Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

More documents

Recommendations

Info

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: b.echelonize(); b [ 1 0 36] [ 0 1 2] sage: a.pivots() (0, 1) sage: b.pivots() (0, 1) sage: a.rank() 2 sage: b.rank() 2 sage: a[2,2] = 5 sage: a.rank() 3 TESTS: sage: matrix(Integers(37),0,0,sparse=True).inverse() [] class sage.matrix.matrix_modn_sparse.Matrix_modn_sparse Bases: sage.matrix.matrix_sparse.Matrix_sparse Create a sparse matrix modulo n. INPUT: •parent - a matrix space •entries –a Python list of triples (i,j,x), where 0
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 [1||2 3] [4||5 6] matrix_from_columns(cols) Return the matrix constructed from self using columns with indices in the columns list. EXAMPLES: sage: M = MatrixSpace(GF(127),3,3,sparse=True) sage: A = M(range(9)); A [0 1 2] [3 4 5] [6 7 8] sage: A.matrix_from_columns([2,1]) [2 1] [5 4] [8 7] matrix_from_rows(rows) Return the matrix constructed from self using rows with indices in the rows list. p INPUT: •rows - list or tuple of row indices EXAMPLE: sage: M = MatrixSpace(GF(127),3,3,sparse=True) sage: A = M(range(9)); A [0 1 2] [3 4 5] [6 7 8] sage: A.matrix_from_rows([2,1]) [6 7 8] [3 4 5] rank(gauss=False) Compute the rank of self. INPUT: •gauss - if True LinBox’ Gaussian elimination is used. If False ‘Symbolic Reordering’ as implemented in LinBox is used. If ‘native’ the native Sage implementation is used. (default: False) EXAMPLE: sage: A = random_matrix(GF(127),200,200,density=0.01,sparse=True) sage: r1 = A.rank(gauss=False) sage: r2 = A.rank(gauss=True) sage: r3 = A.rank(gauss=’native’) sage: r1 == r2 == r3 True sage: r1 155 ALGORITHM: Uses LinBox or native implementation. REFERENCES: 301
Page 1:
Sage Reference Manual: Matrices and
Page 4 and 5:
22 Dense matrices over multivariate
Page 6 and 7:
Page 8 and 9:
Page 10 and 11:
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255: Sage Reference Manual: Matrices and
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401:
Page 402 and 403:
Page 404 and 405:
Page 406 and 407:
Page 408 and 409:
Page 410 and 411:
Page 412 and 413:
Page 414 and 415:
Page 416 and 417:
Page 418 and 419:
Page 420 and 421:
Page 422 and 423:
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
Page 430 and 431:
Page 432 and 433:
Page 434 and 435:
Page 436 and 437:
Page 438 and 439:
Page 440 and 441:
Page 442 and 443:
show all

Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Create successful ePaper yourself

Delete template?

Save as template?