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Mathematica > Mathematics and Algorithms > Number Theory > Algebraic Number Theory >

Built-in Mathematica Symbol

AlgebraicNumberPolynomial

AlgebraicNumberPolynomial[a, x]
gives the polynomial in x corresponding to the AlgebraicNumber object a.

For an algebraic number a of the form AlgebraicNumber[, {c₀, c₁, ...}], AlgebraicNumberPolynomial[a, x] is the polynomial , from which a can be obtained by replacing x with .

Integers and rational numbers:

AlgebraicNumberPolynomial threads automatically over lists:

Addition of algebraic numbers using polynomials:

An equivalent way of performing the same operation:

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

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