Additional symmetries

Former-commit-id: dce9d43c0bfbce7166e6365f40591fbf5f9b4873

qpms/symmetries.py

@@ -53,7 +53,7 @@ class SVWFPointGroupInfo: # only for point groups, coz in svwf_rep() I use I_tyt
         self.svwf_rep_gen_func = svwf_rep_gen_func
         self.irreps = dict()
         for irrepname, irrepgens in irrepgens_dict.items():
-            is1d = isinstance(irrepgens[0], int)
+            is1d = isinstance(irrepgens[0], (int,float,complex))
             irrepdim = 1 if is1d else irrepgens[0].shape[0]
             self.irreps[irrepname] = generate_grouprep(self.permgroup, 
                                                        1 if is1d else np.eye(irrepdim),
@@ -495,6 +495,24 @@ point_group_info = { # representation info of some useful point groups
                                    qpms.IRot3.identity(),
                                 )
     ),
+    'C2' : SVWFPointGroupInfo('C2',
+                 # permutation group generators
+                               (Permutation(0,1), # 180 deg rotation around z axis
+                               ), 
+                 # dictionary with irrep generators
+                               {
+                                    # Bradley, Cracknell p. 57;
+                                    'A': (1,),
+                                    'B': (-1,),    
+                               },
+                 # function that generates a tuple with svwf representation generators
+                               lambda lMax : (qpms.zrotN_tyty(2, lMax),),
+                 # quaternion rep generators
+                                rep3d_gens = (
+                                    qpms.IRot3.zrotN(2),
+                                )
+
+    ),
     'C2v' : SVWFPointGroupInfo('C2v',
                  # permutation group generators
                                (Permutation(0,1, size=4)(2,3), # x -> - x mirror operation (i.e. yz mirror plane)
@@ -546,6 +564,24 @@ point_group_info = { # representation info of some useful point groups
                                    qpms.IRot3.zflip(),
                                 )
     ),
+    'C4' : SVWFPointGroupInfo('C4',
+                 # permutation group generators
+                               (Permutation(0,1,2,3, size=4),), #C4 rotation
+                 # dictionary with irrep generators
+                               {
+                                    # Bradley, Cracknell p. 58
+                                    'A': (1,),
+                                    'B': (-1,),
+                                    '1E': (-1j,),
+                                    '2E': (1j,),
+                               },
+                 # function that generates a tuple with svwf representation generators
+                               lambda lMax : (qpms.zrotN_tyty(4, lMax), ),
+                 # quaternion rep generators
+                               rep3d_gens = (
+                                   qpms.IRot3.zrotN(4),
+                                )
+    ),
     'C4v' : SVWFPointGroupInfo('C4v',
                  # permutation group generators
                                (Permutation(0,1,2,3, size=4), #C4 rotation
@@ -621,4 +657,41 @@ point_group_info = { # representation info of some useful point groups
                                    qpms.IRot3.zflip(),
                                 )
     ),
+    'x_and_z_flip': SVWFPointGroupInfo(
+	'x_and_z_flip',
+	(
+	    Permutation(0,1, size=4), # x -> -x mirror op
+	    Permutation(2,3, size=4), # z -> -z mirror op
+	),
+	{
+	    "P'": (1, 1),
+	    "R'": (-1, 1),
+	    "P''": (-1,-1),
+	    "R''": (1, -1),
+	},
+	lambda lMax : (qpms.xflip_tyty(lMax), qpms.zflip_tyty(lMax)),
+        rep3d_gens = (
+            qpms.IRot3.xflip(),
+            qpms.IRot3.zflip(),
+        )
+
+    ),
+    'y_and_z_flip': SVWFPointGroupInfo(
+	'y_and_z_flip',
+	(
+	    Permutation(0,1, size=4), # y -> -y mirror op
+	    Permutation(2,3, size=4), # z -> -z mirror op
+	),
+	{
+	    "P'": (1, 1),
+	    "R'": (-1, 1),
+	    "P''": (-1,-1),
+	    "R''": (1, -1),
+	},
+	lambda lMax : (qpms.yflip_tyty(lMax), qpms.zflip_tyty(lMax)),
+        rep3d_gens = (
+            qpms.IRot3.yflip(),
+            qpms.IRot3.zflip(),
+        )
+    ),
 }

