AlgebraicNumberTrace

The trace of $a$ over $\mathbb{Q}$ in the field $\mathbb{Q}(a)$: the sum of its conjugates.

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AlgebraicNumberTrace(a)the sum of $a$'s conjugates

Typed signatures

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

Domain: Number theory

Details

• In $\mathbb{Q}(a)$, the field $a$ generates

Examples

Basic #

$(1 + \sqrt 2) + (1 - \sqrt 2)$

live ↗

In$\mathrm{AlgebraicNumberTrace}(1+\sqrt{2})$Out$2$

the cube roots of 2 sum to 0

live ↗

In$\mathrm{AlgebraicNumberTrace}(\sqrt[3]{2})$Out$0$

live ↗

In$\mathrm{AlgebraicNumberTrace}(5+\sqrt{2})$Out$10$

Scope #

live ↗

In$\mathrm{AlgebraicNumberTrace}(2)$Out$2$

live ↗

In$\mathrm{AlgebraicNumberTrace}(-\frac{2}{3})$Out$-\frac{2}{3}$

Properties #

live ↗

In$\mathrm{AlgebraicNumberTrace}(\frac{1+\sqrt{2}}{2})$Out$1$

About

Examples	6
Checked against	Wolfram Language 6 agree
Crosswalk	Wolfram Language

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

See also: AlgebraicNumberNorm, MinimalPolynomial