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| author | Sebastiano Tronto <sebastiano.tronto@gmail.com> | 2019-04-19 11:44:04 +0200 |
|---|---|---|
| committer | Sebastiano Tronto <sebastiano.tronto@gmail.com> | 2019-04-19 11:44:04 +0200 |
| commit | 0cecb6907568997b77bf63941bec5e150ba23e9a (patch) | |
| tree | 54d8660c43b33b70aa26ea418e8d927e6b7b9f82 /README.md | |
| parent | d794bad3364a7bf0c5ca12241d36a9ebb48c68d8 (diff) | |
| download | kummer-degrees-0cecb6907568997b77bf63941bec5e150ba23e9a.tar.gz kummer-degrees-0cecb6907568997b77bf63941bec5e150ba23e9a.zip | |
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| -rw-r--r-- | README.md | 17 |
1 files changed, 5 insertions, 12 deletions
| @@ -2,17 +2,13 @@ | |||
| 2 | A SageMath script that computes the degrees of Kummer Extensions of the rational numbers. | 2 | A SageMath script that computes the degrees of Kummer Extensions of the rational numbers. |
| 3 | It contains the following useful functions: | 3 | It contains the following useful functions: |
| 4 | 4 | ||
| 5 | +-----------------------+ | 5 | ## TotalKummerFailure( G ) |
| 6 | |TotalKummerFailure( G )| | ||
| 7 | +-----------------------+ | ||
| 8 | 6 | ||
| 9 | Outputs the description of the failure of maximality | 7 | Outputs 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. |
| 10 | for 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 | ||
| 12 | stops immediately. | ||
| 13 | 8 | ||
| 14 | Example: | 9 | Example: |
| 15 | 10 | ||
| 11 | ``` | ||
| 16 | sage: TotalKummerFailure([-36,12,-1]) | 12 | sage: TotalKummerFailure([-36,12,-1]) |
| 17 | output: | 13 | output: |
| 18 | M_0 = 24 | 14 | M_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 | ||
| 57 | Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as | 51 | Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as |
| 58 | a list of generators and it may contain torsion. | 52 | a list of generators and it may contain torsion. |
| @@ -61,4 +55,3 @@ sage: KummerDegree([-36,12,-1],120,24) | |||
| 61 | output: | 55 | output: |
| 62 | 2304 | 56 | 2304 |
| 63 | 57 | ||
| 64 | ------------------------------------------------------------------------------- | ||
