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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]

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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]

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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]

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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]