What is algebraic number? - Definition from WhatIs.com
Part of the Mathematics glossary:

An algebraic number is any real number that is a solution of some single-variable polynomial equation whose coefficient s are all integer s. While this is an abstract notion, theoretical mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.

The general form of a single-variable polynomial equation is:

a + a 1 x + a 2 x 2 + a 3 x 3 + ... + a n x n = 0

where a , a 1 , a 2 , ..., a n are the coefficients, and x is the unknown for which the equation is to be solved. A number x is algebraic if and only if there exists some equation of the above form such that a , a 1 , a 2 , ..., a n are all integers.

All rational number s are algebraic. Examples include 25, 7/9, and -0.245245245. Some irrational number s are also algebraic. Examples are 2 1/2 (the square root of 2) and 3 1/3 (the cube root of 3). There are irrational numbers x for which no single-variable, integer-coefficient polynomial equation exists with x as a solution. Examples are pi (the ratio of a circle's circumference to its diameter in a plane) and e (the natural logarithm base). Numbers of this type are known as transcendental number s.

This was last updated in September 2005
Posted by: Margaret Rouse

Related Terms


  • irrational number

    - An irrational number is a real number that cannot be reduced to any ratio between an integer p and a natural number q. (WhatIs.com)

  • Fibonacci sequence

    - The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of th... (WhatIs.com)

  • algorithm

    - An algorithm (pronounced AL-go-rith-um) is a procedure or formula for solving a problem. Algorithms are used throughout almost all areas of information technology. (WhatIs.com)


  • Mathematics

    - Terms related to mathematics, including definitions about logic, algorithms and computations and mathematical terms used in computer science and business.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About algebraic numberPowered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment



    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.