20.500.12556/RUL-164790 Posplošene diskriminante delo diplomskega seminarja Generalized discriminants S standardno definicijo diskriminante lahko dobimo ekvivalentne pogoje o obstoju kompleksnih ničel le do polinomov tretje stopnje z realnimi koeficienti. V tem delu smo pokazali, da za vsak polinom stopnje $n$ obstaja $n−1$ pogojev $\Delta_{1}(f), \ldots,\Delta_{n−1}(f)$, ki nam povejo, ali ima polinom kompleksno ničlo. Vsak pogoj potrebuje za vhodne podatke le 3 koeficiente, v primerjavi s klasično definicijo diskriminante, ki potrebuje vse. Pokazali smo tudi, da je $f(x) = a_{n}(x−r)^n$ natanko tedaj, ko so vsi pogoji enaki $0$. V primeru, ko so vse ničle realne, se da s pomočjo $\Delta_{1}(f)$ postaviti zgornjo in spodnjo mejo za velikost ničel. With the standard definition of the discriminant, we can obtain equivalent conditions for the existence of complex roots only up to polynomials of degree three with real coefficients. In this work, we have shown that for any polynomial of degree $n$, there are $n−1$ conditions $\Delta_{1}(f),...,\Delta_{n−1}(f)$ that indicate whether the polynomial has a complex root. Each condition requires only 3 coefficients as input, compared to the classical definition of the discriminant, which requires all coefficients. We also demonstrated that $f(x) = a_{n}(x−r)^n$ holds if and only if all the conditions are equal to $0$. In the case where all the roots are real, $\Delta_{1}(f)$ can be used to set an upper and lower bound for the values of the roots. polinom rezultanta diskriminanta kompleksne ničle polynomial resultant discriminant complex roots true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2024-11-12 11:28:39 2024-11-12 11:28:48 2024-11-22 14:56:09 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 149791 214765059 15540.pdf 15540.pdf 1 4EA072B0F524EA5736CB3587AB785981 04f85ab7d65282d2c2e9a6aedc4abeb7a8708923871a81ff6a6ef1fc72bf251b 8ace37fc-a0e0-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=195473 Fakulteta za matematiko in fiziko 0 0 0