Homogeneous Integer-Valued Polynomials of Three Variables
dc.contributor.author | B.Langlois, Marie-Andrée | |
dc.contributor.copyright-release | Yes | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.external-examiner | David Wehlau | en_US |
dc.contributor.graduate-coordinator | David Iron | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.thesis-reader | Karl Dilcher | en_US |
dc.contributor.thesis-reader | Rob Noble | en_US |
dc.contributor.thesis-supervisor | Keith Johnson | en_US |
dc.date.accessioned | 2018-06-15T17:02:21Z | |
dc.date.available | 2018-06-15T17:02:21Z | |
dc.date.defence | 2018-06-08 | |
dc.date.issued | 2018-06-15T17:02:21Z | |
dc.description.abstract | A polynomial f in Q[x,y,z] is integer-valued if f(x,y,z)is an integer, whenever x, y, z are integers. This work will look at the case where f is homogeneous and construct polynomials such that the denominators are divisible by the highest prime power possible and find bases for the modules of homogeneous integer-valued polynomials (IVPs). We will present computational methods for constructing such bases and an algebraic method to construct these. We explain the connection between 3-variable homogeneous IVPs of degree m and 3-variable IVPs of degree m, as well as with 2-variable IVPs of degree m evaluated at odd values only, then use linear algebra to calculate bases in both cases. In order to obtain polynomials written as a product of linear factors, we will look into extending the construction of finite projective planes to rings and explain a connection between line coverings of those planes and homogeneous IVPs. | en_US |
dc.identifier.uri | http://hdl.handle.net/10222/73970 | |
dc.language.iso | en | en_US |
dc.subject | number theory | en_US |
dc.subject | homogeneous polynomials | en_US |
dc.subject | integer valued polynomial | en_US |
dc.subject | commutative algebra | en_US |
dc.subject | linear algebra | en_US |
dc.subject | projective plane | en_US |
dc.title | Homogeneous Integer-Valued Polynomials of Three Variables | en_US |
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