|\^/| Maple 13 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2009 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart; > kernelopts(printbytes=false): > > with(LinearAlgebra): > > interface(rtablesize=1000): > > Digits:=15: > > read`MultiStructureBreadth1.mpl`: > > infolevel[MultiStructure]:=1: > > > # DZ, n=5 and (0,0) is 12-fold zero and index is 12. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^5)]; 2 2 5 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 2 8 3 9 4 10 5 2 x - z, x - x z, x - x z, x - x z, x - x z, x - x z + z + y, 11 6 2 x - x z + x z + x y] > > time()-st; 0.071 > > > # DZ, n=50 and (0,0) is 102-fold zero and index is 102. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^50)]; 2 2 50 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 x , x , x , x , x , x , x , x , x , x , x , x , x , x , 50 51 52 2 53 3 54 4 55 5 x - z, x - x z, x - x z, x - x z, x - x z, x - x z, 56 6 57 7 58 8 59 9 60 10 61 11 x - x z, x - x z, x - x z, x - x z, x - x z, x - x z, 62 12 63 13 64 14 65 15 66 16 x - x z, x - x z, x - x z, x - x z, x - x z, 67 17 68 18 69 19 70 20 71 21 x - x z, x - x z, x - x z, x - x z, x - x z, 72 22 73 23 74 24 75 25 76 26 x - x z, x - x z, x - x z, x - x z, x - x z, 77 27 78 28 79 29 80 30 81 31 x - x z, x - x z, x - x z, x - x z, x - x z, 82 32 83 33 84 34 85 35 86 36 x - x z, x - x z, x - x z, x - x z, x - x z, 87 37 88 38 89 39 90 40 91 41 x - x z, x - x z, x - x z, x - x z, x - x z, 92 42 93 43 94 44 95 45 96 46 x - x z, x - x z, x - x z, x - x z, x - x z, 97 47 98 48 99 49 100 50 2 x - x z, x - x z, x - x z, x - x z + z + y, 101 51 2 x - x z + x z + x y] > > time()-st; 0.606 > > > # DZ, n=100 and (0,0) is 202-fold zero and index is 202. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^100)]; 2 2 100 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 96 97 98 99 100 101 102 2 103 3 x , x , x , x , x - z, x - x z, x - x z, x - x z, 104 4 105 5 106 6 107 7 108 8 x - x z, x - x z, x - x z, x - x z, x - x z, 109 9 110 10 111 11 112 12 113 13 x - x z, x - x z, x - x z, x - x z, x - x z, 114 14 115 15 116 16 117 17 118 18 x - x z, x - x z, x - x z, x - x z, x - x z, 119 19 120 20 121 21 122 22 123 23 x - x z, x - x z, x - x z, x - x z, x - x z, 124 24 125 25 126 26 127 27 128 28 x - x z, x - x z, x - x z, x - x z, x - x z, 129 29 130 30 131 31 132 32 133 33 x - x z, x - x z, x - x z, x - x z, x - x z, 134 34 135 35 136 36 137 37 138 38 x - x z, x - x z, x - x z, x - x z, x - x z, 139 39 140 40 141 41 142 42 143 43 x - x z, x - x z, x - x z, x - x z, x - x z, 144 44 145 45 146 46 147 47 148 48 x - x z, x - x z, x - x z, x - x z, x - x z, 149 49 150 50 151 51 152 52 153 53 x - x z, x - x z, x - x z, x - x z, x - x z, 154 54 155 55 156 56 157 57 158 58 x - x z, x - x z, x - x z, x - x z, x - x z, 159 59 160 60 161 61 162 62 163 63 x - x z, x - x z, x - x z, x - x z, x - x z, 164 64 165 65 166 66 167 67 168 68 x - x z, x - x z, x - x z, x - x z, x - x z, 169 69 170 70 171 71 172 72 173 73 x - x z, x - x z, x - x z, x - x z, x - x z, 174 74 175 75 176 76 177 77 178 78 x - x z, x - x z, x - x z, x - x z, x - x z, 179 79 180 80 181 81 182 82 183 83 x - x z, x - x z, x - x z, x - x z, x - x z, 184 84 185 85 186 86 187 87 188 88 x - x z, x - x z, x - x z, x - x z, x - x z, 189 89 190 90 191 91 192 92 193 93 x - x z, x - x z, x - x z, x - x z, x - x z, 194 94 195 95 196 96 197 97 198 98 x - x z, x - x z, x - x z, x - x z, x - x z, 199 99 200 100 2 201 101 2 x - x z, x - x z + z + y, x - x z + x z + x y] > > time()-st; 2.204 > > > # DZ, n=200 and (0,0) is 402-fold zero and index is 402. