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Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))

Then I take a character, namely

character=A[1]
print character(3)

This wcharacter(3) is zeta6, so I would think that the following should be true:

 character(3) in R.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)

Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))

Then I take a character, namely

character=A[1]
print character(3)

This wcharacter(3) is zeta6, so I would think that the following should be true:

 character(3) in R.fractional_ideal(a)
K.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)

Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))
R=K.maximal_order()

Then I take a character, namely

character=A[1]
print character(3)

This wcharacter(3) is zeta6, so I would think that the following should be true:

 character(3) in K.fractional_ideal(a)
R.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)

Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))
R=K.maximal_order()

Then I take a character, namely

character=A[1]
print character(3)

This wcharacter(3) character(3) is zeta6, so I would think that the following should be true:

 character(3) in R.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)

Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))
R=K.maximal_order()

Then I take a character, namely

character=A[1]
print character(3)

This character(3) is zeta6, so I would think that the following should be true:

 character(3) in R.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this is true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)

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Characters and number fields

Hello!

I have again a question. Could you help me? I defined the Q(6th primitive unity) by

A=DirichletGroup(7)
K.<a>=NumberField(cyclotomic_polynomial(6))
R=K.maximal_order()

Then I take a character, namely

character=A[1]
print character(3)

This character(3) is zeta6, so I would think that the following should be true:

 character(3) in R.fractional_ideal(a)

But it is false, I think because we defined Q(6th primitive unity) without using zeta6. Mathemathically this is true, so could you help me to persuade the computer to recognize such a relation? Thank you! :-)