1N = 0: 2 Permutations of 0: 3 0:, even 4 k = 0: 5 (0 choose 0): 1 6 subset 0: |, even 7 w: 8 0: 4.4006e-01 9 v: 10 w(v): 0.440064 11 wedge j = 0: 12 u: 13 0: -8.7641e-01 14 u wedge w: 15 0: -3.8568e-01 16 x: 17 u wedge w(x): -0.385677 18 (u wedge): 19 0: -8.7641e-01 20 star w: 21 0: 4.4006e-01 22 star star w: 23 0: 4.4006e-01 24N = 1: 25 Permutations of 1: 26 0: 0, even 27 k = 0: 28 (1 choose 0): 1 29 subset 0: | 0, even 30 w: 31 0: -7.1072e-01 32 v: 33 w(v): -0.710721 34 wedge j = 0: 35 u: 36 0: -2.0444e-01 37 u wedge w: 38 0: 1.4530e-01 39 x: 40 u wedge w(x): 0.145303 41 (u wedge): 42 0: -2.0444e-01 43 pullback M = 1: 44 L: 45 0: -8.5393e-01 46 L*: 47 0: 1.0000e+00 48 L*w: 49 0: -7.1072e-01 50 k = 1: 51 (1 choose 1): 1 52 subset 0: 0 |, even 53 w: 54 0: -4.9844e-01 55 v: 56 0: 9.6810e-01 57 w(v): -0.482541 58 wedge j = 0: 59 u: 60 0: -7.1189e-01 61 u wedge w: 62 0: 3.5483e-01 63 x: 64 0: 9.9301e-01 65 u wedge w(x): 0.352354 66 (u wedge): 67 0: -7.1189e-01 68 pullback M = 1: 69 L: 70 0: -7.8645e-01 71 L*: 72 0: -7.8645e-01 73 L*w: 74 0: 3.9200e-01 75 interior product matrix pattern: 76 intV[0,0] = V[0] 77 (w int v_0): 78 0: -4.8254e-01 79 (int v_0): 80 0: 9.6810e-01 81 star w: 82 0: -4.9844e-01 83 star star w: 84 0: -4.9844e-01 85N = 2: 86 Permutations of 2: 87 0: 0 1, even 88 1: 1 0, odd 89 k = 0: 90 (2 choose 0): 1 91 subset 0: | 0 1, even 92 w: 93 0: -6.3889e-01 94 v: 95 w(v): -0.638887 96 wedge j = 0: 97 u: 98 0: 9.7209e-01 99 u wedge w: 100 0: -6.2106e-01 101 x: 102 u wedge w(x): -0.621056 103 (u wedge): 104 0: 9.7209e-01 105 pullback M = 1: 106 L: 107 0: 8.3958e-01 1.5564e-01 108 L*: 109 0: 1.0000e+00 110 L*w: 111 0: -6.3889e-01 112 pullback M = 2: 113 L: 114 0: 8.3173e-01 -7.9185e-01 -5.3832e-01 2.1831e-01 115 L*: 116 0: 1.0000e+00 117 L*w: 118 0: -6.3889e-01 119 k = 1: 120 (2 choose 1): 2 121 subset 0: 0 | 1, even 122 subset 1: 1 | 0, odd 123 w: 124 0: 3.1332e-02 7.4829e-01 125 v: 126 0: -6.7041e-01 -1.2642e-01 127 w(v): -0.115601 128 wedge j = 0: 129 u: 130 0: 5.0537e-01 131 u wedge w: 132 0: 1.5834e-02 3.7816e-01 133 x: 134 0: -1.1516e-01 -5.2579e-02 135 u wedge w(x): -0.0217066 136 (u wedge): 137 0: 5.0537e-01 0.0000e+00 0.0000e+00 5.0537e-01 138 wedge j = 1: 139 u: 140 0: -7.4302e-01 9.1177e-01 141 u wedge w: 142 0: -5.8456e-01 143 x: 144 0: 7.0146e-01 -7.8962e-01 7.3216e-01 2.7505e-01 145 u wedge w(x): -0.450731 146 (u wedge): 147 0: -9.1177e-01 -7.4302e-01 148 pullback M = 1: 149 L: 150 0: -4.0927e-01 7.0128e-01 151 L*: 152 0: -4.0927e-01 7.0128e-01 153 L*w: 154 0: 5.1194e-01 155 negative pullback M = 1: 156 L: 157 0: -4.0927e-01 7.0128e-01 158 L*: 159 0: 7.0128e-01 4.0927e-01 160 L*w: 161 0: 3.2823e-01 162 pullback M = 2: 163 L: 164 0: 8.1629e-01 -7.1931e-01 5.4752e-01 -6.4367e-01 165 L*: 166 0: 8.1629e-01 5.4752e-01 -7.1931e-01 -6.4367e-01 167 L*w: 168 0: 4.3528e-01 -5.0419e-01 169 negative pullback M = 2: 170 L: 171 0: 8.1629e-01 -7.1931e-01 5.4752e-01 -6.4367e-01 172 L*: 173 0: -6.4367e-01 7.1931e-01 -5.4752e-01 8.1629e-01 174 L*w: 175 0: 5.1808e-01 5.9366e-01 176 interior product matrix pattern: 177 intV[0,0] = V[0] 178 intV[0,1] = V[1] 179 (w int v_0): 180 0: -1.1560e-01 181 (int v_0): 182 0: -6.7041e-01 -1.2642e-01 183 star w: 184 0: -7.4829e-01 3.1332e-02 185 star star w: 186 0: -3.1332e-02 -7.4829e-01 187 k = 2: 188 (2 choose 2): 1 189 subset 0: 0 1 |, even 190 w: 191 0: 2.9906e-01 192 v: 193 0: -8.1483e-01 3.6126e-01 1.4164e-01 3.6475e-01 194 w(v): -0.104186 195 wedge j = 0: 196 u: 197 0: 4.1139e-01 198 u wedge w: 199 0: 1.2303e-01 200 x: 201 0: 5.7180e-01 8.9367e-01 -3.7286e-01 2.5011e-01 202 u wedge w(x): 0.0585903 203 (u wedge): 204 0: 4.1139e-01 205 pullback M = 2: 206 L: 207 0: -7.3847e-01 8.5710e-01 7.6242e-01 -2.7071e-02 208 L*: 209 0: -6.3348e-01 210 L*w: 211 0: -1.8945e-01 212 interior product matrix pattern: 213 intV[1,0] = V[0] 214 intV[0,0] = -V[1] 215 (w int v_0): 216 0: -1.0804e-01 -2.4368e-01 217 (int v_0): 218 0: -3.6126e-01 -8.1483e-01 219 star w: 220 0: 2.9906e-01 221 star star w: 222 0: 2.9906e-01 223N = 3: 224 Permutations of 3: 225 0: 0 1 2, even 226 1: 0 2 1, odd 227 2: 1 0 2, odd 228 3: 1 2 0, even 229 4: 2 1 0, odd 230 5: 2 0 1, even 231 k = 0: 232 (3 choose 0): 1 233 subset 0: | 0 1 2, even 234 w: 235 0: -7.8527e-01 236 v: 237 w(v): -0.785273 238 wedge j = 0: 239 u: 240 0: -4.1607e-01 241 u wedge w: 242 0: 3.2673e-01 243 x: 244 u wedge w(x): 0.326726 245 (u wedge): 246 0: -4.1607e-01 247 pullback M = 1: 248 L: 249 0: -1.1162e-02 -5.1602e-01 -5.7893e-02 250 L*: 251 0: 1.0000e+00 252 L*w: 253 0: -7.8527e-01 254 pullback M = 2: 255 L: 256 0: -1.5048e-01 -2.6896e-01 9.3065e-01 -5.1508e-01 3.0863e-01 257 5: 7.3348e-01 258 L*: 259 0: 1.0000e+00 260 L*w: 261 0: -7.8527e-01 262 pullback M = 3: 263 L: 264 0: 9.4925e-01 -5.3134e-01 -6.2828e-01 -4.4492e-01 6.9910e-01 265 5: -2.4978e-01 8.0559e-02 -8.9172e-02 1.9506e-01 266 L*: 267 0: 1.0000e+00 268 L*w: 269 0: -7.8527e-01 270 k = 1: 271 (3 choose 1): 3 272 subset 0: 0 | 1 2, even 273 subset 1: 1 | 0 2, odd 274 subset 2: 2 | 0 1, even 275 w: 276 0: 4.6649e-01 -4.5685e-01 -7.1699e-01 277 v: 278 0: 1.5665e-01 -2.1640e-01 7.2654e-01 279 w(v): -0.348987 280 wedge j = 0: 281 u: 282 0: -5.0009e-01 283 u wedge w: 284 0: -2.3329e-01 2.2847e-01 3.5856e-01 285 x: 286 0: 8.8050e-01 -9.6914e-02 3.4416e-01 287 u wedge w(x): -0.104147 288 (u wedge): 289 0: -5.0009e-01 0.0000e+00 0.0000e+00 0.0000e+00 -5.0009e-01 290 5: 0.0000e+00 0.0000e+00 0.0000e+00 -5.0009e-01 291 wedge j = 1: 292 u: 293 0: 6.2172e-01 -6.2324e-01 -2.7127e-02 294 u wedge w: 295 0: 6.7021e-03 -4.3311e-01 4.3447e-01 296 x: 297 0: 5.8240e-01 -1.8885e-01 -5.5782e-03 5.1936e-02 -6.0479e-01 298 5: 8.5265e-01 299 u wedge w(x): -0.288922 300 (u wedge): 301 0: 6.2324e-01 6.2172e-01 0.0000e+00 2.7127e-02 0.0000e+00 302 5: 6.2172e-01 0.0000e+00 2.7127e-02 -6.2324e-01 303 pullback M = 1: 304 L: 305 0: -3.9946e-01 -4.3518e-01 -3.9815e-01 306 L*: 307 0: -3.9946e-01 -4.3518e-01 -3.9815e-01 308 L*w: 309 0: 2.9794e-01 310 negative pullback M = 1: 311 L: 312 0: -3.9946e-01 -4.3518e-01 -3.9815e-01 313 L*: 314 0: -3.9815e-01 4.3518e-01 -3.9946e-01 315 L*w: 316 0: -9.8141e-02 317 pullback M = 2: 318 L: 319 0: -4.6038e-01 -4.4391e-01 -9.6304e-01 -8.8672e-01 3.5819e-01 320 5: 1.3291e-01 321 L*: 322 0: -4.6038e-01 -9.6304e-01 3.5819e-01 -4.4391e-01 -8.8672e-01 323 5: 1.3291e-01 324 L*w: 325 0: -3.1612e-02 1.0272e-01 326 negative pullback M = 2: 327 L: 328 0: -4.6038e-01 -4.4391e-01 -9.6304e-01 -8.8672e-01 3.5819e-01 329 5: 1.3291e-01 330 L*: 331 0: 1.3291e-01 8.8672e-01 -4.4391e-01 -3.5819e-01 -9.6304e-01 332 5: 4.6038e-01 333 L*w: 334 0: -2.4815e-02 -5.7210e-02 335 pullback M = 3: 336 L: 337 0: 6.4982e-01 1.1086e-01 -9.7880e-02 6.2412e-01 -6.4816e-01 338 5: 9.4609e-01 -5.9075e-01 6.7407e-01 -7.9853e-01 339 L*: 340 0: 6.4982e-01 6.2412e-01 -5.9075e-01 1.1086e-01 -6.4816e-01 341 5: 6.7407e-01 -9.7880e-02 9.4609e-01 -7.9853e-01 342 L*w: 343 0: 4.4157e-01 -1.3547e-01 9.4654e-02 344 negative pullback M = 3: 345 L: 346 0: 6.4982e-01 1.1086e-01 -9.7880e-02 6.2412e-01 -6.4816e-01 347 5: 9.4609e-01 -5.9075e-01 6.7407e-01 -7.9853e-01 348 L*: 349 0: -7.9853e-01 -9.4609e-01 -9.7880e-02 -6.7407e-01 -6.4816e-01 350 5: -1.1086e-01 -5.9075e-01 -6.2412e-01 6.4982e-01 351 L*w: 352 0: 1.2990e-01 6.1155e-02 -4.5636e-01 353 interior product matrix pattern: 354 intV[0,0] = V[0] 355 intV[0,1] = V[1] 356 intV[0,2] = V[2] 357 (w int v_0): 358 0: -3.4899e-01 359 (int v_0): 360 0: 1.5665e-01 -2.1640e-01 7.2654e-01 361 k = 2: 362 (3 choose 2): 3 363 subset 0: 0 1 | 2, even 364 subset 1: 0 2 | 1, odd 365 subset 2: 1 2 | 0, even 366 w: 367 0: -1.8782e-01 7.0744e-01 1.7253e-01 368 v: 369 0: 6.5771e-01 5.7049e-01 2.8630e-02 -8.5477e-01 3.3782e-01 370 5: -2.1430e-01 371 w(v): -0.238478 372 wedge j = 0: 373 u: 374 0: -5.7759e-01 375 u wedge w: 376 0: 1.0848e-01 -4.0861e-01 -9.9649e-02 377 x: 378 0: -7.1156e-01 3.7126e-01 -4.3078e-01 -3.1688e-01 4.4620e-01 379 5: 4.2193e-01 380 u wedge w(x): 0.122009 381 (u wedge): 382 0: -5.7759e-01 0.0000e+00 0.0000e+00 0.0000e+00 -5.7759e-01 383 5: 0.0000e+00 0.0000e+00 0.0000e+00 -5.7759e-01 384 wedge j = 1: 385 u: 386 0: 9.1910e-02 8.7977e-01 -5.5295e-02 387 u wedge w: 388 0: -5.9614e-01 389 x: 390 0: 2.9690e-01 6.6471e-01 5.1740e-01 1.4031e-01 1.7736e-01 391 5: 8.2148e-01 -9.2988e-01 7.3394e-01 -8.3483e-01 392 u wedge w(x): 0.306565 393 (u wedge): 394 0: -5.5295e-02 -8.7977e-01 9.1910e-02 395 pullback M = 2: 396 L: 397 0: 8.8443e-01 4.9797e-01 9.8585e-01 -6.3764e-01 -9.9988e-02 398 5: -7.0149e-01 399 L*: 400 0: -1.0549e+00 -5.7063e-01 -7.5532e-01 401 L*w: 402 0: -3.3587e-01 403 negative pullback M = 2: 404 L: 405 0: 8.8443e-01 4.9797e-01 9.8585e-01 -6.3764e-01 -9.9988e-02 406 5: -7.0149e-01 407 L*: 408 0: -7.5532e-01 5.7063e-01 -1.0549e+00 409 L*w: 410 0: 3.6355e-01 411 pullback M = 3: 412 L: 413 0: -9.5909e-01 -1.8504e-01 -7.3579e-01 -5.3436e-01 -1.8697e-01 414 5: -2.4928e-01 -1.7239e-01 -8.6664e-01 -4.3552e-01 415 L*: 416 0: 8.0437e-02 7.9928e-01 4.3086e-01 -1.5409e-01 2.9086e-01 417 5: 1.8975e-01 -9.1438e-02 -5.5707e-01 -1.3461e-01 418 L*w: 419 0: 6.2467e-01 2.6744e-01 -4.0014e-01 420 negative pullback M = 3: 421 L: 422 0: -9.5909e-01 -1.8504e-01 -7.3579e-01 -5.3436e-01 -1.8697e-01 423 5: -2.4928e-01 -1.7239e-01 -8.6664e-01 -4.3552e-01 424 L*: 425 0: -1.3461e-01 5.5707e-01 -9.1438e-02 -1.8975e-01 2.9086e-01 426 5: 1.5409e-01 4.3086e-01 -7.9928e-01 8.0437e-02 427 L*w: 428 0: 4.0360e-01 2.6799e-01 -6.3249e-01 429 interior product matrix pattern: 430 intV[0,0] = -V[1] 431 intV[0,1] = -V[2] 432 intV[1,0] = V[0] 433 intV[1,2] = -V[2] 434 intV[2,1] = V[0] 435 intV[2,2] = V[1] 436 (w int v_0): 437 0: 8.6894e-02 -1.2847e-01 5.6371e-01 438 (int v_0): 439 0: -5.7049e-01 -2.8630e-02 0.0000e+00 6.5771e-01 0.0000e+00 440 5: -2.8630e-02 0.0000e+00 6.5771e-01 5.7049e-01 441 star w: 442 0: 1.7253e-01 -7.0744e-01 -1.8782e-01 443 star star w: 444 0: -1.8782e-01 7.0744e-01 1.7253e-01 445 k = 3: 446 (3 choose 3): 1 447 subset 0: 0 1 2 |, even 448 w: 449 0: -5.7996e-01 450 v: 451 0: -6.7343e-01 7.7333e-01 4.9289e-01 -6.8617e-01 8.4124e-01 452 5: -4.3276e-01 7.7254e-01 5.8776e-01 7.8121e-01 453 w(v): 0.566604 454 wedge j = 0: 455 u: 456 0: -5.0080e-01 457 u wedge w: 458 0: 2.9044e-01 459 x: 460 0: -7.6236e-01 -2.2003e-02 -3.4366e-01 2.4058e-01 -1.7215e-01 461 5: 2.4512e-01 3.5984e-01 8.2625e-01 -7.1276e-01 462 u wedge w(x): -0.0100078 463 (u wedge): 464 0: -5.0080e-01 465 pullback M = 3: 466 L: 467 0: -4.2983e-01 -5.6291e-01 -4.1641e-01 -2.0869e-01 1.9987e-01 468 5: 4.4418e-01 -9.9065e-01 -1.5900e-01 -2.9704e-01 469 L*: 470 0: 1.8149e-01 471 L*w: 472 0: -1.0525e-01 473 interior product matrix pattern: 474 intV[2,0] = V[0] 475 intV[1,0] = -V[1] 476 intV[0,0] = V[2] 