Vieta’s Formula about the Sum of Roots of Polynomials
| Autor: | Karol Pąk, Artur Korniłowicz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
010302 applied physics
060102 archaeology vieta’s formula Applied Mathematics roots of polynomials Mehler–Heine formula 06 humanities and the arts 01 natural sciences Classical orthogonal polynomials Algebra Computational Mathematics 03b35 0103 physical sciences Orthogonal polynomials Vieta's formulas QA1-939 12e05 0601 history and archaeology Mathematics |
| Zdroj: | Formalized Mathematics, Vol 25, Iss 2, Pp 87-92 (2017) |
| ISSN: | 1898-9934 1426-2630 |
| Popis: | Summary In the article we formalized in the Mizar system [2] the Vieta formula about the sum of roots of a polynomial anxn + an− 1 xn− 1 + ··· + a 1 x + a 0 defined over an algebraically closed field. The formula says that x 1 + x 2 + ⋯ + x n − 1 + x n = − a n − 1 a n $x_1 + x_2 + \cdots + x_{n - 1} + x_n = - {{a_{n - 1} } \over {a_n }}$ , where x 1, x 2,…, xn are (not necessarily distinct) roots of the polynomial [12]. In the article the sum is denoted by SumRoots. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|