Wolfram Language & System 11.0 (2016)|Legacy Documentation

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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.
  • Extension->{a1,a2,} specifies the field .
  • The ai 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 ai and any algebraic numbers in the input.
  • GaussianIntegers->True is equivalent to Extension->I.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Factor a polynomial over :

Click for copyable input

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

Click for copyable input
Introduced in 1996
| Updated in 2007