477 (w int v_0): 478 0: -2.8586e-01 4.4850e-01 3.9056e-01 479 (int v_0): 480 0: 4.9289e-01 -7.7333e-01 -6.7343e-01 481 star w: 482 0: -5.7996e-01 483 star star w: 484 0: -5.7996e-01 485N = 4: 486 Permutations of 4: 487 0: 0 1 2 3, even 488 1: 0 1 3 2, odd 489 2: 0 2 1 3, odd 490 3: 0 2 3 1, even 491 4: 0 3 2 1, odd 492 5: 0 3 1 2, even 493 6: 1 0 2 3, odd 494 7: 1 0 3 2, even 495 8: 1 2 0 3, even 496 9: 1 2 3 0, odd 497 10: 1 3 2 0, even 498 11: 1 3 0 2, odd 499 12: 2 1 0 3, odd 500 13: 2 1 3 0, even 501 14: 2 0 1 3, even 502 15: 2 0 3 1, odd 503 16: 2 3 0 1, even 504 17: 2 3 1 0, odd 505 18: 3 1 2 0, odd 506 19: 3 1 0 2, even 507 20: 3 2 1 0, even 508 21: 3 2 0 1, odd 509 22: 3 0 2 1, even 510 23: 3 0 1 2, odd 511 k = 0: 512 (4 choose 0): 1 513 subset 0: | 0 1 2 3, even 514 w: 515 0: -7.4394e-01 516 v: 517 w(v): -0.743937 518 wedge j = 0: 519 u: 520 0: 3.5896e-01 521 u wedge w: 522 0: -2.6704e-01 523 x: 524 u wedge w(x): -0.267043 525 (u wedge): 526 0: 3.5896e-01 527 pullback M = 1: 528 L: 529 0: 1.5959e-01 -6.4365e-01 2.5399e-01 2.9917e-01 530 L*: 531 0: 1.0000e+00 532 L*w: 533 0: -7.4394e-01 534 pullback M = 2: 535 L: 536 0: -1.8009e-01 -5.7793e-01 3.3057e-01 -9.7700e-01 5.4455e-01 537 5: -4.1276e-01 4.3369e-01 6.1429e-02 538 L*: 539 0: 1.0000e+00 540 L*w: 541 0: -7.4394e-01 542 pullback M = 3: 543 L: 544 0: 2.5055e-01 8.6968e-01 7.4232e-01 3.0309e-01 5.9046e-01 545 5: -2.1829e-01 -5.5160e-01 -6.7168e-01 -4.1558e-01 -1.3479e-01 546 10: 6.5574e-01 5.6780e-01 547 L*: 548 0: 1.0000e+00 549 L*w: 550 0: -7.4394e-01 551 pullback M = 4: 552 L: 553 0: 8.2121e-01 -2.9750e-01 -5.7062e-01 6.2420e-01 8.2407e-01 554 5: 5.6269e-01 -3.1815e-01 8.2830e-01 6.0784e-01 -8.7081e-01 555 10: -5.7205e-01 2.8393e-01 -4.5425e-01 -3.5681e-01 8.2933e-01 556 15: 2.4311e-01 557 L*: 558 0: 1.0000e+00 559 L*w: 560 0: -7.4394e-01 561 k = 1: 562 (4 choose 1): 4 563 subset 0: 0 | 1 2 3, even 564 subset 1: 1 | 0 2 3, odd 565 subset 2: 2 | 0 1 3, even 566 subset 3: 3 | 0 1 2, odd 567 w: 568 0: 2.6369e-01 -3.5748e-01 -2.8349e-01 2.2739e-01 569 v: 570 0: 8.8206e-01 -7.8617e-01 -9.1753e-01 4.5956e-01 571 w(v): 0.878243 572 wedge j = 0: 573 u: 574 0: 7.4388e-01 575 u wedge w: 576 0: 1.9615e-01 -2.6592e-01 -2.1089e-01 1.6915e-01 577 x: 578 0: -9.6728e-01 1.3094e-01 8.2809e-01 8.9815e-01 579 u wedge w(x): -0.247262 580 (u wedge): 581 0: 7.4388e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 582 5: 7.4388e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 583 10: 7.4388e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 584 15: 7.4388e-01 585 wedge j = 1: 586 u: 587 0: -2.6993e-01 -2.0090e-01 -3.1502e-02 7.2239e-02 588 u wedge w: 589 0: 1.4947e-01 8.4831e-02 -8.0429e-02 4.5693e-02 -1.9860e-02 590 5: 1.3316e-02 591 x: 592 0: -3.7522e-01 1.0796e-01 -3.3212e-01 6.8021e-01 9.6693e-01 593 5: -6.5846e-02 4.8128e-01 4.0758e-01 594 u wedge w(x): 0.0586624 595 (u wedge): 596 0: 2.0090e-01 -2.6993e-01 0.0000e+00 0.0000e+00 3.1502e-02 597 5: 0.0000e+00 -2.6993e-01 0.0000e+00 -7.2239e-02 0.0000e+00 598 10: 0.0000e+00 -2.6993e-01 0.0000e+00 3.1502e-02 -2.0090e-01 599 15: 0.0000e+00 0.0000e+00 -7.2239e-02 0.0000e+00 -2.0090e-01 600 20: 0.0000e+00 0.0000e+00 -7.2239e-02 -3.1502e-02 601 pullback M = 1: 602 L: 603 0: 7.8673e-01 8.7400e-01 5.0507e-01 5.8168e-01 604 L*: 605 0: 7.8673e-01 8.7400e-01 5.0507e-01 5.8168e-01 606 L*w: 607 0: -1.1590e-01 608 negative pullback M = 1: 609 L: 610 0: 7.8673e-01 8.7400e-01 5.0507e-01 5.8168e-01 611 L*: 612 0: 5.8168e-01 -5.0507e-01 8.7400e-01 -7.8673e-01 613 L*w: 614 0: -9.2737e-02 615 pullback