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Jun
23
comment Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
To clarify, I am interested in worst case complexity. Your answer seems to imply that the best-known algorithms are exponential in run time. Is there a rigorous way to prove this? My investigations in Mathematica also support this conclusion.
Jun
23
comment Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
Thank you. These are some promising ideas. Can you clarify your notation in the equation? Is $\times$ a Cartesian product? What fixes the order of conjugates in that expression?
Jun
23
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Jun
22
revised Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
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Jun
22
awarded  Student
Jun
22
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Jun
22
comment Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
I have done so. Thanks for your careful reading!
Jun
22
revised Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
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Jun
22
comment Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?
If there is no algorithm for computing the minimal polynomial, an efficient algorithm for finding any polynomial with rational coefficients for which this number is a root, will suffice.
Jun
22
asked Is there an efficient algorithm to compute a minimal polynomial for the root of a polynomial with algebraic coefficients?