Algebraic number - Wikipedia
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (+) /, is an algebraic number, because it is a root of the polynomial x 2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero.
Algebraic Number -- from Wolfram MathWorld
6 天之前 · If r is an algebraic number and a_n=1, then it is called an algebraic integer. Any algebraic number is an algebraic period, and if a number is not an algebraic period,...
Algebraic Number - Math is Fun
To be algebraic, a number must be a root of a non-zero polynomial equation with rational coefficients. So x is algebraic in this example: 2x 3 − 5x + 39 = 0
Definition 1.1. The number α ∈ C is said to be algebraic if it satisfies a polynomial equation x n+a 1x −1 +···+a n with rational coefficients a i ∈ Q. We denote the set of algebraic numbers by Q¯. Examples: 1. α = 1 2 √ 2 is algebraic, since it satisfies the equation x2 − 1 2 = 0. 2. α = 3 √ 2+1 is algebraic, since it ...
Algebraic Numbers - Algebra - AllMath
2023年8月8日 · An algebraic number is a fundamental concept of mathematics that comes from the understanding of algebraic equations and number theory. An algebraic number confines a vast range of numbers, containing rational numbers, specific …
Algebraic number - Encyclopedia of Mathematics
2020年2月14日 · An algebraic number is called an algebraic integer if all the coefficients of its minimal polynomial are rational integers. For instance, $i$ and $1+\sqrt2$ are algebraic integers, being roots of the polynomials $x^2+1$ and $x^2-2x-1$.
Algebraic number | Rational, Irrational & Complex | Britannica
Algebraic number, real number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution. Algebraic numbers include all of the natural numbers, all rational numbers, some irrational numbers, and complex numbers of the form pi …
Algebraic Numbers - Wolfram|Alpha
Wolfram|Alpha can be used to detect, compute properties of and perform calculations with algebraic numbers. Learn about properties of algebraic numbers or do arithmetic with them. Compute properties of an algebraic number: Do exact arithmetic on algebraic numbers:
Definition:Algebraic Number - ProofWiki
2024年9月24日 · An algebraic number is an algebraic element of the field extension $\C / \Q$. That is, it is a complex number that is a root of a polynomial with rational coefficients . The set of algebraic numbers can often be seen denoted as $\mathbb A$.
Algebraic number - Simple English Wikipedia, the free ...
A real or complex number is called an algebraic number if it is a solution of some one-variable polynomial equation whose coefficients are all integers. All rational numbers are algebraic numbers, along with some irrational numbers.
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