Algebraic Number Fields

Mathematica 6 adds comprehensive support for algebraic number fields. This gives a table of properties of successive fields

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Text[TraditionalForm[

  Grid[Table[{d, NumberFieldDiscriminant[Sqrt[d]], 

     NumberFieldClassNumber[Sqrt[d]], NumberFieldRegulator[Sqrt[d]], 

     MinimalPolynomial[NumberFieldFundamentalUnits[Sqrt[d]], x], 

     NumberFieldSignature[Sqrt[d]], 

     AlgebraicNumberNorm[NumberFieldIntegralBasis[Sqrt[d]]]}, {d, 

     15}], Frame -> All, Background -> LightYellow]]]

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