From 50d53b44e1e47242f2c8de991ce57f04a0292055 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 20 Sep 2019 11:45:59 +0200 Subject: New documentation --- README.md | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/README.md b/README.md index 9d24126..5f25e52 100644 --- a/README.md +++ b/README.md @@ -141,3 +141,35 @@ M/N is ODD and is read as the previous one. ``` +Uncommenting the line of code: +``` +print_case_list( ret ) +``` +inside the function total_kummer_failure makes the script output the +description of the total failure as a finite list of cases, as below: + +``` + +sage: TotalKummerFailure([25]) +M_0 = 40 +N_0 = 8 + +The following table shows the total failure of Kummer degrees. +The degree of the Kummer extension (M,N) is e / f, where e = phi(M)*N^rank(G) and f is the entry of the table below at the row labelled with gcd(N,N0) and the column labelled with gcd(M,M0). + + | 1 2 4 5 8 10 20 40 + - - - - - - - - - - + 1 | 1 1 1 1 1 1 1 1 + 2 | 2 2 2 2 2 2 2 2 + 4 | 2 2 2 2 2 2 4 4 + 8 | 2 2 2 2 2 2 2 4 + +Failure is 1 if (gcd(M,M0),gcd(N,N0)) is one of the following: +[(1, 1), (2, 1), (4, 1), (5, 1), (8, 1), (10, 1), (20, 1), (40, 1)] + +Failure is 2 if (gcd(M,M0),gcd(N,N0)) is one of the following: +[(1, 2), (2, 2), (4, 2), (5, 2), (8, 2), (10, 2), (20, 2), (40, 2), (1, 4), (2, 4), (4, 4), (5, 4), (8, 4), (10, 4), (1, 8), (2, 8), (4, 8), (5, 8), (8, 8), (10, 8), (20, 8)] + +Failure is 4 if (gcd(M,M0),gcd(N,N0)) is one of the following: +[(20, 4), (40, 4), (40, 8)] +``` -- cgit v1.3