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    • CommentAuthorawllower
    • CommentTimeFeb 8th 2011
     
    I have read a post in MO
    http://mathoverflow.net/questions/48855/galois-theory-generalization-of-abels-theorem-better-version
    and found a somewhat strange answer, i.e. the only answer.
    The answer says that this transformation can change those two polynomials, but why is it acceptable?? It makes the leading coefficient not 1, doesn't it?
    Please inform me, thank you.
  2.  
    It makes the leading coefficient not 1, but then you just divide by that coefficient to get a polynomial of the desired form, no?
    • CommentAuthorawllower
    • CommentTimeFeb 8th 2011
     
    But he required that both the leading coefficient and the coefficient of x are 1, didn't him?
  4.  
    in fact they are both 1, since the transformation proposed has the effect of making the leading coefficent and the coefficent of x equal.
  5.  

    The coefficient of $x^n$ is $a^{n/(n - 1)}$, while that of $x$ is $a * a^{1/(n - 1)} = a^{n/(n - 1)}$, so in canceling one, you cancel both.

    • CommentAuthorvoloch
    • CommentTimeFeb 8th 2011
     
    This is not an appropriate discussion for meta. This could have been asked in the comments of the post in question.
    • CommentAuthorawllower
    • CommentTimeFeb 8th 2011
     
    Well, I didn't have enough reputation points at that time.
    And thank you for telling me how the transformation works.
    In any case, thank you.

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