From 2add0f43d3d2718fb544bedc99217af9d99955b7 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Wed, 31 Jul 2019 16:11:35 +0200 Subject: Just some refactoring --- kummer_degree.sage | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/kummer_degree.sage b/kummer_degree.sage index 6a1ac2a..5a5f073 100644 --- a/kummer_degree.sage +++ b/kummer_degree.sage @@ -1,3 +1,14 @@ +############################################################################### +# This software allows one to compute the degree of certain field extensions # +# of the rational numbers. In particular, it can compute the degree over Q of # +# extensions of the form Q( sqrt[N](G), \zeta_M ), where: # +# - N and M are integers with N dividing M; # +# - G is a finitely generated subgroup of the multiplicative group of Q # +# - \zeta_M is a primitive M-th root of unity # +# The group G does not have to be given in a particular format. A finite set # +# of generators is sufficient. # +############################################################################### + # Computes the "adelic Kummer failure", i.e. the degrees of the intersection # of the the Kummer extension Q(\sqrt{2^n}{G}) with the M-th cyclotomic field # over Q_{2^n}. @@ -58,7 +69,7 @@ def adelic_failure_gb( B, d ): # shortlist, we declare it here and increase it appropriately at each step. M = 1 - for n in range( 1, N+1 ): # 1 \leq n \leq N + for n in range( 1, N+1 ): # We add the new elements to the shortlist, modifying M if needed. # This is not done in case we are in the extra "fake" level (this case -- cgit v1.3