From 0add0f16c11a2c77e474aee0731265f49c13203b Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 20 Sep 2019 11:05:07 +0200 Subject: New documentation --- README.md | 20 +++++++++++++++----- 1 file changed, 15 insertions(+), 5 deletions(-) (limited to 'README.md') diff --git a/README.md b/README.md index a376912..157c9a2 100644 --- a/README.md +++ b/README.md @@ -32,19 +32,29 @@ generators. * The complexity of the calculation of a call of KummerDegree(G,M,N) does not depend on M and N. +Moreover, the results for each group G are cached, so that subsequent +computation of degrees for the same group G only require constant time +(and are very fast). + ## KummerDegree( G, M, N ) -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. +Returns the degree of the Kummer extension Q_{M,N}=Q(\zeta_M,G^{1/N}) over Q. + +INPUT: +* G - a list of generators of the group G +* M - a positive integer +* N - a positive divisor of N -Examples: +OUTPUT: +The degree of the Kummer Extensions Q_{M,N}=Q(\zeta_M,G^{1/N}) over Q. +EXAMPLES: ``` +sage: KummerDegree([5],10,2) +4 sage: KummerDegree([-36,12,-1],120,24) 4608 -``` - -``` sage: KummerDegree([144,27,49/81,-1/125,121/13],36*10^6,36*10^6) 1007769600000000000000000000000000000000000 ``` -- cgit v1.3