20.500.12556/RUL-102999 Tropska geometrija delo diplomskega seminarja Tropical Geometry V diplomskem delu obravnavamo osnove tropske geometrije. Uvedemo pojem tropskega polkolobarja in spoznamo, kako nad tem polkolobarjem tvorimo polinome, kako je definirana ničla tropskega polinoma in kakšne so tropske krivulje, ki jih ta definicija porodi. Za tropske polinome ene spremenljivke dokažemo osnovni izrek tropske algebre. Ogledamo si nekaj lastnosti tropskih krivulj in spoznamo, kaj določa njihova oglišča, kaj določa njihove robove in kaj so njihove dualne subdivizije. Omenimo tudi njihovo povezavo z uravnoteženimi grafi in pokažemo, da lahko za določen primer tropskih krivulj Bézoutjev izrek enostavno prenesemo tudi na tropske krivulje in ga zanje tudi dokažemo. Na koncu si ogledamo še amebe kompleksnih krivulj in kako povezujejo kompleksne krivulje s tropskimi. Omenimo tudi osnovni izrek tropske algebraične geometrije in ga navežemo na pridobljeno znanje. In this thesis, we examine the basic concepts of tropical geometry. We define the tropical semiring, form polynomials over this semiring, define roots of tropical polynomials and examine tropical curves that this definition gives rise to. We prove the fundamental theorem of tropical algebra for the tropical polynomials of one variable. Furthermore, we take a look at some of the properties of tropical curves. We define their edges, their vertices and their dual subdivisions. We mention their connection with balanced graphs and prove Bézout theorem for a particular case of tropical curves. In the end of the thesis, we examine amoebas of complex curves and how they connect complex curves with tropical ones. We mention the fundamental theorem of tropical algebraic geometry and relate it to the newly acquired knowledge. tropska geometrija tropski polkolobar tropski polinom tropska krivulja Bézoutjev izrek tropical geometry tropical semiring tropical polynomial tropical curve Bézout's theorem true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2018-09-13 07:45:39 2018-09-13 07:45:41 2022-08-16 03:39:23 0000-00-00 00:00:00 2018 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514.7 90021 18433113 402.pdf 402.pdf 1 68C7187A744A60C02DDF7258AA234F41 9c96c25f26476516c744c0687bf600fb3d8dd2033fa9c30f6ac09142520e2f9e aecce757-a1b5-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=113380 Fakulteta za matematiko in fiziko 0 0 0