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.matrix.benchmark.matrix_multiply_ZZ(n=300, min=-9, max=9, system=’sage’, times=1) Matrix multiplication over ZZ Given an n x n matrix A over ZZ with random entries between min and max, inclusive, compute A * (A+1). INPUT: •n - matrix dimension (default: 300) •min - minimal value for entries of matrix (default: -9) •max - maximal value for entries of matrix (default: 9) •system - either ‘sage’ or ‘magma’ (default: ‘sage’) •times - number of experiments (default: 1) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.matrix_multiply_ZZ(200) sage: tm = b.matrix_multiply_ZZ(200, system=’magma’) # optional - magma sage.matrix.benchmark.nullspace_GF(n=300, p=16411, system=’sage’) Given a n+1 x n matrix over GF(p) with random entries, compute the nullspace. INPUT: •n - matrix dimension (default: 300) •p - prime number (default: 16411) •system - either ‘magma’ or ‘sage’ (default: ‘sage’) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.nullspace_GF(300) sage: tm = b.nullspace_GF(300, system=’magma’) # optional - magma sage.matrix.benchmark.nullspace_RDF(n=300, min=0, max=10, system=’sage’) Nullspace over RDF: Given a n+1 x n matrix over RDF with random entries between min and max, compute the nullspace. INPUT: •n - matrix dimension (default: 300) •min - minimal value for entries of matrix (default: 0) •max - maximal value for entries of matrix (default: 10‘) •system - either ‘sage’ or ‘magma’ (default: ‘sage’) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.nullspace_RDF(100) # long time sage: tm = b.nullspace_RDF(100, system=’magma’) # optional - magma sage.matrix.benchmark.nullspace_RR(n=300, min=0, max=10, system=’sage’) Nullspace over RR: Given a n+1 x n matrix over RR with random entries between min and max, compute the nullspace. INPUT: 418 Chapter 24. Benchmarks for matrices
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 •n - matrix dimension (default: 300) •min - minimal value for entries of matrix (default: 0) •max - maximal value for entries of matrix (default: 10) •system - either ‘sage’ or ‘magma’ (default: ‘sage’) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.nullspace_RR(100) sage: tm = b.nullspace_RR(100, system=’magma’) # optional - magma sage.matrix.benchmark.nullspace_ZZ(n=200, min=0, max=4294967296, system=’sage’) Nullspace over ZZ: Given a n+1 x n matrix over ZZ with random entries between min and max, compute the nullspace. INPUT: •n - matrix dimension (default: 200) •min - minimal value for entries of matrix (default: 0) •max - maximal value for entries of matrix (default: 2**32) •system - either ‘sage’ or ‘magma’ (default: ‘sage’) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.nullspace_ZZ(200) sage: tm = b.nullspace_ZZ(200, system=’magma’) # optional - magma sage.matrix.benchmark.rank2_GF(n=500, p=16411, system=’sage’) Rank over GF(p): Given a (n + 10) x n matrix over GF(p) with random entries, compute the rank. INPUT: •n - matrix dimension (default: 300) •p - prime number (default: 16411) •system - either ‘magma’ or ‘sage’ (default: ‘sage’) EXAMPLES: sage: import sage.matrix.benchmark as b sage: ts = b.rank2_GF(500) sage: tm = b.rank2_GF(500, system=’magma’) # optional - magma sage.matrix.benchmark.rank2_ZZ(n=400, min=0, max=18446744073709551616L, system=’sage’) Rank 2 over ZZ: Given a (n + 10) x n matrix over ZZ with random entries between min and max, compute the rank. INPUT: •n - matrix dimension (default: 400) •min - minimal value for entries of matrix (default: 0) •max - maximal value for entries of matrix (default: 2**64) •system - either ‘sage’ or ‘magma’ (default: ‘sage’) EXAMPLES: 419
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:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
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: Sage Reference Manual: Matrices and
show all

Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?