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Uporaba polkolobarjev z zaprtjem : delo diplomskega seminarja
Slivnik, Nina (Author), Pretnar, Matija (Mentor) More about this mentor... This link opens in a new window, Oblak, Polona (Co-mentor)

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Abstract
Polkolobar je algebrska struktura, ki podpira seštevanje in množenje, med katerima veljajo določene relacije. Ko dodamo še unarno operacijo zaprtje, dobimo polkolobar z zaprtjem. V diplomskem delu si bomo ogledali, kako definiramo zaprtje na polkolobarju matrik, tri algoritme za izračun zaprtja matrike ter nekaj primerov uporabe polkolobarjev z zaprtjem v programskem jeziku Haskell: dosegljivost v grafu, poti v grafu, polinome in potenčne vrste in 0-1 nahrbtnik s ponavljanjem.

Language:Slovenian
Keywords:Polkolobar, zaprtje, polkolobar matrik, Jacobijev algoritem, algoritem Warshall-Floyd-Kleene, Gaussova metoda, Haskell
Work type:Final seminar paper (mb14)
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
UDC:512
COBISS.SI-ID:18820185 Link is opened in a new window
Views:65
Downloads:29
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Secondary language

Language:English
Title:Application of closed semirings
Abstract:
Semiring is an algebraic structure where we have two binary operations ('addition' and 'multiplication') and relations between them. If we add a unary operation called closure we obtain a closed semiring. In this work we define a closed semiring of matrices, describe three algorithms for computing the closure and some applications of closed semirings in Haskell: reachability in graphs, paths in graphs, polynomials and power series and 0-1 knapsack with repetition.

Keywords:Semiring, closure, matrix semiring, Jacobi's algorithm, Warshall-Floyd- Kleene's algorithm, Gauss method, Haskell

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