ToNumberField

ToNumberField[a,θ]

expresses the algebraic number a in the number field generated by θ.

ToNumberField[{a1,a2,},θ]

expresses the ai in the field generated by θ.

ToNumberField[{a1,a2,}]

expresses the ai in a common extension field generated by a single algebraic number.

Details

Examples

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Basic Examples  (1)

Express in the number field generated by :

Scope  (6)

The generator θ of the number field will autoreduce to an algebraic integer:

Radical expressions:

Root objects:

AlgebraicNumber objects:

Express and in a common extension field:

Express algebraic numbers in the smallest common extension field:

Applications  (1)

Find a primitive element for over :

Properties & Relations  (1)

Convert an algebraic number to an explicit AlgebraicNumber object:

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

Text

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

BibTeX

@misc{reference.wolfram_2020_tonumberfield, author="Wolfram Research", title="{ToNumberField}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ToNumberField.html}", note=[Accessed: 17-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_tonumberfield, organization={Wolfram Research}, title={ToNumberField}, year={2007}, url={https://reference.wolfram.com/language/ref/ToNumberField.html}, note=[Accessed: 17-January-2021 ]}

CMS

Wolfram Language. 2007. "ToNumberField." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToNumberField.html.

APA

Wolfram Language. (2007). ToNumberField. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToNumberField.html