oldtests/staticgroups.c

   1 #include <qpms/groups.h>
   2 const qpms_finite_group_t QPMS_FINITE_GROUP_C2 = {
   3   "C2", // name
   4   2, // order
   5   0, // idi
   6   (qpms_gmi_t[]) { // mt
   7     0, 1,
   8     1, 0,
   9   },
  10   (qpms_gmi_t[]) { // invi
  11     0, 1
  12   },
  13   (qpms_gmi_t[]) {1}, // gens
  14   1, // ngens
  15   (qpms_permutation_t[]){ // permrep
  16     "(1)",
  17     "(0 1)",
  18   },
  19   NULL, // elemlabels
  20   2, // permrep_nelem
  21   (qpms_irot3_t[]) { // rep3d
  22    {{1.0+0.0*I, 0.0+0.0*I}, 1},
  23    {{6.123233995736766e-17+1.0*I, 0.0+0.0*I}, 1},
  24   },
  25   2, // nirreps
  26   (struct qpms_finite_group_irrep_t[]) { // irreps
  27     {
  28       1, // dim
  29       "B", //name
  30       (complex double []) {1, -1} // m
  31     },
  32     {
  33       1, // dim
  34       "A", //name
  35       (complex double []) {1, 1} // m
  36     },
  37   } // end of irreps
  38 };
  39
  40 const qpms_finite_group_t QPMS_FINITE_GROUP_C2v = {
  41   "C2v", // name
  42   4, // order
  43   0, // idi
  44   (qpms_gmi_t[]) { // mt
  45     0, 1, 2, 3,
  46     1, 0, 3, 2,
  47     2, 3, 0, 1,
  48     3, 2, 1, 0,
  49   },
  50   (qpms_gmi_t[]) { // invi
  51     0, 1, 2, 3
  52   },
  53   (qpms_gmi_t[]) {1, 3}, // gens
  54   2, // ngens
  55   (qpms_permutation_t[]){ // permrep
  56     "(3)",
  57     "(0 1)(2 3)",
  58     "(0 2)(1 3)",
  59     "(0 3)(1 2)",
  60   },
  61   NULL, // elemlabels
  62   4, // permrep_nelem
  63   (qpms_irot3_t[]) { // rep3d
  64    {{1.0+0.0*I, 0.0+0.0*I}, 1},
  65    {{0.0+0.0*I, 0.0+1.0*I}, -1},
  66    {{0.0+1.0*I, 0.0+0.0*I}, 1},
  67    {{0.0+0.0*I, 1.0+0.0*I}, -1},
  68   },
  69   4, // nirreps
  70   (struct qpms_finite_group_irrep_t[]) { // irreps
  71     {
  72       1, // dim
  73       "A1", //name
  74       (complex double []) {1, 1, 1, 1} // m
  75     },
  76     {
  77       1, // dim
  78       "A2", //name
  79       (complex double []) {1, -1, 1, -1} // m
  80     },
  81     {
  82       1, // dim
  83       "B2", //name
  84       (complex double []) {1, -1, -1, 1} // m
  85     },
  86     {
  87       1, // dim
  88       "B1", //name
  89       (complex double []) {1, 1, -1, -1} // m
  90     },
  91   } // end of irreps
  92 };
  93
  94 const qpms_finite_group_t QPMS_FINITE_GROUP_C4 = {
  95   "C4", // name
  96   4, // order
  97   0, // idi
  98   (qpms_gmi_t[]) { // mt
  99     0, 1, 2, 3,
 100     1, 2, 3, 0,
 101     2, 3, 0, 1,
 102     3, 0, 1, 2,
 103   },
 104   (qpms_gmi_t[]) { // invi
 105     0, 3, 2, 1
 106   },
 107   (qpms_gmi_t[]) {1}, // gens
 108   1, // ngens
 109   (qpms_permutation_t[]){ // permrep
 110     "(3)",
 111     "(0 1 2 3)",
 112     "(0 2)(1 3)",
 113     "(0 3 2 1)",
 114   },
 115   NULL, // elemlabels
 116   4, // permrep_nelem
 117   (qpms_irot3_t[]) { // rep3d
 118    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 119    {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
 120    {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
 121    {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
 122   },