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^200)]; 2 2 200 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 96 97 98 99 100 101 102 103 104 105 106 107 108 x , x , x , x , x , x , x , x , x , x , x , x , x , 109 110 111 112 113 114 115 116 117 118 119 120 x , x , x , x , x , x , x , x , x , x , x , x , 121 122 123 124 125 126 127 128 129 130 131 132 x , x , x , x , x , x , x , x , x , x , x , x , 133 134 135 136 137 138 139 140 141 142 143 144 x , x , x , x , x , x , x , x , x , x , x , x , 145 146 147 148 149 150 151 152 153 154 155 156 x , x , x , x , x , x , x , x , x , x , x , x , 157 158 159 160 161 162 163 164 165 166 167 168 x , x , x , x , x , x , x , x , x , x , x , x , 169 170 171 172 173 174 175 176 177 178 179 180 x , x , x , x , x , x , x , x , x , x , x , x , 181 182 183 184 185 186 187 188 189 190 191 192 x , x , x , x , x , x , x , x , x , x , x , x , 193 194 195 196 197 198 199 200 201 202 2 x , x , x , x , x , x , x , x - z, x - x z, x - x z, 203 3 204 4 205 5 206 6 207 7 x - x z, x - x z, x - x z, x - x z, x - x z, 208 8 209 9 210 10 211 11 212 12 x - x z, x - x z, x - x z, x - x z, x - x z, 213 13 214 14 215 15 216 16 217 17 x - x z, x - x z, x - x z, x - x z, x - x z, 218 18 219 19 220 20 221 21 222 22 x - x z, x - x z, x - x z, x - x z, x - x z, 223 23 224 24 225 25 226 26 227 27 x - x z, x - x z, x - x z, x - x z, x - x z, 228 28 229 29 230 30 231 31 232 32 x - x z, x - x z, x - x z, x - x z, x - x z, 233 33 234 34 235 35 236 36 237 37 x - x z, x - x z, x - x z, x - x z, x - x z, 238 38 239 39 240 40 241 41 242 42 x - x z, x - x z, x - x z, x - x z, x - x z, 243 43 244 44 245 45 246 46 247 47 x - x z, x - x z, x - x z, x - x z, x - x z, 248 48 249 49 250 50 251 51 252 52 x - x z, x - x z, x - x z, x - x z, x - x z, 253 53 254 54 255 55 256 56 257 57 x - x z, x - x z, x - x z, x - x z, x - x z, 258 58 259 59 260 60 261 61 262 62 x - x z, x - x z, x - x z, x - x z, x - x z, 263 63 264 64 265 65 266 66 267 67 x - x z, x - x z, x - x z, x - x z, x - x z, 268 68 269 69 270 70 271 71 272 72 x - x z, x - x z, x - x z, x - x z, x - x z, 273 73 274 74 275 75 276 76 277 77 x - x z, x - x z, x - x z, x - x z, x - x z, 278 78 279 79 280 80 281 81 282 82 x - x z, x - x z, x - x z, x - x z, x - x z, 283 83 284 84 285 85 286 86 287 87 x - x z, x - x z, x - x z, x - x z, x - x z, 288 88 289 89 290 90 291 91 292 92 x - x z, x - x z, x - x z, x - x z, x - x z, 293 93 294 94 295 95 296 96 297 97 x - x z, x - x z, x - x z, x - x z, x - x z, 298 98 299 99 300 100 301 101 302 102 x - x z, x - x z, x - x z, x - x z, x - x z, 303 103 304 104 305 105 306 106 307 107 x - x z, x - x z, x - x z, x - x z, x - x z, 308 108 309 109 