Professor, David R. Cheriton School of Computer Science University of Waterloo, Canada Internal Member George Labahn Professor, David R. Cheriton School of Computer Science University of Waterloo, Canada Internal Member Arne Storjohann Associate Professor, David R. Cheriton School of Computer Science University of Waterloo, Canada Internal-external Member Kevin Hare Professor, Department of Pure Mathematics University of Waterloo, Canada ii Author's Declaration This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions I am the sole author of Chapters 1, 4, and 7. Chapter 2 is based on an article co- authored with Mark Giesbrecht, B. David Saunders, and Andy Novocin. Chapter 3 is based on collaboration with Mark Giesbrecht, and B. David Saunders. Chapter 5 is based on an article co-authored with Mark Giesbrecht. Chapter 6 is based on collaboration with Mark Giesbrecht, and Andy Novocin.
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