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AlgebraicNumberPolynomial[a,x]

gives the polynomial in x corresponding to the AlgebraicNumber object a.

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AlgebraicNumberPolynomial

AlgebraicNumberPolynomial[a,x]

gives the polynomial in x corresponding to the AlgebraicNumber object a.

Details

Examples

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Basic Examples  (1)

Compute the algebraic number polynomial of an AlgebraicNumber object:

Wolfram Language code: AlgebraicNumber[Sqrt[2] + Sqrt[3], {1, 2, 3, 4}]
Wolfram Language code: AlgebraicNumberPolynomial[%, x]

Scope  (3)

Integers and rational numbers:

Wolfram Language code: AlgebraicNumberPolynomial[2, x]
Wolfram Language code: AlgebraicNumberPolynomial[1 / 2, x]

AlgebraicNumber objects:

Wolfram Language code: AlgebraicNumberPolynomial[AlgebraicNumber[Sqrt[2], {1, 2}], x]

AlgebraicNumberPolynomial threads automatically over lists:

Wolfram Language code: AlgebraicNumberPolynomial[{2, AlgebraicNumber[Sqrt[2], {1, 2}]}, x]

Applications  (1)

Addition of algebraic numbers using polynomials:

Wolfram Language code: {θ, λ} = {AlgebraicNumber[Sqrt[2] + Sqrt[3], {1, 2, 3, 4}], AlgebraicNumber[Sqrt[2] + Sqrt[3], {1, -2, 1, 1}]};
Wolfram Language code: RootReduce[θ + λ]

An equivalent way of performing the same operation:

Wolfram Language code: AlgebraicNumberPolynomial[θ, x] + AlgebraicNumberPolynomial[λ, x]
Wolfram Language code: RootReduce[% /. x -> Sqrt[2] + Sqrt[3]]

Properties & Relations  (1)

AlgebraicNumber by definition is a polynomial function of an algebraic number:

Wolfram Language code: a = AlgebraicNumber[Sqrt[2 + Sqrt[3]], {1, 2, 3, 4}]
Wolfram Language code: b = AlgebraicNumberPolynomial[a, x] /. x -> Sqrt[2 + Sqrt[3]]
Wolfram Language code: RootReduce[b == a]

Possible Issues  (1)

The input must be an AlgebraicNumber object or a rational number:

Wolfram Language code: AlgebraicNumberPolynomial[Sqrt[2], x]
Wolfram Research (2007), AlgebraicNumberPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html.

Text

Wolfram Research (2007), AlgebraicNumberPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html.

CMS

Wolfram Language. 2007. "AlgebraicNumberPolynomial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html.

APA

Wolfram Language. (2007). AlgebraicNumberPolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html

BibTeX

@misc{reference.wolfram_2026_algebraicnumberpolynomial, author="Wolfram Research", title="{AlgebraicNumberPolynomial}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_algebraicnumberpolynomial, organization={Wolfram Research}, title={AlgebraicNumberPolynomial}, year={2007}, url={https://reference.wolfram.com/language/ref/AlgebraicNumberPolynomial.html}, note=[Accessed: 13-June-2026]}