NumberFieldIntegralBasis

NumberFieldIntegralBasis[a]

gives an integral basis for the field generated by the algebraic number a.

Details

Examples

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Basic 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 :

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

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: 22-February-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: 22-February-2025 ]}