def test_look_ahead():
# Section 3.2 [Test Example] Example (d) from [2]
F, a, b, c = free_group("a, b, c")
f = FpGroup(F, [
a**11, b**5, c**4,
(a * c)**3, b**2 * c**-1 * b**-1 * c, a**4 * b**-1 * a**-1 * b
])
H = [c, b, c**2]
table0 = [[1, 2, 0, 0, 0, 0], [3, 0, 4, 5, 6, 7], [0, 8, 9, 10, 11, 12],
[5, 1, 10, 13, 14, 15], [16, 5, 16, 1, 17, 18],
[4, 3, 1, 8, 19, 20], [12, 21, 22, 23, 24, 1],
[25, 26, 27, 28, 1, 24], [2, 10, 5, 16, 22, 28],
[10, 13, 13, 2, 29, 30]]
CosetTable.max_stack_size = 10
C_c = coset_enumeration_c(f, H)
C_c.compress()
C_c.standardize()
assert C_c.table[:10] == table0
def test_look_ahead():
# Section 3.2 [Test Example] Example (d) from [2]
F, a, b, c = free_group("a, b, c")
f = FpGroup(F, [a**11, b**5, c**4, (a*c)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b])
H = [c, b, c**2]
table0 = [[1, 2, 0, 0, 0, 0],
[3, 0, 4, 5, 6, 7],
[0, 8, 9, 10, 11, 12],
[5, 1, 10, 13, 14, 15],
[16, 5, 16, 1, 17, 18],
[4, 3, 1, 8, 19, 20],
[12, 21, 22, 23, 24, 1],
[25, 26, 27, 28, 1, 24],
[2, 10, 5, 16, 22, 28],
[10, 13, 13, 2, 29, 30]]
CosetTable.max_stack_size = 10
C_c = coset_enumeration_c(f, H)
C_c.compress(); C_c.standardize()
assert C_c.table[: 10] == table0
def test_coset_enumeration():
# this test function contains the combined tests for the two strategies
# i.e. HLT and Felsch strategies.
# Example 5.1 from [1]
F, x, y = free_group("x, y")
f = FpGroup(F, [x**3, y**3, x**-1 * y**-1 * x * y])
C_r = coset_enumeration_r(f, [x])
C_r.compress()
C_r.standardize()
C_c = coset_enumeration_c(f, [x])
C_c.compress()
C_c.standardize()
table1 = [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
assert C_r.table == table1
assert C_c.table == table1
# E₁ from [2] Pg. 474
F, r, s, t = free_group("r, s, t")
E1 = FpGroup(
F,
[t**-1 * r * t * r**-2, r**-1 * s * r * s**-2, s**-1 * t * s * t**-2])
C_r = coset_enumeration_r(E1, [])
C_r.compress()
C_c = coset_enumeration_c(E1, [])
C_c.compress()
table2 = [[0, 0, 0, 0, 0, 0]]
assert C_r.table == table2
# test for issue #11449
assert C_c.table == table2
# Cox group from [2] Pg. 474
F, a, b = free_group("a, b")
Cox = FpGroup(F,
[a**6, b**6, (a * b)**2, (a**2 * b**2)**2, (a**3 * b**3)**5])
C_r = coset_enumeration_r(Cox, [a])
C_r.compress()
C_r.standardize()
C_c = coset_enumeration_c(Cox, [a])
C_c.compress()
C_c.standardize()
table3 = [[0, 0, 1, 2], [2, 3, 4, 0], [5, 1, 0, 6], [1, 7, 8, 9],
[9, 10, 11, 1], [12, 2, 9, 13], [14, 9, 2, 11], [3, 12, 15, 16],
[16, 17, 18, 3], [6, 4, 3, 5], [4, 19, 20, 21], [21, 22, 6, 4],
[7, 5, 23, 24], [25, 23, 5, 18], [19, 6, 22,
26], [24, 27, 28, 7],
[29, 8, 7, 30], [8, 31, 32, 33], [33, 34, 13, 8],
[10, 14, 35, 35], [35, 36, 37, 10], [30, 11, 10, 29],
[11, 38, 39, 14], [13, 39, 38, 12], [40, 15, 12, 41],
[42, 13, 34, 43], [44, 35, 14, 45], [15, 46, 47, 34],
[34, 48, 49, 15], [50, 16, 21, 51], [52, 21, 16, 49],
[17, 50, 53, 54], [54, 55, 56, 17], [41, 18, 17, 40],
[18, 28, 27, 25], [26, 20, 19, 19], [20, 57, 58, 59],
[59, 60, 51, 20], [22, 52, 61, 23], [23, 62, 63, 22],
[64, 24, 33, 65], [48, 33, 24, 61], [62, 25, 54, 66],
[67, 54, 25, 68], [57, 26, 59, 69], [70, 59, 26, 63],
[27, 64, 71, 72], [72, 73, 68, 27], [28, 41, 74, 75],
[75, 76, 30, 28], [31, 29, 77, 78], [79, 77, 29, 37],
[38, 30, 76, 80], [78, 81, 82, 31], [43, 32, 31, 42],
[32, 83, 84, 85], [85, 86, 65, 32], [36, 44, 87, 88],
[88, 89, 90, 36], [45, 37, 36, 44], [37, 82, 81, 79],
[80, 74, 41, 38], [39, 42, 91, 92], [92, 93, 45, 39],
[46, 40, 94, 95], [96, 94, 40, 56], [97, 91, 42, 82],
[83, 43, 98, 99], [100, 98, 43, 47], [101, 87, 44, 90],
[82, 45, 93, 97], [95, 102, 103, 46], [104, 47, 46, 105],
[47, 106, 107, 100], [61, 108, 109, 48], [105, 49, 48, 104],
[49, 110, 111, 52], [51, 111, 110, 50], [112, 53, 50, 113],
[114, 51, 60, 115], [116, 61, 52, 117], [53, 118, 119, 60],
[60, 70, 66, 53], [55, 67, 120, 121], [121, 122, 123, 55],
[113, 56, 55, 112], [56, 103, 102, 96], [69, 124, 125, 57],
[115, 58, 57, 114], [58, 126, 127, 128], [128, 128, 69, 58],
[66, 129, 130, 62], [117, 63, 62, 116], [63, 125, 124, 70],
[65, 109, 108, 64], [131, 71, 64, 132], [133, 65, 86, 134],
[135, 66, 70, 136], [68, 130, 129, 67], [137, 120, 67, 138],
[132, 68, 73, 131], [139, 69, 128, 140], [71, 141, 142, 86],
[86, 143, 144, 71], [145, 72, 75, 146], [147, 75, 72, 144],
[73, 145, 148, 120], [120, 149, 150, 73], [74, 151, 152, 94],
[94, 153, 146, 74], [76, 147, 154, 77], [77, 155, 156, 76],
[157, 78, 85, 158], [143, 85, 78, 154], [155, 79, 88, 159],
[160, 88, 79, 161], [151, 80, 92, 162], [163, 92, 80, 156],
[81, 157, 164, 165], [165, 166, 161, 81], [99, 107, 106, 83],
[134, 84, 83, 133], [84, 167, 168, 169], [169, 170, 158, 84],
[87, 171, 172, 93], [93, 163, 159, 87], [89, 160, 173, 174],
[174, 175, 176, 89], [90, 90, 89, 101], [91, 177, 178, 98],
[98, 179, 162, 91], [180, 95, 100, 181], [179, 100, 95, 152],
[153, 96, 121, 148], [182, 121, 96, 183], [177, 97, 165, 184],
[185, 165, 97, 172], [186, 99, 169, 187], [188, 169, 99, 178],
[171, 101, 174, 189], [190, 174, 101, 176], [102, 180, 191, 192],
[192, 193, 183, 102], [103, 113, 194, 195], [195, 196, 105, 103],
[106, 104, 197, 198], [199, 197, 104, 109], [110, 105, 196, 200],
[198, 201, 133, 106], [107, 186, 202, 203], [203, 204, 181, 107],
[108, 116, 205, 206], [206, 207, 132, 108], [109, 133, 201, 199],
[200, 194, 113, 110], [111, 114, 208, 209], [209, 210, 117, 111],
[118, 112, 211, 212], [213, 211, 112, 123], [214, 208, 114, 125],
[126, 115, 215, 216], [217, 215, 115, 119], [218, 205, 116, 130],
[125, 117, 210, 214], [212, 219, 220, 118], [136, 119, 118, 135],
[119, 221, 222, 217], [122, 182, 223, 224], [224, 225, 226, 122],
[138, 123, 122, 137], [123, 220, 219, 213], [124, 139, 227, 228],
[228, 229, 136, 124], [216, 222, 221, 126], [140, 127, 126, 139],
[127, 230, 231, 232], [232, 233, 140, 127], [129, 135, 234, 235],
[235, 236, 138, 129], [130, 132, 207, 218], [141, 131, 237, 238],
[239, 237, 131, 150], [167, 134, 240, 241], [242, 240, 134, 142],
[243, 234, 135, 220], [221, 136, 229, 244], [149, 137, 245, 246],
[247, 245, 137, 226], [220, 138, 236, 243], [244, 227, 139, 221],
[230, 140, 233, 248], [238, 249, 250, 141], [251, 142, 141, 252],
[142, 253, 254, 242], [154, 255, 256, 143], [252, 144, 143, 251],
[144, 257, 258, 147], [146, 258, 257, 145], [259, 148, 145, 260],
[261, 146, 153, 262], [263, 154, 147, 264], [148, 265, 266, 153],
[246, 267, 268, 149], [260, 150, 149, 259], [150, 250, 249, 239],
[162, 269, 270, 151], [262, 152, 151, 261], [152, 271, 272, 179],
[159, 273, 274, 155], [264, 156, 155, 263], [156, 270, 269, 163],
[158, 256, 255, 157], [275, 164, 157, 276], [277, 158, 170, 278],
[279, 159, 163, 280], [161, 274, 273, 160], [281, 173, 160, 282],
[276, 161, 166, 275], [283, 162, 179, 284], [164, 285, 286, 170],
[170, 188, 184, 164], [166, 185, 189, 173], [173, 287, 288, 166],
[241, 254, 253, 167], [278, 168, 167, 277], [168, 289, 290, 291],
[291, 292, 187, 168], [189, 293, 294, 171], [280, 172, 171, 279],