 123   4, // nirreps
 124   (struct qpms_finite_group_irrep_t[]) { // irreps
 125     {
 126       1, // dim
 127       "B", //name
 128       (complex double []) {1, -1, 1, -1} // m
 129     },
 130     {
 131       1, // dim
 132       "2E", //name
 133       (complex double []) {1, 1j, (-1+0j), (-0-1j)} // m
 134     },
 135     {
 136       1, // dim
 137       "A", //name
 138       (complex double []) {1, 1, 1, 1} // m
 139     },
 140     {
 141       1, // dim
 142       "1E", //name
 143       (complex double []) {1, -1j, (-1+0j), 1j} // m
 144     },
 145   } // end of irreps
 146 };
 147
 148 const qpms_finite_group_t QPMS_FINITE_GROUP_C4v = {
 149   "C4v", // name
 150   8, // order
 151   0, // idi
 152   (qpms_gmi_t[]) { // mt
 153     0, 1, 2, 3, 4, 5, 6, 7,
 154     1, 2, 3, 0, 7, 4, 5, 6,
 155     2, 3, 0, 1, 6, 7, 4, 5,
 156     3, 0, 1, 2, 5, 6, 7, 4,
 157     4, 5, 6, 7, 0, 1, 2, 3,
 158     5, 6, 7, 4, 3, 0, 1, 2,
 159     6, 7, 4, 5, 2, 3, 0, 1,
 160     7, 4, 5, 6, 1, 2, 3, 0,
 161   },
 162   (qpms_gmi_t[]) { // invi
 163     0, 3, 2, 1, 4, 5, 6, 7
 164   },
 165   (qpms_gmi_t[]) {1, 7}, // gens
 166   2, // ngens
 167   (qpms_permutation_t[]){ // permrep
 168     "(3)",
 169     "(0 1 2 3)",
 170     "(0 2)(1 3)",
 171     "(0 3 2 1)",
 172     "(3)(0 2)",
 173     "(0 3)(1 2)",
 174     "(1 3)",
 175     "(0 1)(2 3)",
 176   },
 177   NULL, // elemlabels
 178   4, // permrep_nelem
 179   (qpms_irot3_t[]) { // rep3d
 180    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 181    {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
 182    {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
 183    {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
 184    {{0.0+0.0*I, 0.7071067811865477-0.7071067811865474*I}, -1},
 185    {{0.0+0.0*I, 1.0+2.220446049250313e-16*I}, -1},
 186    {{0.0+0.0*I, 0.7071067811865475+0.7071067811865476*I}, -1},
 187    {{0.0+0.0*I, 0.0+1.0*I}, -1},
 188   },
 189   5, // nirreps
 190   (struct qpms_finite_group_irrep_t[]) { // irreps
 191     {
 192       1, // dim
 193       "A1", //name
 194       (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
 195     },
 196     {
 197       1, // dim
 198       "A2", //name
 199       (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
 200     },
 201     {
 202       2, // dim
 203       "E", //name
 204       (complex double []) {
 205         // (3)
 206         1.0, 0.0,
 207         0.0, 1.0,
 208         // (0 1 2 3)
 209         0.0, -1.0,
 210         1.0, 0.0,
 211         // (0 2)(1 3)
 212         -1.0, 0.0,
 213         0.0, -1.0,
 214         // (0 3 2 1)
 215         0.0, 1.0,
 216         -1.0, 0.0,
 217         // (3)(0 2)
 218         0.0, 1.0,
 219         1.0, 0.0,
 220         // (0 3)(1 2)
 221         1.0, 0.0,
 222         0.0, -1.0,
 223         // (1 3)
 224         0.0, -1.0,
 225         -1.0, 0.0,
 226         // (0 1)(2 3)
 227         -1.0, 0.0,
 228         0.0, 1.0,
 229       }
 230     },
 231     {
 232       1, // dim
 233       "B2", //name
 234       (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
 235     },
 236     {
