AlgebraicNumberTrace
gives the trace of the algebraic number a.
Details and Options
- The trace of a is defined to be the sum of the roots of its minimal polynomial.
- AlgebraicNumberTrace[a,Extension->θ] finds the trace of a over the field
.
Examples
open all close allBasic Examples (1)
Scope (4)
Integers and rational numbers:
AlgebraicNumberTrace[2]AlgebraicNumberTrace[-2 / 3]AlgebraicNumberTrace[Sqrt[1 + Sqrt[2]]]Root and AlgebraicNumber objects:
AlgebraicNumberTrace[Root[-1 + #1 + #1 ^ 2 + #1 ^ 3 + #1 ^ 4 &, 1]]AlgebraicNumberTrace[AlgebraicNumber[Sqrt[2] I, {1, 2}]]AlgebraicNumberTrace automatically threads over lists:
AlgebraicNumberTrace[{5 + Sqrt[2], E ^ (Pi * I / 8)}]Options (1)
Properties & Relations (3)
AlgebraicNumberTrace is additive:
{α, β} = {5, (1 + Sqrt[2]) / 2};AlgebraicNumberTrace[α + β, Extension -> Sqrt[2]] == Total@AlgebraicNumberTrace[{α, β}, Extension -> Sqrt[2]]Use ToNumberField to find the trace of 
in the field 
:
𝔽 = ToNumberField[{2 ^ (1 / 3), E ^ (2 * Pi * I / 3)}][[1, 1]]AlgebraicNumberTrace[E ^ (2 * Pi * I / 3), Extension -> 𝔽]The trace is the sum of its minimal polynomial roots:
x /. Solve[MinimalPolynomial[(1 + Sqrt[2]) / 2, x] == 0, x]Simplify[Plus@@%]AlgebraicNumberTrace[(1 + Sqrt[2]) / 2]Text
Wolfram Research (2007), AlgebraicNumberTrace, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberTrace.html.
CMS
Wolfram Language. 2007. "AlgebraicNumberTrace." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlgebraicNumberTrace.html.
APA
Wolfram Language. (2007). AlgebraicNumberTrace. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlgebraicNumberTrace.html