[172, 295, 296, 185], [175, 190, 297, 297], [297, 298, 299, 175],
[282, 176, 175, 281], [176, 294, 293, 190], [184, 296, 295, 177],
[284, 178, 177, 283], [178, 300, 301, 188], [181, 272, 271, 180],
[302, 191, 180, 303], [304, 181, 204, 305], [183, 266, 265, 182],
[306, 223, 182, 307], [303, 183, 193, 302], [308, 184, 188, 309],
[310, 189, 185, 311], [187, 301, 300, 186], [305, 202, 186, 304],
[312, 187, 292, 313], [314, 297, 190, 315], [191, 316, 317, 204],
[204, 318, 319, 191], [320, 192, 195, 321], [322, 195, 192, 319],
[193, 320, 323, 223], [223, 324, 325, 193], [194, 326, 327, 211],
[211, 328, 321, 194], [196, 322, 329, 197], [197, 330, 331, 196],
[332, 198, 203, 333], [318, 203, 198, 329], [330, 199, 206, 334],
[335, 206, 199, 336], [326, 200, 209, 337], [338, 209, 200, 331],
[201, 332, 339, 240], [240, 340, 336, 201], [202, 341, 342, 292],
[292, 343, 333, 202], [205, 344, 345, 210], [210, 338, 334, 205],
[207, 335, 346, 237], [237, 347, 348, 207], [208, 349, 350, 215],
[215, 351, 337, 208], [352, 212, 217, 353], [351, 217, 212, 327],
[328, 213, 224, 323], [354, 224, 213, 355], [349, 214, 228, 356],
[357, 228, 214, 345], [358, 216, 232, 359], [360, 232, 216, 350],
[344, 218, 235, 361], [362, 235, 218, 348], [219, 352, 363, 364],
[364, 365, 355, 219], [222, 358, 366, 367], [367, 368, 353, 222],
[225, 354, 369, 370], [370, 371, 372, 225], [307, 226, 225, 306],
[226, 268, 267, 247], [227, 373, 374, 233], [233, 360, 356, 227],
[229, 357, 361, 234], [234, 375, 376, 229], [248, 231, 230, 230],
[231, 377, 378, 379], [379, 380, 359, 231], [236, 362, 381, 245],
[245, 382, 383, 236], [384, 238, 242, 385], [340, 242, 238, 346],
[347, 239, 246, 381], [386, 246, 239, 387], [388, 241, 291, 389],
[343, 291, 241, 339], [375, 243, 364, 390], [391, 364, 243, 383],
[373, 244, 367, 392], [393, 367, 244, 376], [382, 247, 370, 394],
[395, 370, 247, 396], [377, 248, 379, 397], [398, 379, 248, 374],
[249, 384, 399, 400], [400, 401, 387, 249], [250, 260, 402, 403],
[403, 404, 252, 250], [253, 251, 405, 406], [407, 405, 251, 256],
[257, 252, 404, 408], [406, 409, 277, 253], [254, 388, 410, 411],
[411, 412, 385, 254], [255, 263, 413, 414], [414, 415, 276, 255],
[256, 277, 409, 407], [408, 402, 260, 257], [258, 261, 416, 417],
[417, 418, 264, 258], [265, 259, 419, 420], [421, 419, 259, 268],
[422, 416, 261, 270], [271, 262, 423, 424], [425, 423, 262, 266],
[426, 413, 263, 274], [270, 264, 418, 422], [420, 427, 307, 265],
[266, 303, 428, 425], [267, 386, 429, 430], [430, 431, 396, 267],
[268, 307, 427, 421], [269, 283, 432, 433], [433, 434, 280, 269],
[424, 428, 303, 271], [272, 304, 435, 436], [436, 437, 284, 272],
[273, 279, 438, 439], [439, 440, 282, 273], [274, 276, 415, 426],
[285, 275, 441, 442], [443, 441, 275, 288], [289, 278, 444, 445],
[446, 444, 278, 286], [447, 438, 279, 294], [295, 280, 434, 448],
[287, 281, 449, 450], [451, 449, 281, 299], [294, 282, 440, 447],
[448, 432, 283, 295], [300, 284, 437, 452], [442, 453, 454, 285],
[309, 286, 285, 308], [286, 455, 456, 446], [450, 457, 458, 287],
[311, 288, 287, 310], [288, 454, 453, 443], [445, 456, 455, 289],
[313, 290, 289, 312], [290, 459, 460, 461], [461, 462, 389, 290],
[293, 310, 463, 464], [464, 465, 315, 293], [296, 308, 466, 467],
[467, 468, 311, 296], [298, 314, 469, 470], [470, 471, 472, 298],
[315, 299, 298, 314], [299, 458, 457, 451], [452, 435, 304, 300],
[301, 312, 473, 474], [474, 475, 309, 301], [316, 302, 476, 477],
