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Mathematica > Mathematics and Algorithms > Number Theory > Algebraic Number Theory > Algebraic Numbers >

Built-in Mathematica Symbol

MinimalPolynomial

MinimalPolynomial[s, x]
gives the minimal polynomial in x for which the algebraic number s is a root.

MinimalPolynomial[s] gives a pure function representation of the minimal polynomial of s.

MinimalPolynomial[s, x, Extension->a] finds the characteristic polynomial of s over the field .

Radical expressions:

Root objects:

MinimalPolynomial automatically threads over lists:

Express the minimal polynomial as a pure function:

Find the characteristic polynomial of

over the extension E^(I Pi/4) of

Construct a polynomial with a root

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

Compute the extension that defines the number field

Find the characteristic polynomial of

over F: