kummer-degrees

commit 5cb52882924253a2ec643cc9f259d57e368412a6
parent 6376666f2050a28d09edce77e2ff4dcf9d4c6f1e
Author: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date:   Sun, 30 Jan 2022 14:42:57 +0100

Fixing markdown readme

Diffstat:
M
README.md
 | 
23
+++++++++++++----------

1 file changed, 13 insertions(+), 10 deletions(-)
diff --git a/README.md b/README.md
@@ -4,21 +4,22 @@ the rational numbers. In order to use the functions KummerDegree and
 TotalKummerFailure (described below), simply download the file
 kummer_degree.sage and include it in your SageMath session/project,
 for example with
+
 ```
-attach(\"kummer_degree.sage\")
+attach("kummer_degree.sage")
 ```
 
-A Kummer Extension of Q is a field extension of the form Q_{M,N}:=
-Q(\zeta_M,G^{1/N}), where:
+A Kummer Extension of Q is a field extension of the form Q{M,N}:=
+Q(z,G^1/N ), where:
 
 * M and N are integers with N dividing M;
-* \zeta_M is a root of unity of order M;
+* z is a root of unity of order M;
 * G is a finitely generated subgroup of the multiplicative group Q* of Q;
-* G^{1/N} is the set of all elements x of an algebraic closure of Q such that
+* G^1/N is the set of all elements x of an algebraic closure of Q such that
 x^n belongs to G.
 
 In other words, it is a number field generated by finitely many elements of
-the form a^{1/n} and "at least sufficiently many" roots of unity to make
+the form a^1/n and "at least sufficiently many" roots of unity to make
 this field Galois over Q.
 
 The main importance of this script is to show that, for a fixed group G as
@@ -47,7 +48,7 @@ computation of degrees for the same group G only require constant time
 
 ## KummerDegree( G, M, N )
 
-Returns the degree of the Kummer extension Q_{M,N}=Q(\zeta_M,G^{1/N}) over Q.
+Returns the degree of the Kummer extension Q{M,N}=Q(z,G^1/N ) over Q.
 
 INPUT:
 
@@ -57,9 +58,10 @@ INPUT:
 
 OUTPUT:
 
-The degree of the Kummer Extensions Q_{M,N}=Q(\zeta_M,G^{1/N}) over Q.
+The degree of the Kummer Extensions Q{M,N}=Q(z,G^1/N ) over Q.
 
 EXAMPLES:
+
 ```
 sage: KummerDegree([5],10,2)
 4
@@ -80,8 +82,8 @@ G - a list of generators for the group G
 
 OUPUT:
 
-The first part of the output consist of two positive integers M_0 and N_0.
-N_0 is always a divisor of M_0.
+The first part of the output consist of two positive integers M0 and N0.
+N0 is always a divisor of M0.
 
 The second part of the output can be either one or two tables, depending on
 the group G. In case -1 is not an element of G, there is only one table,
@@ -155,6 +157,7 @@ M/N is ODD and is read as the previous one.
 ```
 
 Uncommenting the line of code:
+
 ```
 print_case_list( ret )
 ```