diff --git a/weyl.c b/weyl.c
index b595829..d51197a 100644
--- a/weyl.c
+++ b/weyl.c
@@ -229,28 +229,26 @@ int weyl_opposition(semisimple_type_t type, int simple_root)
   r = simple_root - offset;
 
   switch(type.factors[factor].series) {
+  case 'B': case 'C': case 'F': case 'G':
+    iota_r = r;
+    break;
+
   case 'A':
     iota_r = type.factors[factor].rank - 1 - r;
     break;
 
-  case 'B': case 'C':
-    iota_r = r;
-    break;
-
   case 'D':
-    ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[factor].series, type.factors[factor].rank);
+    if(type.factors[factor].rank % 2 == 0)
+      iota_r = r;
+    else
+      iota_r = r == 0 ? 1 : r == 1 ? 0 : r;
     break;
 
   case 'E':
-    ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[factor].series, type.factors[factor].rank);
-    break;
-
-  case 'F':
-    ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[factor].series, type.factors[factor].rank);
-    break;
-
-  case 'G':
-    ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[factor].series, type.factors[factor].rank);
+    if(type.factors[factor].rank == 6)
+      iota_r = r;
+    else
+      iota_r = r == 3 || r == 4 ? r : 5 - r;
     break;
 
   default:
@@ -275,50 +273,46 @@ void weyl_cartan_matrix(semisimple_type_t type, int *m)
     for(int i = 0; i < type.factors[k].rank; i++)  // A is the submatrix corresponding to the current simple factor
       A[i] = &m[(i+offset)*rank + offset];
 
+    for(int i = 1; i < type.factors[k].rank; i++) {
+      A[i][i-1] = -1;
+      A[i-1][i] = -1;
+    }
+
+
     switch(type.factors[k].series) {
     case 'A':
-      for(int i = 1; i < type.factors[k].rank; i++) {
-	A[i][i-1] = -1;
-	A[i-1][i] = -1;
-      }
       break;
 
-    case 'B':        // not sure at all about the order of B and C
-      if(type.factors[k].rank >= 2) {
-	A[0][1] = -2;
-	A[1][0] = -1;
-      }
-      for(int i = 2; i < type.factors[k].rank; i++) {
-	A[i][i-1] = -1;
-	A[i-1][i] = -1;
-      }
+    case 'B':
+      ERROR(type.factors[k].rank < 2, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[0][1] = -2;
       break;
 
     case 'C':
-      if(type.factors[k].rank >= 2) {
-	A[0][1] = -1;
-	A[1][0] = -2;
-      }
-      for(int i = 2; i < type.factors[k].rank; i++) {
-	A[i][i-1] = -1;
-	A[i-1][i] = -1;
-      }
+      ERROR(type.factors[k].rank < 2, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[1][0] = -2;
       break;
 
     case 'D':
-      ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      ERROR(type.factors[k].rank < 3, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[0][1] = A[1][0] = 0;
+      A[0][2] = A[2][0] = -1;
       break;
 
     case 'E':
-      ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      ERROR(type.factors[k].rank < 6 || type.factors[k].rank > 8, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[1][2] = A[2][1] = 0;
+      A[1][3] = A[3][1] = -1;
       break;
 
     case 'F':
-      ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      ERROR(type.factors[k].rank != 4, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[3][2] = -2;
       break;
 
     case 'G':
-      ERROR(1, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      ERROR(type.factors[k].rank != 2, "A Weyl group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
+      A[1][0] = -3;
       break;
 
     default: