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authorSebastiano Tronto <sebastiano.tronto@gmail.com>2019-04-19 11:44:04 +0200
committerSebastiano Tronto <sebastiano.tronto@gmail.com>2019-04-19 11:44:04 +0200
commit0cecb6907568997b77bf63941bec5e150ba23e9a (patch)
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parentd794bad3364a7bf0c5ca12241d36a9ebb48c68d8 (diff)
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2A SageMath script that computes the degrees of Kummer Extensions of the rational numbers. 2A SageMath script that computes the degrees of Kummer Extensions of the rational numbers.
3It contains the following useful functions: 3It contains the following useful functions:
4 4
5+-----------------------+ 5## TotalKummerFailure( G )
6|TotalKummerFailure( G )|
7+-----------------------+
8 6
9Outputs the description of the failure of maximality 7Outputs the description of the failure of maximality for all possible values of M and N. Here G is given as a list of generators (not necessarily a basis). G can also contain torsion. If G = <-1>, the program stops immediately.
10for all possible values of M and N. Here G is given as a list of generators
11(not necessarily a basis). G can also contain torsion. If G = <-1>, the program
12stops immediately.
13 8
14Example: 9Example:
15 10
11```
16sage: TotalKummerFailure([-36,12,-1]) 12sage: TotalKummerFailure([-36,12,-1])
17output: 13output:
18M_0 = 24 14M_0 = 24
@@ -48,11 +44,9 @@ This table can be read exactly as the first one.
48 4 | 2 2 2 4 4 4 8 8 44 4 | 2 2 2 4 4 4 8 8
49 8 | 4 4 4 8 8 8 16 16 45 8 | 4 4 4 8 8 8 16 16
50 46
51------------------------------------------------------------------------------- 47```
52 48
53+-----------------------+ 49## KummerDegree( G, M, N )
54|KummerDegree( G, M, N )|
55+-----------------------+
56 50
57Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as 51Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as
58a list of generators and it may contain torsion. 52a list of generators and it may contain torsion.
@@ -61,4 +55,3 @@ sage: KummerDegree([-36,12,-1],120,24)
61output: 55output:
622304 562304
63 57
64-------------------------------------------------------------------------------

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