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| -rw-r--r-- | README.md | 10 |
1 files changed, 9 insertions, 1 deletions
| @@ -29,18 +29,26 @@ generators can slow the script as well. | |||
| 29 | * The code is very fast for groups of small rank (e.g. up to 5) and generated | 29 | * The code is very fast for groups of small rank (e.g. up to 5) and generated |
| 30 | by elements of magnitude 10^6; higher ranks are feasible as well with smaller | 30 | by elements of magnitude 10^6; higher ranks are feasible as well with smaller |
| 31 | generators. | 31 | generators. |
| 32 | * The complexity of the calculation of a call of KummerDegree(G,M,N) does not | ||
| 33 | depend on M and N. | ||
| 32 | 34 | ||
| 33 | 35 | ||
| 34 | ## KummerDegree( G, M, N ) | 36 | ## KummerDegree( G, M, N ) |
| 35 | 37 | ||
| 36 | Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as a list of generators and it may contain torsion. | 38 | Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as a list of generators and it may contain torsion. |
| 37 | 39 | ||
| 38 | Example: | 40 | Examples: |
| 41 | |||
| 39 | ``` | 42 | ``` |
| 40 | sage: KummerDegree([-36,12,-1],120,24) | 43 | sage: KummerDegree([-36,12,-1],120,24) |
| 41 | 4608 | 44 | 4608 |
| 42 | ``` | 45 | ``` |
| 43 | 46 | ||
| 47 | ``` | ||
| 48 | sage: KummerDegree([144,27,49/81,-1/125,121/13],36*10^6,36*10^6) | ||
| 49 | 1007769600000000000000000000000000000000000 | ||
| 50 | ``` | ||
| 51 | |||
| 44 | ## TotalKummerFailure( G ) | 52 | ## TotalKummerFailure( G ) |
| 45 | 53 | ||
| 46 | 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. | 54 | 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. |