 237       1, // dim
 238       "B1", //name
 239       (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
 240     },
 241   } // end of irreps
 242 };
 243
 244 const qpms_finite_group_t QPMS_FINITE_GROUP_D2h = {
 245   "D2h", // name
 246   8, // order
 247   0, // idi
 248   (qpms_gmi_t[]) { // mt
 249     0, 1, 2, 3, 4, 5, 6, 7,
 250     1, 0, 3, 2, 5, 4, 7, 6,
 251     2, 3, 0, 1, 6, 7, 4, 5,
 252     3, 2, 1, 0, 7, 6, 5, 4,
 253     4, 5, 6, 7, 0, 1, 2, 3,
 254     5, 4, 7, 6, 1, 0, 3, 2,
 255     6, 7, 4, 5, 2, 3, 0, 1,
 256     7, 6, 5, 4, 3, 2, 1, 0,
 257   },
 258   (qpms_gmi_t[]) { // invi
 259     0, 1, 2, 3, 4, 5, 6, 7
 260   },
 261   (qpms_gmi_t[]) {1, 3, 7}, // gens
 262   3, // ngens
 263   (qpms_permutation_t[]){ // permrep
 264     "(5)",
 265     "(5)(0 1)(2 3)",
 266     "(5)(0 2)(1 3)",
 267     "(5)(0 3)(1 2)",
 268     "(0 3)(1 2)(4 5)",
 269     "(0 2)(1 3)(4 5)",
 270     "(0 1)(2 3)(4 5)",
 271     "(4 5)",
 272   },
 273   NULL, // elemlabels
 274   6, // permrep_nelem
 275   (qpms_irot3_t[]) { // rep3d
 276    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 277    {{0.0+0.0*I, 0.0+1.0*I}, -1},
 278    {{0.0+1.0*I, 0.0+0.0*I}, 1},
 279    {{0.0+0.0*I, 1.0+0.0*I}, -1},
 280    {{0.0+0.0*I, 0.0+1.0*I}, 1},
 281    {{-1.0+0.0*I, 0.0+0.0*I}, -1},
 282    {{0.0+0.0*I, -1.0+0.0*I}, 1},
 283    {{0.0+1.0*I, 0.0+0.0*I}, -1},
 284   },
 285   8, // nirreps
 286   (struct qpms_finite_group_irrep_t[]) { // irreps
 287     {
 288       1, // dim
 289       "A2\'", //name
 290       (complex double []) {1, -1, 1, -1, -1, 1, -1, 1} // m
 291     },
 292     {
 293       1, // dim
 294       "B1\'", //name
 295       (complex double []) {1, 1, -1, -1, -1, -1, 1, 1} // m
 296     },
 297     {
 298       1, // dim
 299       "A2\'\'", //name
 300       (complex double []) {1, 1, 1, 1, -1, -1, -1, -1} // m
 301     },
 302     {
 303       1, // dim
 304       "B2\'", //name
 305       (complex double []) {1, -1, -1, 1, 1, -1, -1, 1} // m
 306     },
 307     {
 308       1, // dim
 309       "A1\'", //name
 310       (complex double []) {1, 1, 1, 1, 1, 1, 1, 1} // m
 311     },
 312     {
 313       1, // dim
 314       "A1\'\'", //name
 315       (complex double []) {1, -1, 1, -1, 1, -1, 1, -1} // m
 316     },
 317     {
 318       1, // dim
 319       "B2\'\'", //name
 320       (complex double []) {1, 1, -1, -1, 1, 1, -1, -1} // m
 321     },
 322     {
 323       1, // dim
 324       "B1\'\'", //name
 325       (complex double []) {1, -1, -1, 1, -1, 1, 1, -1} // m
 326     },
 327   } // end of irreps
 328 };
 329
 330 const qpms_finite_group_t QPMS_FINITE_GROUP_D3h = {
 331   "D3h", // name
 332   12, // order
 333   0, // idi
 334   (qpms_gmi_t[]) { // mt
 335     0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
 336     1, 2, 0, 5, 3, 4, 8, 6, 7, 10, 11, 9,
 337     2, 0, 1, 4, 5, 3, 7, 8, 6, 11, 9, 10,
 338     3, 4, 5, 0, 1, 2, 10, 11, 9, 8, 6, 7,
 339     4, 5, 3, 2, 0, 1, 9, 10, 11, 6, 7, 8,
 340     5, 3, 4, 1, 2, 0, 11, 9, 10, 7, 8, 6,
 341     6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5,
 342     7, 8, 6, 11, 9, 10, 2, 0, 1, 4, 5, 3,
 343     8, 6, 7, 10, 11, 9, 1, 2, 0, 5, 3, 4,
 344     9, 10, 11, 6, 7, 8, 4, 5, 3, 2, 0, 1,
 345     10, 11, 9, 8, 6, 7, 3, 4, 5, 0, 1, 2,
 346     11, 9, 10, 7, 8, 6, 5, 3, 4, 1, 2, 0,
 347   },
 348   (qpms_gmi_t[]) { // invi
 349     0, 2, 1, 3, 4, 5, 6, 7, 8, 10, 9, 11
 350   },
 351   (qpms_gmi_t[]) {1, 5, 11}, // gens
 352   3, // ngens
 353   (qpms_permutation_t[]){ // permrep
 354     "(4)",
 355     "(4)(0 1 2)",
 356     "(4)(0 2 1)",
 357     "(4)(1 2)",
 358     "(4)(0 1)",
 359     "(4)(0 2)",
 360     "(0 2)(3 4)",
 361     "(1 2)(3 4)",
 362     "(0 1)(3 4)",
 363     "(0 1 2)(3 4)",
 364     "(0 2 1)(3 4)",
 365     "(3 4)",
 366   },
 367   NULL, // elemlabels
 368   5, // permrep_nelem
 369   (qpms_irot3_t[]) { // rep3d
 370    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 371    {{0.5000000000000001+0.8660254037844386*I, 0.0+0.0*I}, 1},
 372    {{-0.4999999999999998+0.8660254037844388*I, 0.0+0.0*I}, 1},
 373    {{0.0+0.0*I, 0.8660254037844388-0.4999999999999998*I}, -1},
 374    {{0.0+0.0*I, 0.8660254037844386+0.5000000000000002*I}, -1},
 375    {{0.0+0.0*I, -5.551115123125783e-17+1.0*I}, -1},
 376    {{0.0+0.0*I, -1.0-5.551115123125783e-17*I}, 1},
 377    {{0.0+0.0*I, -0.5000000000000001-0.8660254037844386*I}, 1},
 378    {{0.0+0.0*I, 0.4999999999999998-0.8660254037844388*I}, 1},
 379    {{0.8660254037844388-0.4999999999999998*I, 0.0+0.0*I}, -1},
 380    {{0.8660254037844386+0.5000000000000002*I, 0.0+0.0*I}, -1},
 381    {{-5.551115123125783e-17+1.0*I, 0.0+0.0*I}, -1},
 382   },
 383   6, // nirreps
 384   (struct qpms_finite_group_irrep_t[]) { // irreps
 385     {
 386       1, // dim
 387       "A2\'", //name
 388       (complex double []) {1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1} // m
 389     },
 390     {
 391       2, // dim
 392       "E\'", //name
 393       (complex double []) {
 394         // (4)
 395         1.0, 0.0,
 396         0.0, 1.0,
 397         // (4)(0 1 2)
 398         -0.5, -0.8660254037844386,
 399         0.8660254037844386, -0.5,
 400         // (4)(0 2 1)
 401         -0.4999999999999999, 0.8660254037844386,
 402         -0.8660254037844386, -0.4999999999999999,
 403         // (4)(1 2)
 404         -0.4999999999999999, -0.8660254037844386,
 405         -0.8660254037844386, 0.4999999999999999,
 406         // (4)(0 1)
 407         -0.49999999999999994, 0.8660254037844385,
 408         0.8660254037844385, 0.49999999999999994,
 409         // (4)(0 2)
 410         0.9999999999999998, 0.0,
 411         0.0, -0.9999999999999998,
 412         // (0 2)(3 4)
 413         0.9999999999999998, 0.0,
 414         0.0, -0.9999999999999998,
 415         // (1 2)(3 4)
 416         -0.4999999999999999, -0.8660254037844384,
 417         -0.8660254037844384, 0.4999999999999999,
 418         // (0 1)(3 4)
 419         -0.4999999999999997, 0.8660254037844384,
 420         0.8660254037844384, 0.4999999999999997,
 421         // (0 1 2)(3 4)
 422         -0.4999999999999997, -0.8660254037844384,
 423         0.8660254037844384, -0.4999999999999997,
 424         // (0 2 1)(3 4)
 425         -0.4999999999999998, 0.8660254037844383,
