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 :

Introduced in 2007
 (6.0)