NumberFieldIntegralBasis
gives an integral basis for the field generated by the algebraic number a.
Details
- NumberFieldIntegralBasis gives a list of algebraic integers generating the module of integers in the field .
- The basis produced by NumberFieldIntegralBasis may not be unique.
Examples
open allclose allBasic Examples (1)
Find an integral basis for the field :
Scope (4)
Radical objects:
Root objects:
AlgebraicNumber objects:
NumberFieldIntegralBasis threads over lists:
Properties & Relations (3)
Elements of an integral basis are all algebraic integers:
Algebraic integers are linear combinations of elements of the integral basis:
Use ToNumberField to find an integral basis for the field :
Tech Notes
Related Guides
History
Text
Wolfram Research (2007), NumberFieldIntegralBasis, Wolfram Language function, https://reference.wolfram.com/language/ref/NumberFieldIntegralBasis.html.
CMS
Wolfram Language. 2007. "NumberFieldIntegralBasis." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NumberFieldIntegralBasis.html.
APA
Wolfram Language. (2007). NumberFieldIntegralBasis. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NumberFieldIntegralBasis.html
BibTeX
@misc{reference.wolfram_2025_numberfieldintegralbasis, author="Wolfram Research", title="{NumberFieldIntegralBasis}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldIntegralBasis.html}", note=[Accessed: 14-April-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_numberfieldintegralbasis, organization={Wolfram Research}, title={NumberFieldIntegralBasis}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldIntegralBasis.html}, note=[Accessed: 14-April-2025 ]}