310 110 311 111 312 112 x - x z, x - x z, x - x z, x - x z, x - x z, 313 113 314 114 315 115 316 116 317 117 x - x z, x - x z, x - x z, x - x z, x - x z, 318 118 319 119 320 120 321 121 322 122 x - x z, x - x z, x - x z, x - x z, x - x z, 323 123 324 124 325 125 326 126 327 127 x - x z, x - x z, x - x z, x - x z, x - x z, 328 128 329 129 330 130 331 131 332 132 x - x z, x - x z, x - x z, x - x z, x - x z, 333 133 334 134 335 135 336 136 337 137 x - x z, x - x z, x - x z, x - x z, x - x z, 338 138 339 139 340 140 341 141 342 142 x - x z, x - x z, x - x z, x - x z, x - x z, 343 143 344 144 345 145 346 146 347 147 x - x z, x - x z, x - x z, x - x z, x - x z, 348 148 349 149 350 150 351 151 352 152 x - x z, x - x z, x - x z, x - x z, x - x z, 353 153 354 154 355 155 356 156 357 157 x - x z, x - x z, x - x z, x - x z, x - x z, 358 158 359 159 360 160 361 161 362 162 x - x z, x - x z, x - x z, x - x z, x - x z, 363 163 364 164 365 165 366 166 367 167 x - x z, x - x z, x - x z, x - x z, x - x z, 368 168 369 169 370 170 371 171 372 172 x - x z, x - x z, x - x z, x - x z, x - x z, 373 173 374 174 375 175 376 176 377 177 x - x z, x - x z, x - x z, x - x z, x - x z, 378 178 379 179 380 180 381 181 382 182 x - x z, x - x z, x - x z, x - x z, x - x z, 383 183 384 184 385 185 386 186 387 187 x - x z, x - x z, x - x z, x - x z, x - x z, 388 188 389 189 390 190 391 191 392 192 x - x z, x - x z, x - x z, x - x z, x - x z, 393 193 394 194 395 195 396 196 397 197 x - x z, x - x z, x - x z, x - x z, x - x z, 398 198 399 199 400 200 2 x - x z, x - x z, x - x z + z + y, 401 201 2 x - x z + x z + x y] > > time()-st; 11.014 > > > # DZ, n=300 and (0,0) is 602-fold zero and index is 602. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^300)]; 2 2 300 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 96 97 98 99 100 101 102 103 104 105 106 107 108 x , x , x , x , x , x , x , x , x , x , x , x , x , 109 110 111 112 113 114 115 116 117 118 119 120 x , x , x , x , x , x , x , x , x , x , x , x , 121 122 123 124 125 126 127 128 129 130 131 132 x , x , x , x , x , x , x , x , x , x , x , x , 133 134 135 136 137 138 139 140 141 142 143 144 x , x , x , x , x , x , x , x , x , x , x , x , 145 146 147 148 149 150 151 152 153 154 155 156 x , x , x , x , x , x , x , x , x , x , x , x , 157 158 159 160 161 162 163 164 165 166 167 168 x , x , x , x , x , x , x , x , x , x , x , x , 169 170 171 172 173 174 175 176 177 178 179 180 x , x , x , x , x , x , x , x , x , x , x , x , 181 182 183 184 185 186 187 188 189 190 191 192 x , x , x , x , x , x , x , x , x , x , x , x , 193 194 195 196 197 198 199 200 201 202 203 204 x , x , x , x , x , x , x , x , x , x , x , x , 205 206 207 208 209 210 211 212 213 214 215 216 x , x , x , x , x , x , x , x , x , x , x , x , 217 218 219 220 221 222 223 224 225 226 227 228 x , x , x , x , x , x , x , x , x , x , x , x , 229 230 231 232 233 234 235 236 237 238 239 240 x , x , x , x , x , x , x , x , x , x , x , x , 241 242 243 244 245 246 247 248 249 250 251 252 x , x , x , x , x , x , x , x , x , x , x , x , 253 254 255 256 257 258 259 260 261 262 263 264 x , x , x , x , x , x , x , x , x , x , x , x , 265 266 267 268 269 270 271 272 273 274 275 276 x , x , x , x , x , x , x , x , x , x , x , x , 277 278 279 280 281 282 283 284 285 286 287 288 x , x , x , x , x , x , x , x , x , x , x , x , 289 290 291 292 293 294 295 296 297 298 299 300 x , x , x , x , x , x , x , x , x , x , x , x - z, 301 302 2 303 3 304 4 305 5 306 6 x - x z, x - x z, x - x z, x - x z, x - x z, x - x z, 307 7 308 8 309 9 310 10 311 11 x - x z, x - x z, x - x z, x - x z, x - x z, 312 12 313 13 314 14 315 15 316 16 x - x z, x - x z, x - x z, x - x z, x - x z, 317 17 318 18 319 19 320 20 321 21 x - x z, x - x z, x - x z, x - x z, x - x z, 322 22 323 23 324 24 325 25 326 26 x - x z, x - x z, x - x z, x - x z, x - x z, 327 27 328 28 329 29 330 30 331 31 x - x z, x - x z, x - x z, x - x z, x - x z, 332 32 333 33 334 34 335 35 336 36 x - x z, x - x z, x - x z, x - x z, x - x z, 337 37 338 38 339 39 340 40 341 41 x - x z, x - x z, x - x z, x - x z, x - x z, 342 42 343 43 344 44 345 45 346 46 x - x z, x - x z, x - x z, x - x z, x - x z, 347 47 348 48 349 49 350 50 351 51 x - x z, x - x z, x - x z, x - x z, x - x z, 352 52 353 53 354 54 355 55 356 56 x - x z, x - x z, x - x z, x - x z, x - x z, 357 57 358 58 359 59 360 60 361 61 x - x z, x - x z, x - x z, x - x z, x - x z, 362 62 363 63 364 64 365 65 366 66 x - x z, x - x z, x - x z, x - x z, x - x z, 367 67 368 68 369 69 370 70 371 71 x - x z, x - x z, x - x z, x - x z, x - x z, 372 72 373 73 374 74 375 75 376 76 x - x z, x - x z, x - x z, x - x z, x - x z, 377 77 378 78 379 79 380 80 381 81 x - x z, x - x z, x - x z, x - x z, x - x z, 382 82 383 83 384 84 385 85 386 86 x - x z, x - x z, x - x z, x - x z, x - x z, 387 87 388 88 389 89 390 90 391 91 x - x z, x - x z, x - x z, x - x z, x - x z, 392 92 393 93 394 94 395 95 396 96 x - x z, x - x z, x - x z, x - x z, x - x z, 397 97 398 98 399 99 400 100 401 101 x - x z, x - x z, x - x z, x - x z, x - x z, 402 102 403 103 404 104 405 105 406 106 x - x z, x - x z, x - x z, x - x z, x - x z, 407 107 408 108 409 109 410 110 411 111 x - x z, x - x z, x - x z, x - x z, x - x z, 412 112 413 113 414 114 415 115 416 116 x - x z, x - x z, x - x z, x - x z, x - x z, 417 117 418 118 419 119 420 120 421 121 x - x z, x - x z, x - x z, x - x z, x - x z, 422 122 423 123 424 124 425 125 426 126 x - x z, x - x z, x - x z, x - x z, x - x z, 427 127 428 128 429 129 430 130 431 131 x - x z, x - x z, x - x z, x - x z, x - x z, 432 132 433 133 434 134 435 135 436 136 x - x z, x - x z, x - x z, x - x z, x - x z, 437 137 438 138 439 139 440 140 441 141 x - x z, x - x z, x - x z, x - x z, x - x z, 442 142 443 143 444 144 445 145 446 146 x - x z, x - x z, x - x z, x - x z, x - x z, 447 147 448 148 449 149 450 150 451 151 x - x z, x - x z, x - x z, x - x z, x - x z, 452 152 453 153 454 154 455 155 456 156 x - x z, x - x z, x - x z, x - x z, x - x z, 457 157 458 158 459 159 460 160 461 161 x - x z, x - x z, x - x z, x - x z, x - x z, 462 162 463 163 464 164 465 165 466 166 x - x z, x - x z, x - x z, x - x z, x - x z, 467 167 468 168 469 169 470 170 471 171 x - x z, x - x z, x - x z, x - x z, x - x z, 472 172 473 173 474 174 475 175 476 