tests/generate_groupcode.py

@@ -2,7 +2,8 @@
 from qpms.symmetries import point_group_info
 
 codestring = "#include <qpms/groups.h>\n"
-for name, info in point_group_info.items():
+for name in sorted(point_group_info.keys()):
+    info = point_group_info[name]
     codestring += 'const qpms_finite_group_t QPMS_FINITE_GROUP_%s = ' %name
     codestring += info.generate_c_source()
     codestring += ";\n\n"

tests/staticgroups.c

@@ -1,4 +1,42 @@
-#include "staticgroups.h"
+#include <qpms/groups.h>
+const qpms_finite_group_t QPMS_FINITE_GROUP_C2 = {
+  "C2", // name
+  2, // order
+  0, // idi
+  (qpms_gmi_t[]) { // mt
+    0, 1,
+    1, 0,
+  },
+  (qpms_gmi_t[]) { // invi
+    0, 1
+  },
+  (qpms_gmi_t[]) {1}, // gens
+  1, // ngens
+  (qpms_permutation_t[]){ // permrep
+    "(1)",
+    "(0 1)",
+  },
+  NULL, // elemlabels
+  2, // permrep_nelem
+  (qpms_irot3_t[]) { // rep3d
+   {{1.0+0.0*I, 0.0+0.0*I}, 1},
+   {{6.123233995736766e-17+1.0*I, 0.0+0.0*I}, 1},
+  },
+  2, // nirreps
+  (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "B", //name
+      (complex double []) {1, -1} // m
+    },
+    {
+      1, // dim
+      "A", //name
+      (complex double []) {1, 1} // m
+    },
+  } // end of irreps
+};
+
 const qpms_finite_group_t QPMS_FINITE_GROUP_C2v = {
   "C2v", // name
   4, // order
@@ -35,6 +73,11 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_C2v = {
       "A1", //name
       (complex double []) {1, 1, 1, 1} // m
     },
+    {
+      1, // dim
+      "A2", //name
+      (complex double []) {1, -1, 1, -1} // m
+    },
     {
       1, // dim
       "B2", //name
@@ -45,10 +88,241 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_C2v = {
       "B1", //name
       (complex double []) {1, 1, -1, -1} // m
     },
+  } // end of irreps
+};
+
+const qpms_finite_group_t QPMS_FINITE_GROUP_C4 = {
+  "C4", // name
+  4, // order
+  0, // idi
+  (qpms_gmi_t[]) { // mt
+    0, 1, 2, 3,
+    1, 2, 3, 0,
+    2, 3, 0, 1,
+    3, 0, 1, 2,
+  },
+  (qpms_gmi_t[]) { // invi
+    0, 3, 2, 1
+  },
+  (qpms_gmi_t[]) {1}, // gens
+  1, // ngens
+  (qpms_permutation_t[]){ // permrep
+    "(3)",
+    "(0 1 2 3)",
+    "(0 2)(1 3)",
+    "(0 3 2 1)",
+  },
+  NULL, // elemlabels
+  4, // permrep_nelem
+  (qpms_irot3_t[]) { // rep3d
+   {{1.0+0.0*I, 0.0+0.0*I}, 1},
+   {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
+   {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
+   {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
+  },
+  4, // nirreps
+  (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "B", //name
+      (complex double []) {1, -1, 1, -1} // m
+    },
+    {
+      1, // dim
+      "2E", //name
+      (complex double []) {1, 1j, (-1+0j), (-0-1j)} // m
+    },
+    {
+      1, // dim
+      "A", //name
+      (complex double []) {1, 1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "1E", //name
+      (complex double []) {1, -1j, (-1+0j), 1j} // m
+    },
+  } // end of irreps
+};
+
+const qpms_finite_group_t QPMS_FINITE_GROUP_C4v = {
+  "C4v", // name
+  8, // order
+  0, // idi
+  (qpms_gmi_t[]) { // mt
+    0, 1, 2, 3, 4, 5, 6, 7,
+    1, 2, 3, 0, 7, 4, 5, 6,
+    2, 3, 0, 1, 6, 7, 4, 5,
+    3, 0, 1, 2, 5, 6, 7, 4,
+    4, 5, 6, 7, 0, 1, 2, 3,
+    5, 6, 7, 4, 3, 0, 1, 2,
+    6, 7, 4, 5, 2, 3, 0, 1,
+    7, 4, 5, 6, 1, 2, 3, 0,
+  },
+  (qpms_gmi_t[]) { // invi
+    0, 3, 2, 1, 4, 5, 6, 7
+  },
+  (qpms_gmi_t[]) {1, 7}, // gens
+  2, // ngens
+  (qpms_permutation_t[]){ // permrep
+    "(3)",
+    "(0 1 2 3)",
+    "(0 2)(1 3)",
+    "(0 3 2 1)",
+    "(3)(0 2)",
+    "(0 3)(1 2)",
+    "(1 3)",
+    "(0 1)(2 3)",
+  },
+  NULL, // elemlabels
+  4, // permrep_nelem
+  (qpms_irot3_t[]) { // rep3d
+   {{1.0+0.0*I, 0.0+0.0*I}, 1},
+   {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
+   {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
+   {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
+   {{0.0+0.0*I, 0.7071067811865477-0.7071067811865474*I}, -1},
+   {{0.0+0.0*I, 1.0+2.220446049250313e-16*I}, -1},
+   {{0.0+0.0*I, 0.7071067811865475+0.7071067811865476*I}, -1},
+   {{0.0+0.0*I, 0.0+1.0*I}, -1},
+  },
+  5, // nirreps
+  (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "A1", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
+    },
     {
       1, // dim
       "A2", //name
-      (complex double []) {1, -1, 1, -1} // m
