M2

src/Algebra/Groups/Group.cs

@@ -0,0 +1,46 @@
+namespace Skeleton.Algebra.Groups;
+
+/// <summary>
+/// a set of elements closed under group operation
+/// </summary>
+/// <typeparam name="TElement"></typeparam>
+public abstract class Group<TElement>
+{
+    /// <summary>
+    /// unit of the group<br/>
+    /// unit * x = x * unit = x for all x in group
+    /// </summary>
+    public abstract TElement GroupUnit { get; }
+    /// <summary>
+    /// inverse of the element under group operation
+    /// </summary>
+    /// <param name="element"></param>
+    /// <returns></returns>
+    public abstract TElement GroupInv(TElement element);
+    /// <summary>
+    /// 
+    /// </summary>
+    /// <param name="a"></param>
+    /// <param name="b"></param>
+    /// <returns></returns>
+    public abstract TElement GroupOperation(TElement a, TElement b);
+
+    /// <summary>
+    /// Commutator of group
+    /// </summary>
+    /// <param name="a">a</param>
+    /// <param name="b">b</param>
+    /// <returns></returns>
+    public TElement GroupCommutator(TElement a, TElement b) =>
+        GroupOperation(GroupOperation(a, b), GroupOperation(GroupInv(a), GroupInv(b)));
+    /// <summary>
+    /// a conjugate of b => aba^{-1}
+    /// </summary>
+    /// <param name="a">a</param>
+    /// <param name="b">b</param>
+    /// <returns>a b a^{-1}</returns>
+    public TElement Conjugation(TElement a, TElement b) =>
+        GroupOperation(a, GroupOperation(b, GroupInv(a)));
+    
+
+}