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dc.contributor.authorTilak, Hrushikesh
dc.date.accessioned2010-08-31 20:09:32 (GMT)
dc.date.available2010-08-31 20:09:32 (GMT)
dc.date.issued2010-08-31T20:09:32Z
dc.date.submitted2010-08-20
dc.identifier.urihttp://hdl.handle.net/10012/5455
dc.description.abstractWe consider the problem of finding a sparse multiple of a polynomial. Given a polynomial f ∈ F[x] of degree d over a field F, and a desired sparsity t = O(1), our goal is to determine if there exists a multiple h ∈ F[x] of f such that h has at most t non-zero terms, and if so, to find such an h. When F = Q, we give a polynomial-time algorithm in d and the size of coefficients in h. For finding binomial multiples we prove a polynomial bound on the degree of the least degree binomial multiple independent of coefficient size. When F is a finite field, we show that the problem is at least as hard as determining the multiplicative order of elements in an extension field of F (a problem thought to have complexity similar to that of factoring integers), and this lower bound is tight when t = 2.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectcomplexityen
dc.subjectpolynomialen
dc.subjectsparseen
dc.subjectmultipleen
dc.subjectalgorithmen
dc.subjectlowerbounden
dc.titleComputing sparse multiples of polynomialsen
dc.typeMaster Thesisen
dc.pendingfalseen
dc.subject.programComputer Scienceen
uws-etd.degree.departmentSchool of Computer Scienceen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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