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Hi, my question is: How can I define a field of numbers by hitting to the field of rationals two roots of the same polynomial ?

sage: alpha=sqrt(-11/2 + sqrt(11^2-4(11))/2) sage: alpha=sqrt(-11/2 - sqrt(11^2-4(11))/2) sage: K=QQ[alpha,beta]

 2 None Iguananaut 1708 ●8 ●33 ●55

Hi, my question is: How can I define a field of numbers by hitting to the field of rationals two roots of the same polynomial ?

sage: alpha=sqrt(-11/2 + sqrt(11^2-4(11))/2) sage: alpha=sqrt(-11/2 - sqrt(11^2-4(11))/2) sage: K=QQ[alpha,beta]

 3 None Iguananaut 1708 ●8 ●33 ●55

Hi, my question is: How can I define a field of numbers by hitting to the field of rationals two roots of the same polynomial ?

sage: alpha=sqrt(-11/2 + sqrt(11^2-4(11))/2) sage: alpha=sqrt(-11/2 - sqrt(11^2-4(11))/2) sage: K=QQ[alpha,beta]

 4 None Iguananaut 1708 ●8 ●33 ●55

How can I define a field of numbers by hitting to the field of rationals two roots of the same polynomial ?

I tried:

sage: alpha=sqrt(-11/2 + sqrt(11^2-4(11))/2)
sage: alpha=sqrt(-11/2 - sqrt(11^2-4(11))/2)
sage: K=QQ[alpha,beta]K=QQ[alpha,beta]