 426         -0.8660254037844383, -0.4999999999999998,
 427         // (3 4)
 428         0.9999999999999996, 0.0,
 429         0.0, 0.9999999999999996,
 430       }
 431     },
 432     {
 433       1, // dim
 434       "A2\'\'", //name
 435       (complex double []) {1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1} // m
 436     },
 437     {
 438       1, // dim
 439       "A1\'", //name
 440       (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
 441     },
 442     {
 443       1, // dim
 444       "A1\'\'", //name
 445       (complex double []) {1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1} // m
 446     },
 447     {
 448       2, // dim
 449       "E\'\'", //name
 450       (complex double []) {
 451         // (4)
 452         1.0, 0.0,
 453         0.0, 1.0,
 454         // (4)(0 1 2)
 455         -0.5, -0.8660254037844386,
 456         0.8660254037844386, -0.5,
 457         // (4)(0 2 1)
 458         -0.4999999999999999, 0.8660254037844386,
 459         -0.8660254037844386, -0.4999999999999999,
 460         // (4)(1 2)
 461         -0.4999999999999999, -0.8660254037844386,
 462         -0.8660254037844386, 0.4999999999999999,
 463         // (4)(0 1)
 464         -0.49999999999999994, 0.8660254037844385,
 465         0.8660254037844385, 0.49999999999999994,
 466         // (4)(0 2)
 467         0.9999999999999998, 0.0,
 468         0.0, -0.9999999999999998,
 469         // (0 2)(3 4)
 470         -0.9999999999999998, 0.0,
 471         0.0, 0.9999999999999998,
 472         // (1 2)(3 4)
 473         0.4999999999999999, 0.8660254037844384,
 474         0.8660254037844384, -0.4999999999999999,
 475         // (0 1)(3 4)
 476         0.4999999999999997, -0.8660254037844384,
 477         -0.8660254037844384, -0.4999999999999997,
 478         // (0 1 2)(3 4)
 479         0.4999999999999997, 0.8660254037844384,
 480         -0.8660254037844384, 0.4999999999999997,
 481         // (0 2 1)(3 4)
 482         0.4999999999999998, -0.8660254037844383,
 483         0.8660254037844383, 0.4999999999999998,
 484         // (3 4)
 485         -0.9999999999999996, 0.0,
 486         0.0, -0.9999999999999996,
 487       }
 488     },
 489   } // end of irreps
 490 };
 491
 492 const qpms_finite_group_t QPMS_FINITE_GROUP_D4h = {
 493   "D4h", // name
 494   16, // order
 495   0, // idi
 496   (qpms_gmi_t[]) { // mt
 497     0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
 498     1, 2, 3, 0, 7, 4, 5, 6, 11, 8, 9, 10, 13, 14, 15, 12,
 499     2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13,
 500     3, 0, 1, 2, 5, 6, 7, 4, 9, 10, 11, 8, 15, 12, 13, 14,
 501     4, 5, 6, 7, 0, 1, 2, 3, 14, 15, 12, 13, 10, 11, 8, 9,
 502     5, 6, 7, 4, 3, 0, 1, 2, 13, 14, 15, 12, 11, 8, 9, 10,
 503     6, 7, 4, 5, 2, 3, 0, 1, 12, 13, 14, 15, 8, 9, 10, 11,
 504     7, 4, 5, 6, 1, 2, 3, 0, 15, 12, 13, 14, 9, 10, 11, 8,
 505     8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7,
 506     9, 10, 11, 8, 15, 12, 13, 14, 3, 0, 1, 2, 5, 6, 7, 4,
 507     10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5,
 508     11, 8, 9, 10, 13, 14, 15, 12, 1, 2, 3, 0, 7, 4, 5, 6,