[478, 476, 302, 325], [341, 305, 479, 480], [481, 479, 305, 317],
[324, 306, 482, 483], [484, 482, 306, 372], [485, 466, 308, 454],
[455, 309, 475, 486], [487, 463, 310, 458], [454, 311, 468, 485],
[486, 473, 312, 455], [459, 313, 488, 489], [490, 488, 313, 342],
[491, 469, 314, 472], [458, 315, 465, 487], [477, 492, 485, 316],
[463, 317, 316, 468], [317, 487, 493, 481], [329, 447, 464, 318],
[468, 319, 318, 463], [319, 467, 448, 322], [321, 448, 467, 320],
[475, 323, 320, 466], [432, 321, 328, 437], [438, 329, 322, 434],
[323, 474, 452, 328], [483, 494, 486, 324], [466, 325, 324, 475],
[325, 485, 492, 478], [337, 422, 433, 326], [437, 327, 326, 432],
[327, 436, 424, 351], [334, 426, 439, 330], [434, 331, 330, 438],
[331, 433, 422, 338], [333, 464, 447, 332], [449, 339, 332, 440],
[465, 333, 343, 469], [413, 334, 338, 418], [336, 439, 426, 335],
[441, 346, 335, 415], [440, 336, 340, 449], [416, 337, 351, 423],
[339, 451, 470, 343], [346, 443, 450, 340], [480, 493, 487, 341],
[469, 342, 341, 465], [342, 491, 495, 490], [361, 407, 414, 344],
[418, 345, 344, 413], [345, 417, 408, 357], [381, 446, 442, 347],
[415, 348, 347, 441], [348, 414, 407, 362], [356, 408, 417, 349],
[423, 350, 349, 416], [350, 425, 420, 360], [353, 424, 436, 352],
[479, 363, 352, 435], [428, 353, 368, 476], [355, 452, 474, 354],
[488, 369, 354, 473], [435, 355, 365, 479], [402, 356, 360, 419],
[405, 361, 357, 404], [359, 420, 425, 358], [476, 366, 358, 428],
[427, 359, 380, 482], [444, 381, 362, 409], [363, 481, 477, 368],
[368, 393, 390, 363], [365, 391, 394, 369], [369, 490, 480, 365],
[366, 478, 483, 380], [380, 398, 392, 366], [371, 395, 496, 497],
[497, 498, 489, 371], [473, 372, 371, 488], [372, 486, 494, 484],
[392, 400, 403, 373], [419, 374, 373, 402], [374, 421, 430, 398],
[390, 411, 406, 375], [404, 376, 375, 405], [376, 403, 400, 393],
[397, 430, 421, 377], [482, 378, 377, 427], [378, 484, 497, 499],
[499, 499, 397, 378], [394, 461, 445, 382], [409, 383, 382, 444],
[383, 406, 411, 391], [385, 450, 443, 384], [492, 399, 384, 453],
[457, 385, 412, 493], [387, 442, 446, 386], [494, 429, 386, 456],
[453, 387, 401, 492], [389, 470, 451, 388], [493, 410, 388, 457],
[471, 389, 462, 495], [412, 390, 393, 399], [462, 394, 391, 410],
[401, 392, 398, 429], [396, 445, 461, 395], [498, 496, 395, 460],
[456, 396, 431, 494], [431, 397, 499, 496], [399, 477, 481, 412],
[429, 483, 478, 401], [410, 480, 490, 462], [496, 497, 484, 431],
[489, 495, 491, 459], [495, 460, 459, 471], [460, 489, 498, 498],
[472, 472, 471, 491]]
C_r.table == table3
C_c.table == table3
# Group denoted by B₂,₄ from [2] Pg. 474
F, a, b = free_group("a, b")
B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \
(a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4])
C_r = coset_enumeration_r(B_2_4, [a])
C_c = coset_enumeration_c(B_2_4, [a])
index_r = 0
for i in range(len(C_r.p)):
if C_r.p[i] == i:
index_r += 1
assert index_r == 1024
index_c = 0
for i in range(len(C_c.p)):
if C_c.p[i] == i:
index_c += 1
assert index_c == 1024
# trivial Macdonald group G(2,2) from [2] Pg. 480
M = FpGroup(F, [
b**-1 * a**-1 * b * a * b**-1 * a * b * a**-2,
a**-1 * b**-1 * a * b * a**-1 * b * a * b**-2
])
C_r = coset_enumeration_r(M, [a])
C_r.compress()
C_r.standardize()
C_c = coset_enumeration_c(M, [a])
C_c.compress()
C_c.standardize()
table4 = [[0, 0, 0, 0]]
assert C_r.table == table4
assert C_c.table == table4
def test_coset_enumeration():
