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authorSebastiano Tronto <sebastiano.tronto@gmail.com>2022-01-30 12:51:13 +0100
committerSebastiano Tronto <sebastiano.tronto@gmail.com>2022-01-30 12:51:13 +0100
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@@ -5,11 +5,12 @@ TotalKummerFailure (described below), simply download the file
5kummer_degree.sage and include it in your SageMath session/project, 5kummer_degree.sage and include it in your SageMath session/project,
6for example with 6for example with
7``` 7```
8attach("kummer_degree.sage") 8attach(\"kummer_degree.sage\")
9``` 9```
10 10
11A Kummer Extension of Q is a field extension of the form Q_{M,N}:= 11A Kummer Extension of Q is a field extension of the form Q_{M,N}:=
12Q(\zeta_M,G^{1/N}), where: 12Q(\zeta_M,G^{1/N}), where:
13
13* M and N are integers with N dividing M; 14* M and N are integers with N dividing M;
14* \zeta_M is a root of unity of order M; 15* \zeta_M is a root of unity of order M;
15* G is a finitely generated subgroup of the multiplicative group Q* of Q; 16* G is a finitely generated subgroup of the multiplicative group Q* of Q;
@@ -28,6 +29,7 @@ possible can be found in the docs folder.
28 29
29The computational complexity of the algorithm has not been computed precisely. 30The computational complexity of the algorithm has not been computed precisely.
30However, we can say the following: 31However, we can say the following:
32
31* The complexity is exponential in the rank r of the group. 33* The complexity is exponential in the rank r of the group.
32* The script can become slow if the generators of the group G are n-th powers 34* The script can become slow if the generators of the group G are n-th powers
33for very high n. 35for very high n.

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