M = 2: 616 L: 617 0: -9.5632e-01 8.7212e-01 -6.3417e-01 5.7161e-01 -8.5299e-01 618 5: -4.6585e-02 -1.2355e-01 -7.6224e-01 619 L*: 620 0: -9.5632e-01 -6.3417e-01 -8.5299e-01 -1.2355e-01 8.7212e-01 621 5: 5.7161e-01 -4.6585e-02 -7.6224e-01 622 L*w: 623 0: 1.8826e-01 -1.3449e-01 624 negative pullback M = 2: 625 L: 626 0: -9.5632e-01 8.7212e-01 -6.3417e-01 5.7161e-01 -8.5299e-01 627 5: -4.6585e-02 -1.2355e-01 -7.6224e-01 628 L*: 629 0: -7.6224e-01 4.6585e-02 5.7161e-01 -8.7212e-01 1.2355e-01 630 5: -8.5299e-01 6.3417e-01 -9.5632e-01 631 L*w: 632 0: -5.7801e-01 -5.9742e-02 633 pullback M = 3: 634 L: 635 0: 1.7964e-02 -1.3200e-01 -8.4531e-01 9.1974e-01 4.6205e-01 636 5: -3.0878e-01 -9.2426e-01 -2.3007e-01 -4.3335e-01 -7.2587e-01 637 10: 5.4066e-02 5.9836e-01 638 L*: 639 0: 1.7964e-02 9.1974e-01 -9.2426e-01 -7.2587e-01 -1.3200e-01 640 5: 4.6205e-01 -2.3007e-01 5.4066e-02 -8.4531e-01 -3.0878e-01 641 10: -4.3335e-01 5.9836e-01 642 L*w: 643 0: -2.2709e-01 -1.2246e-01 1.4640e-01 644 negative pullback M = 3: 645 L: 646 0: 1.7964e-02 -1.3200e-01 -8.4531e-01 9.1974e-01 4.6205e-01 647 5: -3.0878e-01 -9.2426e-01 -2.3007e-01 -4.3335e-01 -7.2587e-01 648 10: 5.4066e-02 5.9836e-01 649 L*: 650 0: 5.9836e-01 4.3335e-01 -3.0878e-01 8.4531e-01 -5.4066e-02 651 5: -2.3007e-01 -4.6205e-01 -1.3200e-01 -7.2587e-01 9.2426e-01 652 10: 9.1974e-01 -1.7964e-02 653 L*w: 654 0: 2.8262e-01 1.6896e-01 -7.8663e-01 655 pullback M = 4: 656 L: 657 0: 6.3375e-01 -3.0028e-02 9.4808e-01 6.3855e-02 -5.1181e-02 658 5: 7.3297e-01 -9.2044e-01 -2.6976e-01 3.4461e-01 -1.2073e-01 659 10: 7.5831e-01 -7.9239e-01 6.9351e-01 9.7345e-01 -6.8279e-01 660 15: -1.2872e-02 661 L*: 662 0: 6.3375e-01 -5.1181e-02 3.4461e-01 6.9351e-01 -3.0028e-02 663 5: 7.3297e-01 -1.2073e-01 9.7345e-01 9.4808e-01 -9.2044e-01 664 10: 7.5831e-01 -6.8279e-01 6.3855e-02 -2.6976e-01 -7.9239e-01 665 15: -1.2872e-02 666 L*w: 667 0: 2.4541e-01 -1.4359e-02 2.0880e-01 3.3498e-01 668 negative pullback M = 4: 669 L: 670 0: 6.3375e-01 -3.0028e-02 9.4808e-01 6.3855e-02 -5.1181e-02 671 5: 7.3297e-01 -9.2044e-01 -2.6976e-01 3.4461e-01 -1.2073e-01 672 10: 7.5831e-01 -7.9239e-01 6.9351e-01 9.7345e-01 -6.8279e-01 673 15: -1.2872e-02 674 L*: 675 0: -1.2872e-02 7.9239e-01 -2.6976e-01 -6.3855e-02 6.8279e-01 676 5: 7.5831e-01 9.2044e-01 9.4808e-01 9.7345e-01 1.2073e-01 677 10: 7.3297e-01 3.0028e-02 -6.9351e-01 3.4461e-01 5.1181e-02 678 15: 6.3375e-01 679 L*w: 680 0: -2.2470e-01 -1.3639e-01 1.2560e-02 -1.7646e-01 681 interior product matrix pattern: 682 intV[0,0] = V[0] 683 intV[0,1] = V[1] 684 intV[0,2] = V[2] 685 intV[0,3] = V[3] 686 (w int v_0): 687 0: 8.7824e-01 688 (int v_0): 689 0: 8.8206e-01 -7.8617e-01 -9.1753e-01 4.5956e-01 690 k = 2: 691 (4 choose 2): 6 692 subset 0: 0 1 | 2 3, even 693 subset 1: 0 2 | 1 3, odd 694 subset 2: 0 3 | 1 2, even 695 subset 3: 1 2 | 0 3, even 696 subset 4: 1 3 | 0 2, odd 697 subset 5: 2 3 | 0 1, even 698 w: 699 0: 9.4113e-01 1.5232e-01 -5.0107e-01 -2.3200e-01 4.8558e-02 700 5: 5.2142e-01 701 v: 702 0: -8.9591e-01 8.4061e-01 -2.2518e-01 3.4966e-02 1.6809e-01 703 5: 8.1800e-01 9.0384e-01 8.7769e-01 704 w(v): -0.847405 705 wedge j = 0: 706 u: 707 0: 4.7703e-01 708 u wedge w: 709 0: 4.4895e-01 7.2659e-02 -2.3903e-01 -1.1067e-01 2.3164e-02 710 5: 2.4873e-01 711 x: 712 0: 2.0731e-01 -9.8742e-01 -7.1849e-01 9.6120e-01 -4.7646e-01 713 5: 6.4692e-01 -8.0816e-01 7.0296e-01 714 u wedge w(x): -0.435001 715 (u wedge): 716 0: 4.7703e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 717 5: 0.0000e+00 0.0000e+00 4.7703e-01 0.0000e+00 0.0000e+00 718 10: 