+      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
+    },
+    {
+      2, // dim
+      "E", //name
+      (complex double []) {
+        // (3)
+        1.0, 0.0, 
+        0.0, 1.0, 
+        // (0 1 2 3)
+        0.0, -1.0, 
+        1.0, 0.0, 
+        // (0 2)(1 3)
+        -1.0, 0.0, 
+        0.0, -1.0, 
+        // (0 3 2 1)
+        0.0, 1.0, 
+        -1.0, 0.0, 
+        // (3)(0 2)
+        0.0, 1.0, 
+        1.0, 0.0, 
+        // (0 3)(1 2)
+        1.0, 0.0, 
+        0.0, -1.0, 
+        // (1 3)
+        0.0, -1.0, 
+        -1.0, 0.0, 
+        // (0 1)(2 3)
+        -1.0, 0.0, 
+        0.0, 1.0, 
+      }
+    },
+    {
+      1, // dim
+      "B2", //name
+      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
+    },
+    {
+      1, // dim
+      "B1", //name
+      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
+    },
+  } // end of irreps
+};
+
+const qpms_finite_group_t QPMS_FINITE_GROUP_D2h = {
+  "D2h", // name
+  8, // order
+  0, // idi
+  (qpms_gmi_t[]) { // mt
+    0, 1, 2, 3, 4, 5, 6, 7,
+    1, 0, 3, 2, 5, 4, 7, 6,
+    2, 3, 0, 1, 6, 7, 4, 5,
+    3, 2, 1, 0, 7, 6, 5, 4,
+    4, 5, 6, 7, 0, 1, 2, 3,
+    5, 4, 7, 6, 1, 0, 3, 2,
+    6, 7, 4, 5, 2, 3, 0, 1,
+    7, 6, 5, 4, 3, 2, 1, 0,
+  },
+  (qpms_gmi_t[]) { // invi
+    0, 1, 2, 3, 4, 5, 6, 7
+  },
+  (qpms_gmi_t[]) {1, 3, 7}, // gens
+  3, // ngens
+  (qpms_permutation_t[]){ // permrep
+    "(5)",
+    "(5)(0 1)(2 3)",
+    "(5)(0 2)(1 3)",
+    "(5)(0 3)(1 2)",
+    "(0 3)(1 2)(4 5)",
+    "(0 2)(1 3)(4 5)",
+    "(0 1)(2 3)(4 5)",
+    "(4 5)",
+  },
+  NULL, // elemlabels
+  6, // permrep_nelem
+  (qpms_irot3_t[]) { // rep3d
+   {{1.0+0.0*I, 0.0+0.0*I}, 1},
+   {{0.0+0.0*I, 0.0+1.0*I}, -1},
+   {{0.0+1.0*I, 0.0+0.0*I}, 1},
+   {{0.0+0.0*I, 1.0+0.0*I}, -1},
+   {{0.0+0.0*I, 0.0+1.0*I}, 1},
+   {{-1.0+0.0*I, 0.0+0.0*I}, -1},
+   {{0.0+0.0*I, -1.0+0.0*I}, 1},
+   {{0.0+1.0*I, 0.0+0.0*I}, -1},
+  },
+  8, // nirreps
+  (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "A2\'", //name
+      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
+    },
+    {
+      1, // dim
+      "B1\'", //name
+      (complex double []) {1, 1, -1, -1, -1, -1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "A2\'\'", //name
+      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
+    },
+    {
+      1, // dim
+      "B2\'", //name
+      (complex double []) {1, -1, -1, 1, 1, -1, -1, 1} // m
+    },
+    {
+      1, // dim
+      "A1\'", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "A1\'\'", //name
+      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
+    },
+    {
+      1, // dim
+      "B2\'\'", //name
+      (complex double []) {1, 1, -1, -1, 1, 1, -1, -1} // m
+    },
+    {
+      1, // dim
+      "B1\'\'", //name
+      (complex double []) {1, -1, -1, 1, -1, 1, 1, -1} // m
     },
   } // end of irreps
 };
@@ -108,6 +382,11 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D3h = {
   },
   6, // nirreps
   (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "A2\'", //name
+      (complex double []) {1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1} // m
+    },
     {
       2, // dim
       "E\'", //name
@@ -150,6 +429,21 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D3h = {
         0.0, 0.9999999999999996, 
       }
     },
+    {
+      1, // dim
+      "A2\'\'", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1} // m
+    },
+    {
+      1, // dim
+      "A1\'", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "A1\'\'", //name
+      (complex double []) {1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1} // m
+    },
     {
       2, // dim
       "E\'\'", //name
@@ -192,26 +486,6 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D3h = {
         0.0, -0.9999999999999996, 
       }
     },
-    {
-      1, // dim
-      "A2\'", //name
-      (complex double []) {1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1} // m
-    },
-    {
-      1, // dim
-      "A1\'\'", //name
-      (complex double []) {1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1} // m
-    },
-    {
-      1, // dim
-      "A1\'", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
-    },
-    {
-      1, // dim
-      "A2\'\'", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1} // m
-    },
   } // end of irreps
 };
 
@@ -284,8 +558,13 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D4h = {
   (struct qpms_finite_group_irrep_t[]) { // irreps
     {
       1, // dim
-      "B1\'\'", //name
+      "A2\'", //name
-      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1} // m
+      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "B1\'", //name
+      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1} // m
     },
     {
       2, // dim
@@ -341,6 +620,36 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D4h = {
         0.0, 1.0, 
       }
     },
+    {
+      1, // dim
+      "A2\'\'", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1} // m
+    },
+    {
+      1, // dim
+      "B2\'", //name
+      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1} // m
+    },
+    {
+      1, // dim
+      "A1\'", //name
+      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
+    },
+    {
+      1, // dim
+      "A1\'\'", //name
+      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1} // m
+    },
+    {
+      1, // dim
+      "B2\'\'", //name
+      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1} // m
+    },
+    {
+      1, // dim
+      "B1\'\'", //name
+      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1} // m
+    },
     {
       2, // dim
       "E\'\'", //name
@@ -395,41 +704,6 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_D4h = {
         0.0, -1.0, 
       }
     },
-    {
-      1, // dim
-      "B1\'", //name
-      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1} // m
-    },
-    {
-      1, // dim
-      "A2\'\'", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1} // m
-    },
-    {
-      1, // dim
-      "B2\'", //name
-      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1} // m
-    },
-    {
-      1, // dim
-      "A1\'\'", //name
-      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1} // m
-    },
-    {
-      1, // dim
-      "A2\'", //name
-      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1} // m
-    },
-    {
-      1, // dim
-      "B2\'\'", //name
-      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1} // m
-    },
-    {
-      1, // dim
-      "A1\'", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
-    },
   } // end of irreps
 };
 
@@ -463,184 +737,110 @@ const qpms_finite_group_t QPMS_FINITE_GROUP_trivial_g = {
   } // end of irreps
 };
 
