| 11. | Let an algebraic extension of a field, generated by an element whose minimal polynomial has degree.
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| 12. | Although the quadratic integers belonging to a given quadratic field form a minimal polynomial of degree four.
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| 13. | :: As for minimal polynomials : sorry I wasn't more clear on this point.
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| 14. | The "'minimal polynomial "'is thus defined to be the monic polynomial which generates.
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| 15. | We then compute the minimal polynomial of random elements of F until we find an element with order 15.
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| 16. | If 60?could be trisected, the degree of a minimal polynomial of over would be a power of two.
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| 17. | This is the minimal polynomial of " a " and it encodes many important properties of " a ".
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| 18. | In this case, if is the image of in, the minimal polynomial of is the quotient of by its leading coefficient.
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| 19. | The factors of the minimal polynomial " m " are the elementary divisors of the largest degree corresponding to distinct eigenvalues.
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| 20. | Subtracting one side from the other, factoring, and disregarding trivial factors will then yield the minimal polynomial of certain Salem numbers.
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