20.500.12556/DKUM-84627 Racionalne involucije na študijskem programu 2. stopnje Matematika Rational involutions magistrsko delo V magistrskem delu določamo dvodimenzionalne racionalne involucije s pomočjo določenih metod v računski komutativni algebri. Najprej poiščemo vse dvodimenzionalne racionalne involucije, ki imajo v števcih in imenovalcih polinome stopnje ena, nato pa poiščemo vse dvodimenzionalne racionalne involucije, ki imajo v števcih in imenovalcih polinome stopnje dve. Zapisana je teorija, ki se uporablja pri določanju teh involucij, kot tudi vsi algoritmi, ki omogočajo iskanje rešitev. In this master thesis we obtain two-dimensional rational involutions using methods in computational commutative algebra. The first result we present are all two-dimensional rational involutions which have in the nominator and the denominator polynomials of degree one, whereas the second result are all two-dimensional rational involutions which have in the nominator and denominator polynomials of degree two. All the theory that is used in order to find all such involutions is described in this thesis, as well as all the algorithms which helped us find the solutions. racionalne involucije ideal groebnerjeva baza afina raznoterost polinomi rational involutions ideal groebner basis affine variety polynomials true true false [I. Mastev] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-06-29 21:39:20 2023-08-30 13:52:54 2023-08-31 03:11:26 0000-00-00 00:00:00 2023 0 Maribor 0 Maribor VIII, 58 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.622(043.2) 162695427 MAG_Mastev_Ivan_2023.pdf MAG_Mastev_Ivan_2023.pdf 1 F0C841A83B7A4F509A4A04E927619409 8807d042c612b6c7951a9b4cb46a57d1a60565365b06b605c4ae93994ee6d296 9bc32b19-1e99-11ee-9ba3-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=168624 Fakulteta za naravoslovje in matematiko 0 0 0