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| -rw-r--r-- | README.md | 4 |
1 files changed, 3 insertions, 1 deletions
| @@ -5,11 +5,12 @@ TotalKummerFailure (described below), simply download the file | |||
| 5 | kummer_degree.sage and include it in your SageMath session/project, | 5 | kummer_degree.sage and include it in your SageMath session/project, |
| 6 | for example with | 6 | for example with |
| 7 | ``` | 7 | ``` |
| 8 | attach("kummer_degree.sage") | 8 | attach(\"kummer_degree.sage\") |
| 9 | ``` | 9 | ``` |
| 10 | 10 | ||
| 11 | A Kummer Extension of Q is a field extension of the form Q_{M,N}:= | 11 | A Kummer Extension of Q is a field extension of the form Q_{M,N}:= |
| 12 | Q(\zeta_M,G^{1/N}), where: | 12 | Q(\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 | ||
| 29 | The computational complexity of the algorithm has not been computed precisely. | 30 | The computational complexity of the algorithm has not been computed precisely. |
| 30 | However, we can say the following: | 31 | However, 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 |
| 33 | for very high n. | 35 | for very high n. |
