PolynomialRoot

The $k$-th root of the polynomial $p$ in its one unknown, in Wolfram's order: real roots first, increasing, then complex roots by real part and imaginary part. Wolfram's Root; compute-engine's Root is the $n$-th root.

PolynomialRoot(p, k)the $k$-th root of $p$, exact: rational and quadratic roots are written as radicals, others stay a name for the root

Typed signatures

Type	Package	Applies
(any, integer) -> number	number-theory	always

Domain: Number theory

Details

• A root of degree 3 or more stays PolynomialRoot(p, k), an exact algebraic number that MinimalPolynomial, NumberFieldDiscriminant and the other number-field heads read
• Roots of a reducible $p$ are left unevaluated rather than reduced to a factor's

Examples

Basic #

the first root of $x^2 + x + 1$ is the one with negative imaginary part, $(-1 - i\sqrt 3)/2$

live ↗

In$\mathrm{PolynomialRoot}(x^2+x+1, 1)$Out$\frac{1}{2}(-\sqrt{3}i-1)$

real roots come in increasing order: $-\sqrt 2$ first

live ↗

In$\mathrm{PolynomialRoot}(x^2-2, 1)$Out$-\sqrt{2}$

a cubic's root is its own name

live ↗

In$\mathrm{PolynomialRoot}(x^3-x^2-2x-8, 1)$Out$\mathrm{PolynomialRoot}(x^3-x^2-2x-8, 1)$

About

Examples	3
Checked against	Wolfram Language 2 agree1 differ

Implementation

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

Wolfram's Root, which compute-engine's nth-root Root would shadow.

See also: MinimalPolynomial, NumberFieldIntegralBasis, Root