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NumberFieldSignature

NumberFieldSignature[a]
gives the signature of the field generated by the algebraic number .
  • NumberFieldSignature[a] gives a list of the number of real roots and the number of pairs of conjugate roots for the minimal polynomial of .
Find the signature of the number field :
A number field with signature :
Find the signature of the number field :
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Click for copyable input
Out[1]=
 
A number field with signature :
In[1]:=
Click for copyable input
Out[1]=
Radical expressions:
Root objects:
NumberFieldSignature threads automatically over lists:
Signatures of Galois extension fields of are of the form or for some integer :
The number field is not a Galois extension of :
The minimal polynomial of has two real roots and a pair of complex roots:
The signature of the number field generated by :
The degree of a number field:
Use Exponent and MinimalPolynomial to verify the result:
Find the signature of the number field :
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