 509     12, 13, 14, 15, 8, 9, 10, 11, 6, 7, 4, 5, 2, 3, 0, 1,
 510     13, 14, 15, 12, 11, 8, 9, 10, 5, 6, 7, 4, 3, 0, 1, 2,
 511     14, 15, 12, 13, 10, 11, 8, 9, 4, 5, 6, 7, 0, 1, 2, 3,
 512     15, 12, 13, 14, 9, 10, 11, 8, 7, 4, 5, 6, 1, 2, 3, 0,
 513   },
 514   (qpms_gmi_t[]) { // invi
 515     0, 3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 11, 14, 13, 12, 15
 516   },
 517   (qpms_gmi_t[]) {1, 7, 15}, // gens
 518   3, // ngens
 519   (qpms_permutation_t[]){ // permrep
 520     "(5)",
 521     "(5)(0 1 2 3)",
 522     "(5)(0 2)(1 3)",
 523     "(5)(0 3 2 1)",
 524     "(5)(0 2)",
 525     "(5)(0 3)(1 2)",
 526     "(5)(1 3)",
 527     "(5)(0 1)(2 3)",
 528     "(0 1)(2 3)(4 5)",
 529     "(0 2)(4 5)",
 530     "(0 3)(1 2)(4 5)",
 531     "(1 3)(4 5)",
 532     "(0 1 2 3)(4 5)",
 533     "(0 2)(1 3)(4 5)",
 534     "(0 3 2 1)(4 5)",
 535     "(4 5)",
 536   },
 537   NULL, // elemlabels
 538   6, // permrep_nelem
 539   (qpms_irot3_t[]) { // rep3d
 540    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 541    {{0.7071067811865476+0.7071067811865475*I, 0.0+0.0*I}, 1},
 542    {{2.220446049250313e-16+1.0*I, 0.0+0.0*I}, 1},
 543    {{-0.7071067811865474+0.7071067811865477*I, 0.0+0.0*I}, 1},
 544    {{0.0+0.0*I, 0.7071067811865477-0.7071067811865474*I}, -1},
 545    {{0.0+0.0*I, 1.0+2.220446049250313e-16*I}, -1},
 546    {{0.0+0.0*I, 0.7071067811865475+0.7071067811865476*I}, -1},
 547    {{0.0+0.0*I, 0.0+1.0*I}, -1},
 548    {{0.0+0.0*I, -1.0+0.0*I}, 1},
 549    {{0.0+0.0*I, -0.7071067811865476-0.7071067811865475*I}, 1},
 550    {{0.0+0.0*I, -2.220446049250313e-16-1.0*I}, 1},
 551    {{0.0+0.0*I, 0.7071067811865474-0.7071067811865477*I}, 1},
 552    {{0.7071067811865477-0.7071067811865474*I, 0.0+0.0*I}, -1},
 553    {{1.0+2.220446049250313e-16*I, 0.0+0.0*I}, -1},
 554    {{0.7071067811865475+0.7071067811865476*I, 0.0+0.0*I}, -1},
 555    {{0.0+1.0*I, 0.0+0.0*I}, -1},
 556   },
 557   10, // nirreps
 558   (struct qpms_finite_group_irrep_t[]) { // irreps
 559     {
 560       1, // dim
 561       "A2\'", //name
 562       (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1} // m
 563     },
 564     {
 565       1, // dim
 566       "B1\'", //name
 567       (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1} // m
 568     },
 569     {
 570       2, // dim
 571       "E\'", //name
 572       (complex double []) {
 573         // (5)
 574         1.0, 0.0,
 575         0.0, 1.0,
 576         // (5)(0 1 2 3)
 577         0.0, -1.0,
 578         1.0, 0.0,
 579         // (5)(0 2)(1 3)
 580         -1.0, 0.0,
 581         0.0, -1.0,
 582         // (5)(0 3 2 1)
 583         0.0, 1.0,
 584         -1.0, 0.0,
 585         // (5)(0 2)
 586         0.0, 1.0,
 587         1.0, 0.0,
 588         // (5)(0 3)(1 2)
 589         1.0, 0.0,
 590         0.0, -1.0,
 591         // (5)(1 3)
 592         0.0, -1.0,
 593         -1.0, 0.0,
 594         // (5)(0 1)(2 3)
 595         -1.0, 0.0,
 596         0.0, 1.0,
 597         // (0 1)(2 3)(4 5)
 598         -1.0, 0.0,
 599         0.0, 1.0,
 600         // (0 2)(4 5)
 601         0.0, 1.0,
 602         1.0, 0.0,
