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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.
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Radical expressions:
Root and AlgebraicNumber objects:
Transcendental expressions:
Approximate numeric expressions:
AlgebraicIntegerQ automatically threads over lists:
Recognize a Pisot number []:
The sum and product of algebraic integers are algebraic integers:
The leading coefficient of the MinimalPolynomial is 1 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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