# this test function contains the combined tests for the two strategies
# i.e. HLT and Felsch strategies.
# Example 5.1 from [1]
F, x, y = free_group("x, y")
f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y])
C_r = coset_enumeration_r(f, [x])
C_r.compress(); C_r.standardize()
C_c = coset_enumeration_c(f, [x])
C_c.compress(); C_c.standardize()
table1 = [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
assert C_r.table == table1
assert C_c.table == table1
# E₁ from [2] Pg. 474
F, r, s, t = free_group("r, s, t")
E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2])
C_r = coset_enumeration_r(E1, [r])
C_r.compress(); C_r.standardize()
C_c = coset_enumeration_c(E1, [r])
C_c.compress(); C_c.standardize()
table2 = [[0, 0, 0, 0, 0, 0]]
assert C_r.table == table2
assert C_c.table == table2
# Cox group from [2] Pg. 474
F, a, b = free_group("a, b")
Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5])
C_r = coset_enumeration_r(Cox, [a])
C_r.compress(); C_r.standardize()
C_c = coset_enumeration_c(Cox, [a])
C_c.compress(); C_c.standardize()
table3 = [[0, 0, 1, 2],
[2, 3, 4, 0],
[5, 1, 0, 6],
[1, 7, 8, 9],
[9, 10, 11, 1],
[12, 2, 9, 13],
[14, 9, 2, 11],
[3, 12, 15, 16],
[16, 17, 18, 3],
[6, 4, 3, 5],
[4, 19, 20, 21],
[21, 22, 6, 4],
[7, 5, 23, 24],
[25, 23, 5, 18],
[19, 6, 22, 26],
[24, 27, 28, 7],
[29, 8, 7, 30],
[8, 31, 32, 33],
[33, 34, 13, 8],
[10, 14, 35, 35],
[35, 36, 37, 10],
[30, 11, 10, 29],
[11, 38, 39, 14],
[13, 39, 38, 12],
[40, 15, 12, 41],
[42, 13, 34, 43],
[44, 35, 14, 45],
[15, 46, 47, 34],
[34, 48, 49, 15],
[50, 16, 21, 51],
[52, 21, 16, 49],
[17, 50, 53, 54],
[54, 55, 56, 17],
[41, 18, 17, 40],
[18, 28, 27, 25],
[26, 20, 19, 19],
[20, 57, 58, 59],
[59, 60, 51, 20],
[22, 52, 61, 23],
[23, 62, 63, 22],
[64, 24, 33, 65],
[48, 33, 24, 61],
[62, 25, 54, 66],
[67, 54, 25, 68],
[57, 26, 59, 69],
[70, 59, 26, 63],
[27, 64, 71, 72],
[72, 73, 68, 27],
[28, 41, 74, 75],
[75, 76, 30, 28],
[31, 29, 77, 78],
[79, 77, 29, 37],
[38, 30, 76, 80],
[78, 81, 82, 31],
[43, 32, 31, 42],
[32, 83, 84, 85],
[85, 86, 65, 32],
[36, 44, 87, 88],
[88, 89, 90, 36],
[45, 37, 36, 44],
[37, 82, 81, 79],
[80, 74, 41, 38],
[39, 42, 91, 92],
[92, 93, 45, 39],
[46, 40, 94, 95],
[96, 94, 40, 56],
[97, 91, 42, 82],
[83, 43, 98, 99],
[100, 98, 43, 47],
[101, 87, 44, 90],
[82, 45, 93, 97],
[95, 102, 103, 46],
[104, 47, 46, 105],
[47, 106, 107, 100],
[61, 108, 109, 48],
[105, 49, 48, 104],
[49, 110, 111, 52],
[51, 111, 110, 50],
[112, 53, 50, 113],
[114, 51, 60, 115],
[116, 61, 52, 117],
[53, 118, 119, 60],
[60, 70, 66, 53],
[55, 67, 120, 121],
[121, 122, 123, 55],
[113, 56, 55, 112],
[56, 103, 102, 96],
[69, 124, 125, 57],
[115, 58, 57, 114],
[58, 126, 127, 128],
[128, 128, 69, 58],
[66, 129, 130, 62],
[117, 63, 62, 116],
[63, 125, 124, 70],
[65, 109, 108, 64],
[131, 71, 64, 132],
[133, 65, 86, 134],
[135, 66, 70, 136],
[68, 130, 129, 67],
[137, 120, 67, 138],
[132, 68, 73, 131],
[139, 69, 128, 140],
[71, 141, 142, 86],
[86, 143, 144, 71],
[145, 72, 75, 146],
[147, 75, 72, 144],
[73, 145, 148, 120],
[120, 149, 150, 73],
[74, 151, 152, 94],
[94, 153, 146, 74],
[76, 147, 154, 77],
