Examples for

Algebraic Numbers

The set of algebraic numbers is composed of all the complex numbers that are roots of nonzero polynomials with rational coefficients. Notable subsets of this set are the integers, the rational numbers and the constructible numbers. Wolfram|Alpha can be used to detect, compute properties of and perform calculations with algebraic numbers.
Algebraic Numbers

Learn about properties of algebraic numbers or do arithmetic with them.

Compute properties of an algebraic number:

cbrt(3)

Do exact arithmetic on algebraic numbers:

(3+(1-sqrt(2))/(1+sqrt(2)))^(1/3)
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Identification of Algebraics

Differentiate between algebraic and transcendental (i.e. nonalgebraic) numbers.

Determine whether a number is algebraic:

Is sin(pi/17) an algebraic number?
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Algebraic Integers

Work with the subset of algebraic numbers composed of roots of monic polynomials with integer coefficients.

Identify algebraic integers and units:

Is 1/(1+sqrt(5)) an algebraic integer?
do the algebraic units contain Sqrt[2]+Sqrt[3]?
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Minimal Polynomials

Find the polynomial of least degree that yields zero when applied to an algebraic number.

Compute the minimal polynomial of an algebraic number:

minimal polynomial of sqrt(2+sqrt(2+sqrt(2)))
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