AlgebraicIntegerQ

Whether the algebraic number $a$ is an algebraic integer: a root of a monic polynomial over $\mathbb{Z}$ .

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AlgebraicIntegerQ(a)whether

a

is an algebraic integer; unevaluated when

a

isn't read as an algebraic number

Typed signatures

Type	Package	Applies
`(number) -> boolean`	`number-theory`	always

Domain: Number theory

Details

Wolfram answers False for anything it doesn't recognize as an algebraic integer, a symbol included; this stays unevaluated instead

Examples

Basic #

$(1 + \sqrt{-3})/2$ is integral: $-3 \equiv 1 \pmod 4$

\mathrm{AlgebraicIntegerQ}(\frac{1+\sqrt{-3}}{2})

Out

\mathrm{True}

but $(1 + \sqrt{-5})/2$ is not: $-5 \not\equiv 1 \pmod 4$

\mathrm{AlgebraicIntegerQ}(\frac{1+\sqrt{-5}}{2})

Out

\mathrm{False}

$(1 + \sqrt[3]{19} + \sqrt[3]{19}^2)/3$ is integral, since $19 \equiv 1 \pmod 9$

\mathrm{AlgebraicIntegerQ}(\frac{1}{3}(1+\sqrt[3]{19}+19^{\frac{2}{3}}))

Out

\mathrm{True}

About

primitive · kernela kernel — an algorithm over mutable state that would not be readable as a tree

nativeenginetypescriptpackages/ce-patches/src/compute-engine/library/algebraic-numbers.ts

mappedwolframpackages/oracle/src/mappings.ts