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AlgebraicNumberTrace[a]

gives the trace of the algebraic number a.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Extension  
Properties & Relations  
See Also
Tech Notes
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AlgebraicNumberTrace

AlgebraicNumberTrace[a]

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

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Basic Examples  (1)

Scope  (4)

Integers and rational numbers:

Radical expressions:

Root and AlgebraicNumber objects:

AlgebraicNumberTrace automatically threads over lists:

Options  (1)

Extension  (1)

Trace of over :

Properties & Relations  (3)

AlgebraicNumberTrace is additive:

Use ToNumberField to find the trace of in the field :

The trace is the sum of its minimal polynomial roots:

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

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

BibTeX

@misc{reference.wolfram_2025_algebraicnumbertrace, author="Wolfram Research", title="{AlgebraicNumberTrace}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AlgebraicNumberTrace.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_algebraicnumbertrace, organization={Wolfram Research}, title={AlgebraicNumberTrace}, year={2007}, url={https://reference.wolfram.com/language/ref/AlgebraicNumberTrace.html}, note=[Accessed: 13-August-2025]}