-const qpms_finite_group_t QPMS_FINITE_GROUP_C4v = {
+const qpms_finite_group_t QPMS_FINITE_GROUP_x_and_z_flip = {
-  "C4v", // name
+  "x_and_z_flip", // name
-  8, // order
+  4, // order
   0, // idi
   (qpms_gmi_t[]) { // mt
-    0, 1, 2, 3, 4, 5, 6, 7,
+    0, 1, 2, 3,
-    1, 2, 3, 0, 7, 4, 5, 6,
+    1, 0, 3, 2,
-    2, 3, 0, 1, 6, 7, 4, 5,
+    2, 3, 0, 1,
-    3, 0, 1, 2, 5, 6, 7, 4,
+    3, 2, 1, 0,
-    4, 5, 6, 7, 0, 1, 2, 3,
-    5, 6, 7, 4, 3, 0, 1, 2,
-    6, 7, 4, 5, 2, 3, 0, 1,
-    7, 4, 5, 6, 1, 2, 3, 0,
   },
   (qpms_gmi_t[]) { // invi
-    0, 3, 2, 1, 4, 5, 6, 7
+    0, 1, 2, 3
   },
-  (qpms_gmi_t[]) {1, 7}, // gens
+  (qpms_gmi_t[]) {1, 3}, // gens
   2, // ngens
   (qpms_permutation_t[]){ // permrep
     "(3)",
-    "(0 1 2 3)",
+    "(3)(0 1)",
-    "(0 2)(1 3)",
-    "(0 3 2 1)",
-    "(3)(0 2)",
-    "(0 3)(1 2)",
-    "(1 3)",
     "(0 1)(2 3)",
+    "(2 3)",
   },
   NULL, // elemlabels
   4, // permrep_nelem
   (qpms_irot3_t[]) { // rep3d
    {{1.0+0.0*I, 0.0+0.0*I}, 1},
-   {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
-   {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
-   {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
-   {{0.0+0.0*I, 0.7071067811865477-0.7071067811865474*I}, -1},
-   {{0.0+0.0*I, 1.0+2.220446049250313e-16*I}, -1},
-   {{0.0+0.0*I, 0.7071067811865475+0.7071067811865476*I}, -1},
    {{0.0+0.0*I, 0.0+1.0*I}, -1},
-  },
-  5, // nirreps
-  (struct qpms_finite_group_irrep_t[]) { // irreps
-    {
-      2, // dim
-      "E", //name
-      (complex double []) {
-        // (3)
-        1.0, 0.0, 
-        0.0, 1.0, 
-        // (0 1 2 3)
-        0.0, -1.0, 
-        1.0, 0.0, 
-        // (0 2)(1 3)
-        -1.0, 0.0, 
-        0.0, -1.0, 
-        // (0 3 2 1)
-        0.0, 1.0, 
-        -1.0, 0.0, 
-        // (3)(0 2)
-        0.0, 1.0, 
-        1.0, 0.0, 
-        // (0 3)(1 2)
-        1.0, 0.0, 
-        0.0, -1.0, 
-        // (1 3)
-        0.0, -1.0, 
-        -1.0, 0.0, 
-        // (0 1)(2 3)
-        -1.0, 0.0, 
-        0.0, 1.0, 
-      }
-    },
-    {
-      1, // dim
-      "A1", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
-    },
-    {
-      1, // dim
-      "B2", //name
-      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
-    },
-    {
-      1, // dim
-      "B1", //name
-      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
-    },
-    {
-      1, // dim
-      "A2", //name
-      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
-    },
-  } // end of irreps
-};
-
-const qpms_finite_group_t QPMS_FINITE_GROUP_D2h = {
-  "D2h", // name
-  8, // order
-  0, // idi
-  (qpms_gmi_t[]) { // mt
-    0, 1, 2, 3, 4, 5, 6, 7,
-    1, 0, 3, 2, 5, 4, 7, 6,
-    2, 3, 0, 1, 6, 7, 4, 5,
-    3, 2, 1, 0, 7, 6, 5, 4,
-    4, 5, 6, 7, 0, 1, 2, 3,
-    5, 4, 7, 6, 1, 0, 3, 2,
-    6, 7, 4, 5, 2, 3, 0, 1,
-    7, 6, 5, 4, 3, 2, 1, 0,
-  },
-  (qpms_gmi_t[]) { // invi
-    0, 1, 2, 3, 4, 5, 6, 7
-  },
-  (qpms_gmi_t[]) {1, 3, 7}, // gens
-  3, // ngens
-  (qpms_permutation_t[]){ // permrep
-    "(5)",
-    "(5)(0 1)(2 3)",
-    "(5)(0 2)(1 3)",
-    "(5)(0 3)(1 2)",
-    "(0 3)(1 2)(4 5)",
-    "(0 2)(1 3)(4 5)",
-    "(0 1)(2 3)(4 5)",
-    "(4 5)",
-  },
-  NULL, // elemlabels
-  6, // permrep_nelem
-  (qpms_irot3_t[]) { // rep3d
-   {{1.0+0.0*I, 0.0+0.0*I}, 1},