[77, 155, 156, 76],
[157, 78, 85, 158],
[143, 85, 78, 154],
[155, 79, 88, 159],
[160, 88, 79, 161],
[151, 80, 92, 162],
[163, 92, 80, 156],
[81, 157, 164, 165],
[165, 166, 161, 81],
[99, 107, 106, 83],
[134, 84, 83, 133],
[84, 167, 168, 169],
[169, 170, 158, 84],
[87, 171, 172, 93],
[93, 163, 159, 87],
[89, 160, 173, 174],
[174, 175, 176, 89],
[90, 90, 89, 101],
[91, 177, 178, 98],
[98, 179, 162, 91],
[180, 95, 100, 181],
[179, 100, 95, 152],
[153, 96, 121, 148],
[182, 121, 96, 183],
[177, 97, 165, 184],
[185, 165, 97, 172],
[186, 99, 169, 187],
[188, 169, 99, 178],
[171, 101, 174, 189],
[190, 174, 101, 176],
[102, 180, 191, 192],
[192, 193, 183, 102],
[103, 113, 194, 195],
[195, 196, 105, 103],
[106, 104, 197, 198],
[199, 197, 104, 109],
[110, 105, 196, 200],
[198, 201, 133, 106],
[107, 186, 202, 203],
[203, 204, 181, 107],
[108, 116, 205, 206],
[206, 207, 132, 108],
[109, 133, 201, 199],
[200, 194, 113, 110],
[111, 114, 208, 209],
[209, 210, 117, 111],
[118, 112, 211, 212],
[213, 211, 112, 123],
[214, 208, 114, 125],
[126, 115, 215, 216],
[217, 215, 115, 119],
[218, 205, 116, 130],
[125, 117, 210, 214],
[212, 219, 220, 118],
[136, 119, 118, 135],
[119, 221, 222, 217],
[122, 182, 223, 224],
[224, 225, 226, 122],
[138, 123, 122, 137],
[123, 220, 219, 213],
[124, 139, 227, 228],
[228, 229, 136, 124],
[216, 222, 221, 126],
[140, 127, 126, 139],
[127, 230, 231, 232],
[232, 233, 140, 127],
[129, 135, 234, 235],
[235, 236, 138, 129],
[130, 132, 207, 218],
[141, 131, 237, 238],
[239, 237, 131, 150],
[167, 134, 240, 241],
[242, 240, 134, 142],
[243, 234, 135, 220],
[221, 136, 229, 244],
[149, 137, 245, 246],
[247, 245, 137, 226],
[220, 138, 236, 243],
[244, 227, 139, 221],
[230, 140, 233, 248],
[238, 249, 250, 141],
[251, 142, 141, 252],
[142, 253, 254, 242],
[154, 255, 256, 143],
[252, 144, 143, 251],
[144, 257, 258, 147],
[146, 258, 257, 145],
[259, 148, 145, 260],
[261, 146, 153, 262],
[263, 154, 147, 264],
[148, 265, 266, 153],
[246, 267, 268, 149],
[260, 150, 149, 259],
[150, 250, 249, 239],
[162, 269, 270, 151],
[262, 152, 151, 261],
[152, 271, 272, 179],
[159, 273, 274, 155],
[264, 156, 155, 263],
[156, 270, 269, 163],
[158, 256, 255, 157],
[275, 164, 157, 276],
[277, 158, 170, 278],
[279, 159, 163, 280],
[161, 274, 273, 160],
[281, 173, 160, 282],
[276, 161, 166, 275],
[283, 162, 179, 284],
[164, 285, 286, 170],
[170, 188, 184, 164],
[166, 185, 189, 173],
[173, 287, 288, 166],
[241, 254, 253, 167],
[278, 168, 167, 277],
[168, 289, 290, 291],
[291, 292, 187, 168],
[189, 293, 294, 171],
[280, 172, 171, 279],
[172, 295, 296, 185],
[175, 190, 297, 297],
[297, 298, 299, 175],
[282, 176, 175, 281],
[176, 294, 293, 190],
[184, 296, 295, 177],
[284, 178, 177, 283],
[178, 300, 301, 188],
[181, 272, 271, 180],
[302, 191, 180, 303],
[304, 181, 204, 305],
[183, 266, 265, 182],
[306, 223, 182, 307],
[303, 183, 193, 302],
[308, 184, 188, 309],
[310, 189, 185, 311],
[187, 301, 300, 186],
[305, 202, 186, 304],
[312, 187, 292, 313],
[314, 297, 190, 315],
[191, 316, 317, 204],
[204, 318, 319, 191],
[320, 192, 195, 321],
[322, 195, 192, 319],
[193, 320, 323, 223],
[223, 324, 325, 193],
