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Extension

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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 Q[a] consisting of the rationals extended by the algebraic number a.
  • Extension->{a1, a2, ...} specifies the field Q[a_1,a_2,…].
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Factor a polynomial over :
In[1]:=
Click for copyable input
Out[1]=
 
PolynomialGCD over the field generated by the algebraic numbers present in the coefficients:
In[1]:=
Click for copyable input
Out[1]=
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