MinimalPolynomial

MinimalPolynomial[s,x]

gives the minimal polynomial in x for which the algebraic number s is a root.

Details and Options

Examples

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Basic Examples  (2)

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

MinimalPolynomial automatically threads over lists:

Generalizations & Extensions  (1)

Express the minimal polynomial as a pure function:

Options  (1)

Extension  (1)

Find the characteristic polynomial of over the extension TemplateBox[{}, Rationals][ⅇ^(ⅈ pi/4)] of :

The characteristic polynomial is a power of the minimal polynomial of :

Applications  (2)

Construct a polynomial with a root :

The degree of the number field generated by (2-I)/Sqrt[5]:

Properties & Relations  (1)

Compute the extension that defines the number field :

Find the characteristic polynomial of over :

The characteristic polynomial is a power of the minimal polynomial of :

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_minimalpolynomial, author="Wolfram Research", title="{MinimalPolynomial}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MinimalPolynomial.html}", note=[Accessed: 10-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_minimalpolynomial, organization={Wolfram Research}, title={MinimalPolynomial}, year={2007}, url={https://reference.wolfram.com/language/ref/MinimalPolynomial.html}, note=[Accessed: 10-June-2023 ]}