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BUILT-IN MATHEMATICA SYMBOL
Extension
Extension
is an option for various polynomial and algebraic functions that specifies generators for the algebraic number field to be used.
Details
- 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. - Extension->{a1, a2, ...} specifies the field
. - The
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
and any algebraic numbers in the input. - GaussianIntegers->True is equivalent to Extension->I.
Examplesopen all
Basic Examples (2)
Factor a polynomial over 
:
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PolynomialGCD over the field generated by the algebraic numbers present in the coefficients:
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New in 3 | Last modified in 6