-   {{0.0+0.0*I, 0.0+1.0*I}, -1},
-   {{0.0+1.0*I, 0.0+0.0*I}, 1},
-   {{0.0+0.0*I, 1.0+0.0*I}, -1},
-   {{0.0+0.0*I, 0.0+1.0*I}, 1},
-   {{-1.0+0.0*I, 0.0+0.0*I}, -1},
    {{0.0+0.0*I, -1.0+0.0*I}, 1},
    {{0.0+1.0*I, 0.0+0.0*I}, -1},
   },
-  8, // nirreps
+  4, // nirreps
   (struct qpms_finite_group_irrep_t[]) { // irreps
     {
       1, // dim
-      "B1\'\'", //name
+      "P\'\'", //name
-      (complex double []) {1, -1, -1, 1, -1, 1, 1, -1} // m
+      (complex double []) {1, -1, 1, -1} // m
     },
     {
       1, // dim
-      "A2\'\'", //name
+      "P\'", //name
-      (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
+      (complex double []) {1, 1, 1, 1} // m
     },
     {
       1, // dim
-      "B1\'", //name
+      "R\'\'", //name
-      (complex double []) {1, 1, -1, -1, -1, -1, 1, 1} // m
+      (complex double []) {1, 1, -1, -1} // m
     },
     {
       1, // dim
-      "A2\'", //name
+      "R\'", //name
-      (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
+      (complex double []) {1, -1, -1, 1} // m
+    },
+  } // end of irreps
+};
+
+const qpms_finite_group_t QPMS_FINITE_GROUP_y_and_z_flip = {
+  "y_and_z_flip", // name
+  4, // order
+  0, // idi
+  (qpms_gmi_t[]) { // mt
+    0, 1, 2, 3,
+    1, 0, 3, 2,
+    2, 3, 0, 1,
+    3, 2, 1, 0,
+  },
+  (qpms_gmi_t[]) { // invi
+    0, 1, 2, 3
+  },
+  (qpms_gmi_t[]) {1, 3}, // gens
+  2, // ngens
+  (qpms_permutation_t[]){ // permrep
+    "(3)",
+    "(3)(0 1)",
+    "(0 1)(2 3)",
+    "(2 3)",
+  },
+  NULL, // elemlabels
+  4, // permrep_nelem
+  (qpms_irot3_t[]) { // rep3d
+   {{1.0+0.0*I, 0.0+0.0*I}, 1},
+   {{0.0+0.0*I, 1.0+0.0*I}, -1},
+   {{0.0+0.0*I, 0.0+1.0*I}, 1},
+   {{0.0+1.0*I, 0.0+0.0*I}, -1},
+  },
+  4, // nirreps
+  (struct qpms_finite_group_irrep_t[]) { // irreps
+    {
+      1, // dim
+      "P\'\'", //name
+      (complex double []) {1, -1, 1, -1} // m
     },
     {
       1, // dim
-      "A1\'\'", //name
+      "P\'", //name
-      (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
+      (complex double []) {1, 1, 1, 1} // m
     },
     {
       1, // dim
-      "B2\'", //name
+      "R\'\'", //name
-      (complex double []) {1, -1, -1, 1, 1, -1, -1, 1} // m
+      (complex double []) {1, 1, -1, -1} // m
     },
     {
       1, // dim
-      "B2\'\'", //name
+      "R\'", //name
-      (complex double []) {1, 1, -1, -1, 1, 1, -1, -1} // m
+      (complex double []) {1, -1, -1, 1} // m
-    },
-    {
-      1, // dim
-      "A1\'", //name
-      (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
     },
   } // end of irreps
 };

tests/staticgroups.h

@@ -1,10 +1,14 @@
 #ifndef STATICGROUPS_H
 #define STATICGROUPS_H
 #include <qpms/groups.h>
+extern const qpms_finite_group_t QPMS_FINITE_GROUP_C2;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_C2v;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_trivial_g;
+extern const qpms_finite_group_t QPMS_FINITE_GROUP_C4;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_C4v;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_D3h;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_D2h;
 extern const qpms_finite_group_t QPMS_FINITE_GROUP_D4h;
+extern const qpms_finite_group_t QPMS_FINITE_GROUP_x_and_z_flip;
+extern const qpms_finite_group_t QPMS_FINITE_GROUP_y_and_z_flip;
 #endif