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Extension

Extension
is an option for various polynomial and algebraic functions that specifies generators for the algebraic number field to be used.

For polynomial functions, Extension determines the algebraic number field in which the coefficients are assumed to lie.

The setting Extension->a specifies the field consisting of the rationals extended by the algebraic number a.

The a_i must be exact numbers, and can involve radicals as well as Root and AlgebraicNumber objects.

Extension->Automatic specifies that any algebraic numbers that appear in the input should be included in the extension field.

For polynomial functions, the default setting Extension->None specifies that all coefficients are required to be rational. Any algebraic numbers appearing in input are treated like independent variables.

Extension->{a₁, a₂, ...} includes both the a_i and any algebraic numbers in the input.

Factor a polynomial over

PolynomialGCD over the field generated by the algebraic numbers present in the coefficients:

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