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

initial	v1
10	10	> when can it happen that `g` is not in `factors`?
11	11
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~~.
	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.] I tried removing the check and got run-time errors, so my mathematics must be wrong...