Changes between Initial Version and Version 1 of Ticket #18589, comment 28


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Timestamp:
06/04/15 12:40:00 (7 years ago)
Author:
cremona
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  • Ticket #18589, comment 28

    initial v1  
    1010> when can it happen that `g` is not in `factors`?
    1111
    12 Very good question!  I think it always happens, since the operation f --> mult(f) applies the multiplication-by-a map to the roots, so must take f to another irreducible factor of the same degree;  the fact being checked is that the resulting cycle has the correct length, which is (l-1)/2 divided by deg(f), so that the product of the f's in the cycle gives the kernel polynomial.  I will delete the check.
     12Very good question!  I think it always happens, since the operation f --> mult(f) applies the multiplication-by-a map to the roots, so must take f to another irreducible factor of the same degree;  the fact being checked is that the resulting cycle has the correct length, which is (l-1)/2 divided by deg(f), so that the product of the f's in the cycle gives the kernel polynomial. [I will delete the check.]  I tried removing the check and got run-time errors, so my mathematics must be wrong...