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 4.7703e-01 719 15: 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 720 20: 0.0000e+00 4.7703e-01 0.0000e+00 0.0000e+00 0.0000e+00 721 25: 0.0000e+00 0.0000e+00 0.0000e+00 4.7703e-01 0.0000e+00 722 30: 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 723 35: 4.7703e-01 724 wedge j = 1: 725 u: 726 0: 2.9008e-01 1.5075e-01 -9.5663e-01 -6.9372e-01 727 u wedge w: 728 0: -9.9057e-01 -5.6326e-01 -4.3375e-01 2.8600e-01 729 x: 730 0: 8.7614e-02 -5.5981e-01 4.1114e-01 9.1749e-01 -3.7016e-01 731 5: -4.9479e-01 -3.4250e-01 2.8268e-01 -1.8432e-01 4.4155e-01 732 10: 5.9688e-01 -7.4634e-01 733 u wedge w(x): 0.377565 734 (u wedge): 735 0: -9.5663e-01 -1.5075e-01 0.0000e+00 2.9008e-01 0.0000e+00 736 5: 0.0000e+00 -6.9372e-01 0.0000e+00 -1.5075e-01 0.0000e+00 737 10: 2.9008e-01 0.0000e+00 0.0000e+00 -6.9372e-01 9.5663e-01 738 15: 0.0000e+00 0.0000e+00 2.9008e-01 0.0000e+00 0.0000e+00 739 20: 0.0000e+00 -6.9372e-01 9.5663e-01 1.5075e-01 740 wedge j = 2: 741 u: 742 0: -8.6722e-01 -3.8501e-01 8.8852e-01 9.5774e-02 -6.6658e-01 743 5: 1.6054e-02 744 u wedge w: 745 0: -5.7097e-01 746 x: 747 0: -8.4414e-01 -7.0774e-01 8.9762e-03 3.6565e-01 3.9703e-01 748 5: -6.7742e-01 -9.5197e-02 -5.9403e-01 -7.3056e-01 -7.3361e-01 749 10: 9.3656e-01 8.4796e-01 5.2428e-01 -8.9313e-01 6.5618e-02 750 15: 5.9341e-01 751 u wedge w(x): -0.576003 752 (u wedge): 753 0: 1.6054e-02 6.6658e-01 9.5774e-02 8.8852e-01 3.8501e-01 754 5: -8.6722e-01 755 pullback M = 2: 756 L: 757 0: 4.8556e-01 7.4037e-01 9.1990e-01 7.0991e-01 -2.0408e-01 758 5: -6.8744e-01 5.4403e-01 9.7044e-01 759 L*: 760 0: -3.3637e-01 -1.8270e-01 6.8416e-02 -4.8750e-01 5.0649e-01 761 5: 1.7594e-01 762 L*w: 763 0: -1.4924e-01 764 negative pullback M = 2: 765 L: 766 0: 4.8556e-01 7.4037e-01 9.1990e-01 7.0991e-01 -2.0408e-01 767 5: -6.8744e-01 5.4403e-01 9.7044e-01 768 L*: 769 0: 1.7594e-01 -5.0649e-01 -4.8750e-01 6.8416e-02 1.8270e-01 770 5: -3.3637e-01 771 L*w: 772 0: 1.5032e-01 773 pullback M = 3: 774 L: 775 0: -8.7798e-01 -5.1988e-01 -3.0551e-01 -4.5998e-01 9.3861e-01 776 5: 6.2693e-01 -8.3359e-01 3.3612e-01 6.0071e-02 -1.8260e-01 777 10: 4.9155e-01 -8.7632e-01 778 L*: 779 0: -1.0632e+00 -7.2847e-01 -5.2650e-01 6.2781e-01 -5.4709e-02 780 5: -3.4837e-01 -6.9096e-01 -3.0741e-01 7.1360e-01 4.9497e-01 781 10: 5.1756e-01 7.4146e-01 -3.9168e-02 7.1459e-02 6.0575e-01 782 15: -1.5434e-01 -1.1307e+00 -3.2407e-01 783 L*w: 784 0: -1.1777e+00 -7.5776e-01 -5.1758e-01 785 negative pullback M = 3: 786 L: 787 0: -8.7798e-01 -5.1988e-01 -3.0551e-01 -4.5998e-01 9.3861e-01 788 5: 6.2693e-01 -8.3359e-01 3.3612e-01 6.0071e-02 -1.8260e-01 789 10: 4.9155e-01 -8.7632e-01 790 L*: 791 0: -3.2407e-01 1.1307e+00 -1.5434e-01 6.0575e-01 -7.1459e-02 792 5: -3.9168e-02 -7.4146e-01 5.1756e-01 -4.9497e-01 -7.1360e-01 793 10: -3.0741e-01 6.9096e-01 -3.4837e-01 5.4709e-02 6.2781e-01 794 15: -5.2650e-01 7.2847e-01 -1.0632e+00 795 L*w: 796 0: -2.1987e-01 1.3994e-01 -1.0310e+00 797 pullback M = 4: 798 L: 799 0: -9.4566e-01 -7.0382e-01 2.1323e-02 6.7554e-01 4.0173e-01 800 5: -8.0673e-01 4.6571e-01 1.5665e-01 -2.9256e-01 9.9166e-01 801 10: -2.7217e-01 1.8503e-01 3.9038e-01 4.6708e-01 -4.1968e-02 802 15: -9.6358e-01 803 L*: 804 0: 1.0456e+00 -1.1437e+00 -1.6694e-01 1.6236e-01 5.0257e-01 805 5: -5.2377e-01 -4.4897e-01 2.6362e-01 3.1363e-02 2.6909e-02 806 10: -1.9867e-01 1.1853e-01 -4.1952e-01 2.2659e-02 6.4750e-01 807 15: 1.2016e-01 -4.4825e-01 2.0967e-01 -3.1058e-01 1.7041e-01 808 20: 1.9578e-02 -2.4226e-01 -1.8367e-01 8.5507e-02 4.3473e-01 809 25: -8.0013e-01 3.6265e-01 -3.0461e-01 7.0418e-01 -1.0420e+00 810 30: -3.1127e-01 1.8781e-01 7.8048e-03 1.2880e-01 -4.4218e-01 811 35: 2.7002e-01 812 L*w: 813 0: 6.0717e-01 -3.5219e-01 -6.5613e-01 -1.8428e-01 -3.3288e-01 814 5: -1.7881e-01 815 negative pullback M = 4: 816 L: 817 0: -9.4566e-01 -7.0382e-01 2.1323e-02 6.7554e-01 4.0173e-01 818 5: -8.0673e-01 4.6571e-01 1.5665e-01 -2.9256e-01 9.9166e-01 819 10: -2.7217e-01 1.8503e-01 3.9038e-01 4.6708e-01 -4.1968e-02 820 15: -9.6358e-01 821 L*: 822 0: 2.7002e-01 4.4218e-01 1.2880e-01 7.8048e-03 -1.8781e-01 823 5: -3.1127e-01 1.0420e+00 7.0418e-01 3.0461e-01 -3.6265e-01 824 10: -8.0013e-01 -4.3473e-01 8.5507e-02 1.8367e-01 -2.4226e-01 825 15: 1.9578e-02 -1.7041e-01 -3.1058e-01 2.0967e-01 4.4825e-01 826 20: 1.2016e-01 6.4750e-01 -2.2659e-02 -4.1952e-01 -1.1853e-01 827 25: -1.9867e-01 -2.6909e-02 -3.1363e-02 2.6362e-01 4.4897e-01 828 30: -5.2377e-01 -5.0257e-01 1.6236e-01 -1.6694e-01 1.1437e+00 829 35: 1.0456e+00 830 L*w: 831 0: 8.3704e-02 7.5386e-01 5.5081e-02 -1.6467e-01 1.2585e-01 832 5: -1.1361e-02 833 interior product matrix pattern: 834 intV[1,0] = V[0] 835 intV[0,0] = -V[1] 836 intV[2,1] = V[0] 837 intV[0,1] = -V[2] 838 intV[3,2] = V[0] 839 intV[0,2] = -V[3] 840 intV[2,3] = V[1] 841 intV[1,3] = -V[2] 842 intV[3,4] = V[1] 843 intV[1,4] = -V[3] 844 intV[3,5] = V[2] 845 intV[2,5] = -V[3] 846 (w int v_0): 847 0: -7.3931e-01 -8.9711e-01 -3.4971e-01 3.7232e-01 848 (int v_0): 849 0: -8.4061e-01 2.2518e-01 -3.4966e-02 0.0000e+00 0.0000e+00 850 5: 0.0000e+00 -8.9591e-01 0.0000e+00 0.0000e+00 2.2518e-01 851 10: -3.4966e-02 0.0000e+00 0.0000e+00 -8.9591e-01 0.0000e+00 852 15: 8.4061e-01 0.0000e+00 -3.4966e-02 0.0000e+00 0.0000e+00 853 20: -8.9591e-01 0.0000e+00 8.4061e-01 -2.2518e-01 854 star w: 855 0: 5.2142e-01 -4.8558e-02 -2.3200e-01 -5.0107e-01 -1.5232e-01 856 5: 9.4113e-01 857 star star w: 858 0: 9.4113e-01 1.5232e-01 -5.0107e-01 -2.3200e-01 4.8558e-02 859 5: 5.2142e-01 860 k = 3: 861 (4 choose 3): 4 862 subset 0: 0 1 2 | 3, even 863 subset 1: 0 1 3 | 2, odd 864 subset 2: 0 2 3 | 1, even 865 subset 3: 1 2 3 | 0, odd 866 w: 867 0: -3.7517e-01 6.1766e-01 9.8353e-01 -1.2600e-01 868 v: 869 0: -2.5691e-01 -2.8870e-01 1.0936e-02 -3.8726e-01 8.4560e-01 870 5: -6.7717e-01 -9.7375e-01 -5.5894e-01 -2.5643e-01 8.0538e-01 871 10: -2.0257e-01 -5.4053e-01 872 w(v): -0.102079 873 wedge j = 0: 874 u: 875 0: 8.5022e-01 876 u wedge w: 877 0: -3.1898e-01 5.2515e-01 8.3622e-01 -1.0713e-01 878 x: 879 0: -8.0037e-01 4.5905e-01 -1.5464e-01 6.7704e-01 -8.6982e-01 880 5: -9.9576e-01 7.5080e-01 -9.6707e-01 -5.1927e-01 6.8438e-01 881 10: -1.5516e-01 -6.6693e-01 882 u wedge w(x): -0.26249 883 (u wedge): 884 0: 8.5022e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 885 5: 8.5022e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 886 10: 8.5022e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 887 15: 8.5022e-01 888 wedge j = 1: 889 u: 890 0: -5.3738e-01 -3.2322e-01 4.7929e-01 1.4265e-01 891 u wedge w: 892 0: 7.3516e-01 893 x: 894 0: 8.3074e-01 4.8066e-03 -2.4025e-01 -7.5128e-01 1.7846e-01 895 5: -4.2150e-01 6.3963e-01 4.8965e-01 4.3057e-01 -3.0549e-01 896 10: 2.0139e-01 -4.2717e-01 -2.1362e-01 2.2242e-01 7.8195e-02 897 15: -4.3793e-01 898 u wedge w(x): -0.0636979 899 (u wedge): 900 0: -1.4265e-01 4.7929e-01 3.2322e-01 -5.3738e-01 901 pullback M = 3: 902 L: 903 0: 1.8703e-01 9.8369e-01 5.9181e-02 -2.3898e-01 7.2997e-01 904 5: -6.2029e-01 -1.9544e-01 -4.0435e-01 -9.1224e-01 9.6188e-01 905 10: -9.5261e-01 -6.7639e-01 906 L*: 907 0: -2.5250e-01 -9.7686e-01 -1.0705e+00 -9.5144e-01 908 L*w: 