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@@ -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
30by elements of magnitude 10^6; higher ranks are feasible as well with smaller 30by elements of magnitude 10^6; higher ranks are feasible as well with smaller
31generators. 31generators.
32* The complexity of the calculation of a call of KummerDegree(G,M,N) does not
33depend on M and N.
32 34
33 35
34## KummerDegree( G, M, N ) 36## KummerDegree( G, M, N )
35 37
36Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as a list of generators and it may contain torsion. 38Returns 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
38Example: 40Examples:
41
39``` 42```
40sage: KummerDegree([-36,12,-1],120,24) 43sage: KummerDegree([-36,12,-1],120,24)
414608 444608
42``` 45```
43 46
47```
48sage: KummerDegree([144,27,49/81,-1/125,121/13],36*10^6,36*10^6)
491007769600000000000000000000000000000000000
50```
51
44## TotalKummerFailure( G ) 52## TotalKummerFailure( G )
45 53
46Outputs 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. 54Outputs 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.

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