- * @param G Metric of the surrounding space */
-ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G);
+ * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
+ * @param rl Representation label
+ * @return List of components of the transformed vector*/
+ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl = 0);
+
+/** The second form of Moebius transformations defined by a 2x2 Clifford matrix M
+ * This function takes the transformation matrix M as a single entity.
+ *
+ * @param M the defining matrix
+ * @param v Vector to be transformed
+ * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
+ * @param rl Representation label
+ * @return List of components of the transformed vector*/
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0);
+