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ID: INPUT{id.yaml} Title: > Algebraic numbers of degree 2 Definition: > The list contains the complex roots of irreducible polynomials $f(x) = a_2 x^2 + a_1 x + a_0$ in $\mathbb{Z}[x]$ of degree 2. Parameters: a2: display: $a_2$ type: Z constraints: $a_2 \neq 0$ a1: display: $a_1$ type: Z a0: display: $a_0$ type: Z constraints: $a_0 \neq 0$ n: type: Z constraints: $1\leq n \leq 2$ Comments: comment-n: > $n$ is the index of the root, where we order the roots by their real parts if they are real, otherwise by their imaginary parts. Formulas: Programs: References: Links: Wiki: title: "Wikipedia: Algebraic number" url: https://en.wikipedia.org/wiki/Algebraic_number Similar tables: Keywords: Tags: - zero - algebraic Data properties: type: C complete: no Display properties: number-header: $n$<sup>th</sup> root of $f(x)$ group parameters: - [a2, a1, a0] - [n] Numbers: INPUT{numbers.yaml}
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Algebraic numbers of degree 2
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Numbers
$a_2$, $a_1$, $a_0$
$n$ 
$n$
th
root of $f(x)$
INPUT{numbers.yaml} (not shown in preview)
Definition
The list contains the complex roots of irreducible polynomials $f(x) = a_2 x^2 + a_1 x + a_0$ in $\mathbb{Z}[x]$ of degree 2.
Parameters
$a_2$
— integer ($a_2 \neq 0$)
$a_1$
— integer
$a_0$
— integer ($a_0 \neq 0$)
$n$
— integer ($1\leq n \leq 2$)
Comments
(1)
$n$ is the index of the root, where we order the roots by their real parts if they are real, otherwise by their imaginary parts.
Links
[1]
Wikipedia: Algebraic number
Data properties
Entries are of type: complex number
Table is complete: no