[194, 326, 327, 211],
[211, 328, 321, 194],
[196, 322, 329, 197],
[197, 330, 331, 196],
[332, 198, 203, 333],
[318, 203, 198, 329],
[330, 199, 206, 334],
[335, 206, 199, 336],
[326, 200, 209, 337],
[338, 209, 200, 331],
[201, 332, 339, 240],
[240, 340, 336, 201],
[202, 341, 342, 292],
[292, 343, 333, 202],
[205, 344, 345, 210],
[210, 338, 334, 205],
[207, 335, 346, 237],
[237, 347, 348, 207],
[208, 349, 350, 215],
[215, 351, 337, 208],
[352, 212, 217, 353],
[351, 217, 212, 327],
[328, 213, 224, 323],
[354, 224, 213, 355],
[349, 214, 228, 356],
[357, 228, 214, 345],
[358, 216, 232, 359],
[360, 232, 216, 350],
[344, 218, 235, 361],
[362, 235, 218, 348],
[219, 352, 363, 364],
[364, 365, 355, 219],
[222, 358, 366, 367],
[367, 368, 353, 222],
[225, 354, 369, 370],
[370, 371, 372, 225],
[307, 226, 225, 306],
[226, 268, 267, 247],
[227, 373, 374, 233],
[233, 360, 356, 227],
[229, 357, 361, 234],
[234, 375, 376, 229],
[248, 231, 230, 230],
[231, 377, 378, 379],
[379, 380, 359, 231],
[236, 362, 381, 245],
[245, 382, 383, 236],
[384, 238, 242, 385],
[340, 242, 238, 346],
[347, 239, 246, 381],
[386, 246, 239, 387],
[388, 241, 291, 389],
[343, 291, 241, 339],
[375, 243, 364, 390],
[391, 364, 243, 383],
[373, 244, 367, 392],
[393, 367, 244, 376],
[382, 247, 370, 394],
[395, 370, 247, 396],
[377, 248, 379, 397],
[398, 379, 248, 374],
[249, 384, 399, 400],
[400, 401, 387, 249],
[250, 260, 402, 403],
[403, 404, 252, 250],
[253, 251, 405, 406],
[407, 405, 251, 256],
[257, 252, 404, 408],
[406, 409, 277, 253],
[254, 388, 410, 411],
[411, 412, 385, 254],
[255, 263, 413, 414],
[414, 415, 276, 255],
[256, 277, 409, 407],
[408, 402, 260, 257],
[258, 261, 416, 417],
[417, 418, 264, 258],
[265, 259, 419, 420],
[421, 419, 259, 268],
[422, 416, 261, 270],
[271, 262, 423, 424],
[425, 423, 262, 266],
[426, 413, 263, 274],
[270, 264, 418, 422],
[420, 427, 307, 265],
[266, 303, 428, 425],
[267, 386, 429, 430],
[430, 431, 396, 267],
[268, 307, 427, 421],
[269, 283, 432, 433],
[433, 434, 280, 269],
[424, 428, 303, 271],
[272, 304, 435, 436],
[436, 437, 284, 272],
[273, 279, 438, 439],
[439, 440, 282, 273],
[274, 276, 415, 426],
[285, 275, 441, 442],
[443, 441, 275, 288],
[289, 278, 444, 445],
[446, 444, 278, 286],
[447, 438, 279, 294],
[295, 280, 434, 448],
[287, 281, 449, 450],
[451, 449, 281, 299],
[294, 282, 440, 447],
[448, 432, 283, 295],
[300, 284, 437, 452],
[442, 453, 454, 285],
[309, 286, 285, 308],
[286, 455, 456, 446],
[450, 457, 458, 287],
[311, 288, 287, 310],
[288, 454, 453, 443],
[445, 456, 455, 289],
[313, 290, 289, 312],
[290, 459, 460, 461],
[461, 462, 389, 290],
[293, 310, 463, 464],
[464, 465, 315, 293],
[296, 308, 466, 467],
[467, 468, 311, 296],
[298, 314, 469, 470],
[470, 471, 472, 298],
[315, 299, 298, 314],
[299, 458, 457, 451],
[452, 435, 304, 300],
[301, 312, 473, 474],
[474, 475, 309, 301],
[316, 302, 476, 477],
[478, 476, 302, 325],
[341, 305, 479, 480],
[481, 479, 305, 317],
[324, 306, 482, 483],
[484, 482, 306, 372],
[485, 466, 308, 454],
[455, 309, 475, 486],
[487, 463, 310, 458],
[454, 311, 468, 485],
[486, 473, 312, 455],
[459, 313, 488, 489],
