gives the norm of the algebraic number a.
AlgebraicNumberNorm
gives the norm of the algebraic number a.
Details and Options
- The norm of a is defined to be the product of the roots of its minimal polynomial.
- AlgebraicNumberNorm [a,Extension->θ] finds the norm of a over the field .
Examples
open all close allBasic Examples (1)
Norms of algebraic numbers:
Scope (4)
Integers and rational numbers:
Radical expressions:
Root and AlgebraicNumber objects:
AlgebraicNumberNorm automatically threads over lists:
Options (1)
Extension (1)
Norm of over :
Applications (1)
is irreducible in :
Since AlgebraicNumberNorm is multiplicative, having a prime norm implies the original number is prime:
Properties & Relations (3)
AlgebraicNumberNorm is multiplicative:
Units in a number field have norm :
Compute the smallest field that includes , i.e. :
Compute the norm in that field:
Neat Examples (1)
Plot of norms of elements in :
Tech Notes
Related Guides
History
Text
Wolfram Research (2007), AlgebraicNumberNorm, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html.
CMS
Wolfram Language. 2007. "AlgebraicNumberNorm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html.
APA
Wolfram Language. (2007). AlgebraicNumberNorm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html
BibTeX
@misc{reference.wolfram_2025_algebraicnumbernorm, author="Wolfram Research", title="{AlgebraicNumberNorm}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_algebraicnumbernorm, organization={Wolfram Research}, title={AlgebraicNumberNorm}, year={2007}, url={https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html}, note=[Accessed: 04-January-2026]}