909 0: -1.4417e+00 910 negative pullback M = 3: 911 L: 912 0: 1.8703e-01 9.8369e-01 5.9181e-02 -2.3898e-01 7.2997e-01 913 5: -6.2029e-01 -1.9544e-01 -4.0435e-01 -9.1224e-01 9.6188e-01 914 10: -9.5261e-01 -6.7639e-01 915 L*: 916 0: -9.5144e-01 1.0705e+00 -9.7686e-01 2.5250e-01 917 L*w: 918 0: 2.5598e-02 919 pullback M = 4: 920 L: 921 0: -4.9748e-01 -3.0328e-01 -8.7441e-01 -5.8880e-01 -9.1914e-01 922 5: -2.2123e-01 -4.3706e-01 3.3706e-01 4.1845e-01 7.4420e-01 923 10: -1.5180e-01 -3.5261e-01 -3.7428e-01 -8.5541e-01 -6.4351e-01 924 15: 8.8954e-02 925 L*: 926 0: 4.3644e-01 -3.7015e-01 2.7337e-01 5.2209e-01 4.8975e-01 927 5: -5.3437e-01 1.3514e-01 1.6866e-01 -1.3189e-01 -3.0169e-01 928 10: 2.2875e-01 6.9647e-02 -4.2467e-01 3.1722e-01 2.2549e-01 929 15: -2.5489e-01 930 L*w: 931 0: -1.8928e-01 -4.0214e-01 7.9348e-02 6.0915e-01 932 negative pullback M = 4: 933 L: 934 0: -4.9748e-01 -3.0328e-01 -8.7441e-01 -5.8880e-01 -9.1914e-01 935 5: -2.2123e-01 -4.3706e-01 3.3706e-01 4.1845e-01 7.4420e-01 936 10: -1.5180e-01 -3.5261e-01 -3.7428e-01 -8.5541e-01 -6.4351e-01 937 15: 8.8954e-02 938 L*: 939 0: -2.5489e-01 -2.2549e-01 3.1722e-01 4.2467e-01 -6.9647e-02 940 5: 2.2875e-01 3.0169e-01 -1.3189e-01 1.6866e-01 -1.3514e-01 941 10: -5.3437e-01 -4.8975e-01 -5.2209e-01 2.7337e-01 3.7015e-01 942 15: 4.3644e-01 943 L*w: 944 0: 2.1484e-01 4.8076e-01 -6.1060e-01 6.7379e-01 945 interior product matrix pattern: 946 intV[3,0] = V[0] 947 intV[1,0] = -V[1] 948 intV[0,0] = V[2] 949 intV[4,1] = V[0] 950 intV[2,1] = -V[1] 951 intV[0,1] = V[3] 952 intV[5,2] = V[0] 953 intV[2,2] = -V[2] 954 intV[1,2] = V[3] 955 intV[5,3] = V[1] 956 intV[4,3] = -V[2] 957 intV[3,3] = V[3] 958 (w int v_0): 959 0: -2.4330e-01 -4.8919e-01 1.6756e-01 1.4518e-01 -1.5730e-01 960 5: -2.1630e-01 961 (int v_0): 962 0: 1.0936e-02 -3.8726e-01 0.0000e+00 0.0000e+00 2.8870e-01 963 5: 0.0000e+00 -3.8726e-01 0.0000e+00 0.0000e+00 2.8870e-01 964 10: -1.0936e-02 0.0000e+00 -2.5691e-01 0.0000e+00 0.0000e+00 965 15: -3.8726e-01 0.0000e+00 -2.5691e-01 0.0000e+00 -1.0936e-02 966 20: 0.0000e+00 0.0000e+00 -2.5691e-01 -2.8870e-01 967 star w: 968 0: 1.2600e-01 9.8353e-01 -6.1766e-01 -3.7517e-01 969 star star w: 970 0: 3.7517e-01 -6.1766e-01 -9.8353e-01 1.2600e-01 971 k = 4: 972 (4 choose 4): 1 973 subset 0: 0 1 2 3 |, even 974 w: 975 0: -2.5480e-01 976 v: 977 0: 1.0979e-01 -5.6223e-01 -6.8199e-02 6.1742e-02 -6.2533e-01 978 5: -1.5664e-01 -3.9865e-01 -2.5882e-01 8.7131e-01 2.7764e-01 979 10: 2.1143e-01 -8.8580e-01 9.5433e-01 2.6095e-02 3.9046e-01 980 15: -7.6788e-01 981 w(v): 0.0196566 982 wedge j = 0: 983 u: 984 0: 7.6849e-01 985 u wedge w: 986 0: -1.9581e-01 987 x: 988 0: -5.1168e-01 -2.8257e-01 -5.0308e-01 -4.1424e-01 -7.8720e-01 989 5: -8.0635e-01 8.3809e-01 -6.9425e-01 -5.4188e-01 4.1450e-02 990 10: -2.7054e-01 9.3937e-01 -8.3739e-01 3.8953e-01 6.9703e-01 991 15: 6.5400e-01 992 u wedge w(x): 0.179666 993 (u wedge): 994 0: 7.6849e-01 995 pullback M = 4: 996 L: 997 0: 6.0675e-01 4.7193e-01 -5.4014e-01 2.2124e-02 1.5380e-01 998 5: -2.6649e-01 4.5758e-01 2.9025e-02 6.1407e-01 -6.9521e-01 999 10: -9.8726e-01 -3.4833e-01 -8.2794e-01 -3.3814e-01 -3.8553e-01 1000 15: 6.5902e-01 1001 L*: 1002 0: 4.3994e-01 1003 L*w: 1004 0: -1.1210e-01 1005 interior product matrix pattern: 1006 intV[3,0] = V[0] 1007 intV[2,0] = -V[1] 1008 intV[1,0] = V[2] 1009 intV[0,0] = -V[3] 1010 (w int v_0): 1011 0: 1.5732e-02 1.7377e-02 -1.4326e-01 -2.7975e-02 1012 (int v_0): 1013 0: -6.1742e-02 -6.8199e-02 5.6223e-01 1.0979e-01 1014 star w: 1015 0: -2.5480e-01 1016 star star w: 1017 0: -2.5480e-01 1018