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Built-in Mathematica Symbol

AlgebraicIntegerQ

AlgebraicIntegerQ[a]
yields True if a is an algebraic integer, and yields False otherwise.

A number is considered to be an algebraic integer if the leading coefficient of its minimal polynomial is 1.

Radical expressions:

Transcendental expressions:

Approximate numeric expressions:

AlgebraicIntegerQ automatically threads over lists:

Recognize a Pisot number [more info]:

The sum and product of algebraic integers are algebraic integers:

The leading coefficient of the MinimalPolynomial is one for algebraic integers:

If a number is an algebraic integer it is an algebraic number:

Use NumberFieldIntegralBasis to get the integral basis for a number field:

Any integer linear combination will be an algebraic integer:

In some cases it is not known whether the number is an algebraic integer:

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