Removed some commented code, changed README.md

1 files changed, 12 insertions, 22 deletions

diff --git a/README.md b/README.md
index 94ad39d..5fbdb34 100644
--- a/README.md
+++ b/README.md
@@ -9,39 +9,29 @@ Outputs the description of the failure of maximality for all possible values of
 Example:
 
 ```
+
 sage: TotalKummerFailure([-36,12,-1])
 M_0 = 24
 N_0 = 8
 
-The following table shows the total failure of Kummer degrees in
- case the quotient M/N is EVEN.
-Columns correspond to values of M, rows to values of N
-
-The degree of the Kummer extension (M,N) can be extracted by taking
-the value f (failure) of the entry at (gcd(N,N0),gcd(M,M0)) and
-simply computing ed(M,N) / f, where ed(M,N) is the expected degree
-of the Kummer extension.
-In this case (-1 is in G), we have ed(M,N) = 2^e*phi(M)*N^r,
-where e=1 if N is even and e=0 if N is odd.
-where r is the rank of G.
+The following table shows the total failure of Kummer degrees in case the quotient M/N is EVEN.
+The degree of the Kummer extension (M,N) is e / f, where e = phi(M)*N^rank(G) if N is odd and e = 2*phi(M)*N^rank(G) if N is even 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   3   4   6   8    12   24
-  -   -   -   -   -   -   -   -    -    -
-  1   |   1   1   1   1   1   1    1    1
-  2   |   4   4   4   4   4   4    8    8
-  4   |   4   4   4   4   4   8    8    16
-  8   |   8   8   8   8   8   16   16   32
+      |   1   2   3   4   6   8   12   24
+  -   -   -   -   -   -   -   -   -    -
+  1   |   1   1   1   1   1   1   1    1
+  2   |   4   4   4   4   4   4   8    8
+  4   |   4   4   4   4   4   8   8    16
+  8   |   8   8   8   8   8   8   8    16
 
-The following table shows the total failure of Kummer degrees in
-case the quotient M/N is ODD.
-This table can be read exactly as the first one.
+The following table shows the total failure of Kummer degrees if the quotient M/N is ODD and is read as the previous one.
 
       |   1   2   3   4   6   8   12   24
   -   -   -   -   -   -   -   -   -    -
   1   |   1   1   1   1   1   1   1    1
   2   |   2   2   2   2   4   2   4    4
   4   |   2   2   2   4   4   4   8    8
-  8   |   4   4   4   8   8   8   16   16
+  8   |   4   4   4   4   4   4   8    8
 
 ```
 
@@ -52,5 +42,5 @@ Returns the degree of the Kummer extension Q_{M,N}. Again, G is given simply as
 Example:
 ```
 sage: KummerDegree([-36,12,-1],120,24)
-2304
+4608
 ```