Watson Ladd on Mon, 03 Apr 2017 06:53:30 +0200 |
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Reuse of data in rnfkummer/computing order of galois elements without it |
Dear all, I have a program which computes many rnfkummer's over the same base field K. All the rnfkummers are quadratic extensions. This ends up taking a very, very long time, particularly as many of the extensions have galois groups which contain elements of orders which are two large and are thus thrown out, so the time spent computing the extensions is wasted. My questions are as follows: 1: Can anything be done to accelerate the repeated rnfkummers? 2: Is there a way to determine the maximal order of an element of the Galois group of the resulting field without computing the field via rnfkummer? I know about bnrgaloismat, but it doesn't seem as though the resulting representation of the galois group can be used to find the order of elements easily. An affirmative answer to 2 would render 1 superfluous. Sincerely, Watson