 603         // (0 3)(1 2)(4 5)
 604         1.0, 0.0,
 605         0.0, -1.0,
 606         // (1 3)(4 5)
 607         0.0, -1.0,
 608         -1.0, 0.0,
 609         // (0 1 2 3)(4 5)
 610         0.0, -1.0,
 611         1.0, 0.0,
 612         // (0 2)(1 3)(4 5)
 613         -1.0, 0.0,
 614         0.0, -1.0,
 615         // (0 3 2 1)(4 5)
 616         0.0, 1.0,
 617         -1.0, 0.0,
 618         // (4 5)
 619         1.0, 0.0,
 620         0.0, 1.0,
 621       }
 622     },
 623     {
 624       1, // dim
 625       "A2\'\'", //name
 626       (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1} // m
 627     },
 628     {
 629       1, // dim
 630       "B2\'", //name
 631       (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1} // m
 632     },
 633     {
 634       1, // dim
 635       "A1\'", //name
 636       (complex double []) {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} // m
 637     },
 638     {
 639       1, // dim
 640       "A1\'\'", //name
 641       (complex double []) {1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1} // m
 642     },
 643     {
 644       1, // dim
 645       "B2\'\'", //name
 646       (complex double []) {1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1} // m
 647     },
 648     {
 649       1, // dim
 650       "B1\'\'", //name
 651       (complex double []) {1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1} // m
 652     },
 653     {
 654       2, // dim
 655       "E\'\'", //name
 656       (complex double []) {
 657         // (5)
 658         1.0, 0.0,
 659         0.0, 1.0,
 660         // (5)(0 1 2 3)
 661         0.0, -1.0,
 662         1.0, 0.0,
 663         // (5)(0 2)(1 3)
 664         -1.0, 0.0,
 665         0.0, -1.0,
 666         // (5)(0 3 2 1)
 667         0.0, 1.0,
 668         -1.0, 0.0,
 669         // (5)(0 2)
 670         0.0, 1.0,
 671         1.0, 0.0,
 672         // (5)(0 3)(1 2)
 673         1.0, 0.0,
 674         0.0, -1.0,
 675         // (5)(1 3)
 676         0.0, -1.0,
 677         -1.0, 0.0,
 678         // (5)(0 1)(2 3)
 679         -1.0, 0.0,
 680         0.0, 1.0,
 681         // (0 1)(2 3)(4 5)
 682         1.0, 0.0,
 683         0.0, -1.0,
 684         // (0 2)(4 5)
 685         0.0, -1.0,
 686         -1.0, 0.0,
 687         // (0 3)(1 2)(4 5)
 688         -1.0, 0.0,
 689         0.0, 1.0,
 690         // (1 3)(4 5)
 691         0.0, 1.0,
 692         1.0, 0.0,
 693         // (0 1 2 3)(4 5)
 694         0.0, 1.0,
 695         -1.0, 0.0,
 696         // (0 2)(1 3)(4 5)
 697         1.0, 0.0,
 698         0.0, 1.0,
 699         // (0 3 2 1)(4 5)
 700         0.0, -1.0,
 701         1.0, 0.0,
 702         // (4 5)
 703         -1.0, 0.0,
 704         0.0, -1.0,
 705       }
 706     },
 707   } // end of irreps
 708 };
 709
 710 const qpms_finite_group_t QPMS_FINITE_GROUP_trivial_g = {
 711   "trivial_g", // name
 712   1, // order
 713   0, // idi
 714   (qpms_gmi_t[]) { // mt
 715     0,
 716   },
 717   (qpms_gmi_t[]) { // invi
 718     0
 719   },
 720   (qpms_gmi_t[]) {0}, // gens
 721   1, // ngens
 722   (qpms_permutation_t[]){ // permrep
 723     "()",