[490, 488, 313, 342],
[491, 469, 314, 472],
[458, 315, 465, 487],
[477, 492, 485, 316],
[463, 317, 316, 468],
[317, 487, 493, 481],
[329, 447, 464, 318],
[468, 319, 318, 463],
[319, 467, 448, 322],
[321, 448, 467, 320],
[475, 323, 320, 466],
[432, 321, 328, 437],
[438, 329, 322, 434],
[323, 474, 452, 328],
[483, 494, 486, 324],
[466, 325, 324, 475],
[325, 485, 492, 478],
[337, 422, 433, 326],
[437, 327, 326, 432],
[327, 436, 424, 351],
[334, 426, 439, 330],
[434, 331, 330, 438],
[331, 433, 422, 338],
[333, 464, 447, 332],
[449, 339, 332, 440],
[465, 333, 343, 469],
[413, 334, 338, 418],
[336, 439, 426, 335],
[441, 346, 335, 415],
[440, 336, 340, 449],
[416, 337, 351, 423],
[339, 451, 470, 343],
[346, 443, 450, 340],
[480, 493, 487, 341],
[469, 342, 341, 465],
[342, 491, 495, 490],
[361, 407, 414, 344],
[418, 345, 344, 413],
[345, 417, 408, 357],
[381, 446, 442, 347],
[415, 348, 347, 441],
[348, 414, 407, 362],
[356, 408, 417, 349],
[423, 350, 349, 416],
[350, 425, 420, 360],
[353, 424, 436, 352],
[479, 363, 352, 435],
[428, 353, 368, 476],
[355, 452, 474, 354],
[488, 369, 354, 473],
[435, 355, 365, 479],
[402, 356, 360, 419],
[405, 361, 357, 404],
[359, 420, 425, 358],
[476, 366, 358, 428],
[427, 359, 380, 482],
[444, 381, 362, 409],
[363, 481, 477, 368],
[368, 393, 390, 363],
[365, 391, 394, 369],
[369, 490, 480, 365],
[366, 478, 483, 380],
[380, 398, 392, 366],
[371, 395, 496, 497],
[497, 498, 489, 371],
[473, 372, 371, 488],
[372, 486, 494, 484],
[392, 400, 403, 373],
[419, 374, 373, 402],
[374, 421, 430, 398],
[390, 411, 406, 375],
[404, 376, 375, 405],
[376, 403, 400, 393],
[397, 430, 421, 377],
[482, 378, 377, 427],
[378, 484, 497, 499],
[499, 499, 397, 378],
[394, 461, 445, 382],
[409, 383, 382, 444],
[383, 406, 411, 391],
[385, 450, 443, 384],
[492, 399, 384, 453],
[457, 385, 412, 493],
[387, 442, 446, 386],
[494, 429, 386, 456],
[453, 387, 401, 492],
[389, 470, 451, 388],
[493, 410, 388, 457],
[471, 389, 462, 495],
[412, 390, 393, 399],
[462, 394, 391, 410],
[401, 392, 398, 429],
[396, 445, 461, 395],
[498, 496, 395, 460],
[456, 396, 431, 494],
[431, 397, 499, 496],
[399, 477, 481, 412],
[429, 483, 478, 401],
[410, 480, 490, 462],
[496, 497, 484, 431],
[489, 495, 491, 459],
[495, 460, 459, 471],
[460, 489, 498, 498],
[472, 472, 471, 491]]
C_r.table == table3
C_c.table == table3
# Group denoted by B₂,₄ from [2] Pg. 474
F, a, b = free_group("a, b")
B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \
(a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4])
C_r = coset_enumeration_r(B_2_4, [a])
C_c = coset_enumeration_c(B_2_4, [a])
index_r = 0
for i in range(len(C_r.p)):
if C_r.p[i] == i:
index_r += 1
assert index_r == 1024
index_c = 0
for i in range(len(C_c.p)):
if C_c.p[i] == i:
index_c += 1
assert index_c == 1024
# trivial Macdonald group G(2,2) from [2] Pg. 480
M = FpGroup(F, [b**-1*a**-1*b*a*b**-1*a*b*a**-2, a**-1*b**-1*a*b*a**-1*b*a*b**-2])
C_r = coset_enumeration_r(M, [a])
C_r.compress(); C_r.standardize()
C_c = coset_enumeration_c(M, [a])
C_c.compress(); C_c.standardize()
table4 = [[0, 0, 0, 0]]
assert C_r.table == table4
assert C_c.table == table4
