From a5c0210e2ff37acaf4fe58130d2b67365677b559 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 20 Sep 2019 10:40:58 +0200 Subject: New documentation --- README.md | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/README.md b/README.md index f575151..7e9afdc 100644 --- a/README.md +++ b/README.md @@ -10,6 +10,23 @@ Q(\zeta_M,G^{1/N}), where: * G^{1/N} is the set of all elements x of an algebraic closure of Q such that x^n belongs to G. +The main importance of this script is to show that, for a fixed group G as +above, one can compute in a finite time a finite-case-distinction formula +that computes the degrees [Q_{M,N}:Q] of such extensions when M and N vary. +A preprint by A. Perucca, P. Sgobba and S. Tronto that explains how this is +possible can be found in the docs folder. + +I have not computed accurately the complexity of the code. However, I can +say the following: +* The complexity is exponential in the rank r of the group. +* The script can become slow if the generators of the group G are n-th powers +for very high n. +* The generators given are factored as product of prime powers, so very large +generators can slow the script as well. +* The code is very fast for groups of small rank (e.g. up to 5) and generated +by elements of magnitude 10^6; higher ranks are feasible as well with smaller +generators. + It contains the following useful functions: ## TotalKummerFailure( G ) -- cgit v1.3