 724   },
 725   NULL, // elemlabels
 726   0, // permrep_nelem
 727   (qpms_irot3_t[]) { // rep3d
 728    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 729   },
 730   1, // nirreps
 731   (struct qpms_finite_group_irrep_t[]) { // irreps
 732     {
 733       1, // dim
 734       "A", //name
 735       (complex double []) {1} // m
 736     },
 737   } // end of irreps
 738 };
 739
 740 const qpms_finite_group_t QPMS_FINITE_GROUP_x_and_z_flip = {
 741   "x_and_z_flip", // name
 742   4, // order
 743   0, // idi
 744   (qpms_gmi_t[]) { // mt
 745     0, 1, 2, 3,
 746     1, 0, 3, 2,
 747     2, 3, 0, 1,
 748     3, 2, 1, 0,
 749   },
 750   (qpms_gmi_t[]) { // invi
 751     0, 1, 2, 3
 752   },
 753   (qpms_gmi_t[]) {1, 3}, // gens
 754   2, // ngens
 755   (qpms_permutation_t[]){ // permrep
 756     "(3)",
 757     "(3)(0 1)",
 758     "(0 1)(2 3)",
 759     "(2 3)",
 760   },
 761   NULL, // elemlabels
 762   4, // permrep_nelem
 763   (qpms_irot3_t[]) { // rep3d
 764    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 765    {{0.0+0.0*I, 0.0+1.0*I}, -1},
 766    {{0.0+0.0*I, -1.0+0.0*I}, 1},
 767    {{0.0+1.0*I, 0.0+0.0*I}, -1},
 768   },
 769   4, // nirreps
 770   (struct qpms_finite_group_irrep_t[]) { // irreps
 771     {
 772       1, // dim
 773       "P\'\'", //name
 774       (complex double []) {1, -1, 1, -1} // m
 775     },
 776     {
 777       1, // dim
 778       "P\'", //name
 779       (complex double []) {1, 1, 1, 1} // m
 780     },
 781     {
 782       1, // dim
 783       "R\'\'", //name
 784       (complex double []) {1, 1, -1, -1} // m
 785     },
 786     {
 787       1, // dim
 788       "R\'", //name
 789       (complex double []) {1, -1, -1, 1} // m
 790     },
 791   } // end of irreps
 792 };
 793
 794 const qpms_finite_group_t QPMS_FINITE_GROUP_y_and_z_flip = {
 795   "y_and_z_flip", // name
 796   4, // order
 797   0, // idi
 798   (qpms_gmi_t[]) { // mt
 799     0, 1, 2, 3,
 800     1, 0, 3, 2,
 801     2, 3, 0, 1,
 802     3, 2, 1, 0,
 803   },
 804   (qpms_gmi_t[]) { // invi
 805     0, 1, 2, 3
 806   },
 807   (qpms_gmi_t[]) {1, 3}, // gens
 808   2, // ngens
 809   (qpms_permutation_t[]){ // permrep
 810     "(3)",
 811     "(3)(0 1)",
 812     "(0 1)(2 3)",
 813     "(2 3)",
 814   },
 815   NULL, // elemlabels
 816   4, // permrep_nelem
 817   (qpms_irot3_t[]) { // rep3d
 818    {{1.0+0.0*I, 0.0+0.0*I}, 1},
 819    {{0.0+0.0*I, 1.0+0.0*I}, -1},
 820    {{0.0+0.0*I, 0.0+1.0*I}, 1},
 821    {{0.0+1.0*I, 0.0+0.0*I}, -1},
 822   },
 823   4, // nirreps
 824   (struct qpms_finite_group_irrep_t[]) { // irreps
 825     {
 826       1, // dim
 827       "P\'\'", //name
 828       (complex double []) {1, -1, 1, -1} // m
 829     },
 830     {
 831       1, // dim
 832       "P\'", //name
 833       (complex double []) {1, 1, 1, 1} // m
 834     },
 835     {
 836       1, // dim
 837       "R\'\'", //name
 838       (complex double []) {1, 1, -1, -1} // m
 839     },
 840     {
 841       1, // dim
 842       "R\'", //name
 843       (complex double []) {1, -1, -1, 1} // m
 844     },
 845   } // end of irreps
 846 };
 847
 848