176 x - x z, x - x z, x - x z, x - x z, x - x z, 477 177 478 178 479 179 480 180 481 181 x - x z, x - x z, x - x z, x - x z, x - x z, 482 182 483 183 484 184 485 185 486 186 x - x z, x - x z, x - x z, x - x z, x - x z, 487 187 488 188 489 189 490 190 491 191 x - x z, x - x z, x - x z, x - x z, x - x z, 492 192 493 193 494 194 495 195 496 196 x - x z, x - x z, x - x z, x - x z, x - x z, 497 197 498 198 499 199 500 200 501 201 x - x z, x - x z, x - x z, x - x z, x - x z, 502 202 503 203 504 204 505 205 506 206 x - x z, x - x z, x - x z, x - x z, x - x z, 507 207 508 208 509 209 510 210 511 211 x - x z, x - x z, x - x z, x - x z, x - x z, 512 212 513 213 514 214 515 215 516 216 x - x z, x - x z, x - x z, x - x z, x - x z, 517 217 518 218 519 219 520 220 521 221 x - x z, x - x z, x - x z, x - x z, x - x z, 522 222 523 223 524 224 525 225 526 226 x - x z, x - x z, x - x z, x - x z, x - x z, 527 227 528 228 529 229 530 230 531 231 x - x z, x - x z, x - x z, x - x z, x - x z, 532 232 533 233 534 234 535 235 536 236 x - x z, x - x z, x - x z, x - x z, x - x z, 537 237 538 238 539 239 540 240 541 241 x - x z, x - x z, x - x z, x - x z, x - x z, 542 242 543 243 544 244 545 245 546 246 x - x z, x - x z, x - x z, x - x z, x - x z, 547 247 548 248 549 249 550 250 551 251 x - x z, x - x z, x - x z, x - x z, x - x z, 552 252 553 253 554 254 555 255 556 256 x - x z, x - x z, x - x z, x - x z, x - x z, 557 257 558 258 559 259 560 260 561 261 x - x z, x - x z, x - x z, x - x z, x - x z, 562 262 563 263 564 264 565 265 566 266 x - x z, x - x z, x - x z, x - x z, x - x z, 567 267 568 268 569 269 570 270 571 271 x - x z, x - x z, x - x z, x - x z, x - x z, 572 272 573 273 574 274 575 275 576 276 x - x z, x - x z, x - x z, x - x z, x - x z, 577 277 578 278 579 279 580 280 581 281 x - x z, x - x z, x - x z, x - x z, x - x z, 582 282 583 283 584 284 585 285 586 286 x - x z, x - x z, x - x z, x - x z, x - x z, 587 287 588 288 589 289 590 290 591 291 x - x z, x - x z, x - x z, x - x z, x - x z, 592 292 593 293 594 294 595 295 596 296 x - x z, x - x z, x - x z, x - x z, x - x z, 597 297 598 298 599 299 600 300 2 x - x z, x - x z, x - x z, x - x z + z + y, 601 301 2 x - x z + x z + x y] > > time()-st; 41.368 > > > # DZ, n=400 and (0,0) is 802-fold zero and index is 802. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^400)]; 2 2 400 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 96 97 98 99 100 101 102 103 104 105 106 107 108 x , x , x , x , x , x , x , x , x , x , x , x , x , 109 110 111 112 113 114 115 116 117 118 119 120 x , x , x , x , x , x , x , x , x , x , x , x , 121 122 123 124 125 126 127 128 129 130 131 132 x , x , x , x , x , x , x , x , x , x , x , x , 133 134 135 136 137 138 139 140 141 142 143 144 x , x , x , x , x , x , x , x , x , x , x , x , 145 146 147 148 149 150 151 152 153 154 155 156 x , x , x , x , x , x , x , x , x , x , x , x , 157 158 159 160 161 162 163 164 165 166 167 168 x , x , x , x , x , x , x , x , x , x , x , x , 169 170 171 172 173 174 175 176 177 178 179 180 x , x , x , x , x , x , x , x , x , x , x , x , 181 182 183 184 185 186 187 188 189 190 191 192 x , x , x , x , x , x , x , x , x , x , x , x , 193 194 195 196 197 198 199 200 201 202 203 204 x , x , x , x , x , x , x , x , x , x , x , x , 205 206 207 208 209 210 211 212 213 214 215 216 x , x , x , x , x , x , x , x , x , x , x , x , 217 218 219 220 221 222 223 224 225 226 227 228 x , x , x , x , x , x , x , x , x , x , x , x , 229 230 231 232 233 234 235 236 237 238 239 240 x , x , x , x , x , x , x , x , x , x , x , x , 241 242 243 244 245 246 247 248 249 250 251 252 x , x , x , x , x , x , x , x , x , x , x , x , 253 254 255 256 257 258 259 260 261 262 263 264 x , x , x , x , x , x , x , x , x , x , x , x , 265 266 267 268 269 270 271 272 273 274 275 276 x , x , x , x , x , x , x , x , x , x , x , x , 277 278 279 280 281 282 283 284 285 286 287 288 x , x , x , x , x , x , x , x , x , x , x , x , 289 290 291 292 293 294 295 296 297 298 299 300 x , x , x , x , x , x , x , x , x , x , x , x , 301 302 303 304 305 306 307 308 309 310 311 312 x , x , x , x , x , x , x , x , x , x , x , x , 313 314 315 316 317 318 319 320 321 322 323 324 x , x , x , x , x , x , x , x , x , x , x , x , 325 326 327 328 329 330 331 332 333 334 335 336 x , x , x , x , x , x , x , x , x , x , x , x , 337 338 339 340 341 342 343 344 345 346 347 348 x , x , x , x , x , x , x , x , x , x , x , x , 349 350 351 352 353 354 355 356 357 358 359 360 x , x , x , x , x , x , x , x , x , x , x , x , 361 362 363 364 365 366 367 368 369 370 371 372 x , x , x , x , x , x , x , x , x , x , x , x , 373 374 375 376 377 378 379 380 381 382 383 384 x , x , x , x , x , x , x , x , x , x , x , x , 385 386 387 388 389 390 391 392 393 394 395 396 x , x , x , x , x , x , x , x , x , x , x , x , 397 398 399 400 401 402 2 403 3 x , x , x , x - z, x - x z, x - x z, x - x z, 404 4 405 5 406 6 407 7 408 8 x - x z, x - x z, x - x z, x - x z, x - x z, 409 9 410 10 411 11 412 12 413 13 x - x z, x - x z, x - x z, x - x z, x - x z, 414 14 415 15 416 16 417 17 418 18 x - x z, x - x z, x - x z, x - x z, x - x z, 419 19 420 20 421 21 422 22 423 23 x - x z, x - x z, x - x z, x - x z, x - x z, 424 24 425 25 426 26 427 27 428 28 x - x z, x - x z, x - x z, x - x z, x - x z, 429 29 430 30 431 31 432 32 433 33 x - x z, x - x z, x - x z, x - x z, x - x z, 434 34 435 35 436 36 437 37 438 38 x - x z, x - x z, x - x z, x - x z, x - x z, 439 39 440 40 441 41 442 42 443 43 x - x z, x - x z, x - x z, x - x z, x - x z, 444 44 445 45 446 46 447 47 448 48 x - x z, x - x z, x - x z, x - x z, x - x z, 449 49 450 50 451 51 452 52 453 53 x - x z, x - x z, x - x z, x - x z, x - x z, 454 54 455 55 456 56 457 57 458 58 x - x z, x - x z, x - x z, x - x z, x - x z, 459 59 460 60 461 61 462 62 463 63 x - x z, x - x z, x - x z, x - x z, x - x z, 464 64 465 65 466 66 467 67 468 68 x - x z, x - x z, x - x z, x - x z, x - x z, 469 69 470 70 471 71 472 72 473 73 x - x z, x - x z, x - x z, x - x z, x - x z, 474 74 475 75 476 76 477 77 478 78 x - x z, x - x z, x - x z, x - x z, x - x z, 479 79 480 80 481 81 482 82 483 83 x - x z, x - x z, x - x z, x - x z, x - x z, 484 84 485 85 486 86 487 87 488 88 x - x z, x - x z, x - x z, x - x z, x - x z, 489 89 490 90 491 91 492 92 493 93 x - x z, x - x z, x - x z, x - x z, x - x z, 494 94 495 95 496 96 497 97 498 98 x - x z, x - x z, x - x z, x - x z, x - x z, 499 99 500 100 501 101 502 102 503 103 x - x z, x - x z, x - x z, x - x z, x - x z, 504 104 505 105 506 106 507 107 508 108 x - x z, x - x z, x - x z, x - x z, x - x z, 509 109 510 110 511 111 512 112 513 113 x - x z, x - x z, x - x z, x - x z, x - x z, 514 114 515 115 516 116 517 117 518 118 x - x z, x - x z, x - x z, x - x z, x - x z, 519 119 520 120 521 121 522 122 523 123 x - x z, x - x z, x - x z, x - x z, x - x z, 524 124 525 125 526 126 527 127 528 128 x - x z, x - x z, x - x z, x - x z, x - x z, 529 129 530 130 531 131 532 132 533 133 x - x z, x - x z, x - x z, x - x z, x - x z, 534 134 535 135 536 136 537 137 538 138 x - x z, x - x z, x - x z, x - x z, x - x z, 539 139 540 140 541 141 542 142 543 143 x - x z, x - x z, x - x z, x - x z, x - x z, 544 144 545 145 546 146 547 147 548 148 x - x z, x - x z, x - x z, x - x z, x - x z, 549 149 550 150 551 151 552 152 553 153 x - x z, x - x z, x - x z, x - x z, x - x z, 554 154 555 155 556 156 557 157 558 158 x - x z, x - x z, x - x z, x - x z, x - x z, 559 159 560 160 561 161 562 162 563 163 x - x z, x - x z, x - x z, x - x z, x - x z, 564 164 565 165 566 166 567 167 568 168 x - x z, x - x z, x - x z, x - x z, x - x z, 569 169 570 170 571 171 572 172 573 173 x - x z, x - x z, x - x z, x - x z, x - x z, 574 174 575 175 576 176 577 177 578 178 x - x z, x - x z, x - x z, x - x z, x - x z, 579 179 580 180 581 181 582 182 583 183 x - x z, x - x z, x - x z, x - x z, x - x z, 584 184 585 185 586 186 587 187 588 188 x - x z, x - x z, x - x z, x - x z, x - x z, 589 189 590 190 591 191 592 192 593 193 x - x z, x - x z, x - x z, x - x z, x - x z, 594 194 595 195 596 196 597 197 598 198 x - x z, x - x z, x - x z, x - x z, x - x z, 599 199 600 200 601 201 602 202 603 203 x - x z, x - x z, x - x z, x - x z, x - x z, 604 204 605 205 606 206 607 207 608 208 x - x z, x - x z, x - x z, x - x z, x - x z, 609 209 610 210 611 211 612 212 613 213 x - x z, x - x z, x - x z, x - x z, x - x z, 614 214 615 215 616 216 617 217 618 218 x - x z, x - x z, x - x z, x - x z, x - x z, 619 219 620 220 621 221 622 222 623 223 x - x z, x - x z, x - x z, x - x z, x - x z, 624 224 625 225 626 226 627 227 628 228 x - x z, x - x z, x - x z, x - x z, x - x z, 629 229 630 230 631 231 632 232 633 233 x - x z, x - x z, x - x z, x - x z, x - x z, 634 234 635 235 636 236 637 237 638 238 x - x z, x - x z, x - x z, x - x z, x - x z, 639 239 640 240 641 241 642 242 643 243 x - x z, x - x z, x - x z, x - x z, x - x z, 644 244 645 245 646 246 647 247 648 248 x - x z, x - x z, x - x z, x - x z, x - x z, 649 249 650 250 651 251 652 252 653 253 x - x z, x - x z, x - x z, x - x z, x - x z, 654 254 655 255 656 256 657 257 658 258 x - x z, x - x z, x - x z, x - x z, x - x z, 659 259 660 260 661 261 662 262 663 263 x - x z, x - x z, x - x z, x - x z, x - x z, 664 264 665 265 666 266 667 267 668 268 x - x z, x - x z, x - x z, x - x z, x - x z, 669 269 670 270 671 271 672 272 673 273 x - x z, x - x z, x - x z, x - x z, x - x z, 674 274 675 275 676 276 677 277 678 278 x - x z, x - x z, x - x z, x - x z, x - x z, 679 279 680 280 681 281 682 282 683 283 x - x z, x - x z, x - x z, x - x z, x - x z, 684 284 685 285 686 286 687 287 688 288 x - x z, x - x z, x - x z, x - x z, x - x z, 689 289 690 290 691 291 692 292 693 293 x - x z, x - x z, x - x z, x - x z, x - x z, 694 294 695 295 696 296 697 297 698 298 x - x z, x - x z, x - x z, x - x z, x - x z, 699 299 700 300 701 301 702 302 703 303 x - x z, x - x z, x - x z, x - x z, x - x z, 704 304 705 305 706 306 707 307 708 308 x - x z, x - x z, x - x z, x - x z, x - x z, 709 309 710 310 711 311 712 312 713 313 x - x z, x - x z, x - x z, x - x z, x - x z, 714 314 715 315 716 316 717 317 718 318 x - x z, x - x z, x - x z, x - x z, x - x z, 719 319 720 320 721 321 722 322 723 323 x - x z, x - x z, x - x z, x - x z, x - x z, 724 324 725 325 726 326 727 327 728 328 x - x z, x - x z, x - x z, x - x z, x - x z, 729 329 730 330 731 331 732 332 733 333 x - x z, x - x z, x - x z, x - x z, x - x z, 734 334 735 335 736 336 737 337 738 338 x - x z, x - x z, x - x z, x - x z, x - x z, 739 339 740 340 741 341 742 342 743 343 x - x z, x - x z, x - x z, x - x z, x - x z, 744 344 745 345 746 346 747 347 748 348 x - x z, x - x z, x - x z, x - x z, x - x z, 749 349 750 350 751 351 752 352 753 353 x - x z, x - x z, x - x z, x - x z, x - x z, 754 354 755 355 756 356 757 357 758 358 x - x z, x - x z, x - x z, x - x z, x - x z, 759 359 760 360 761 361 762 362 763 363 x - x z, x - x z, x - x z, x - x z, x - x z, 764 364 765 365 766 366 767 367 768 368 x - x z, x - x z, x - x z, x - x z, x - x z, 769 369 770 370 771 371 772 372 773 373 x - x z, x - x z, x - x z, x - x z, x - x z, 774 374 775 375 776 376 777 377 778 378 x - x z, x - x z, x - x z, x - x z, x - x z, 779 379 780 380 781 381 782 382 783 383 x - x z, x - x z, x - x z, x - x z, x - x z, 784 384 785 385 786 386 787 387 788 388 x - x z, x - x z, x - x z, x - x z, x - x z, 789 389 790 390 791 391 792 392 793 393 x - x z, x - x z, x - x z, x - x z, x - x z, 794 394 795 395 796 396 797 397 798 398 x - x z, x - x z, x - x z, x - x z, x - x z, 799 399 800 400 2 801 401 2 x - x z, x - x z + z + y, x - x z + x z + x y] > > time()-st; 102.108 > > > # DZ, n=500 and (0,0) is 1002-fold zero and index is 1002. > > mroot:=Vector([0,0,0]); [0] [ ] mroot := [0] [ ] [0] > > lsys:=[x^2*sin(y),y-z^2,z+sin(x^500)]; 2 2 500 lsys := [x sin(y), y - z , z + sin(x )] > > st:=time(): > > MultiStructure(lsys,[x,y,z],mroot); MultiStructure: 2 3 4 The dual basis of original polynomial at isolated zero is:, [1, x, x , x , x , 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 x , x , x , x , x , x , x , x , x , x , x , x , x , x , x , 96 97 98 99 100 101 102 103 104 105 106 107 108 x , x , x , x , x , x , x , x , x , x , x , x , x , 109 110 111 112 113 114 115 116 117 118 119 120 x , x , x , x , x , x , x , x , x , x , x , x , 121 122 123 124 125 126 127 128 129 130 131 132 x , x , x , x , x , x , x , x , x , x , x , x , 133 134 135 136 137 138 139 140 141 142 143 144 x , x , x , x , x , x , x , x , x , x , x , x , 145 146 147 148 149 150 151 152 153 154 155 156 x , x , x , x , x , x , x , x , x , x , x , x , 157 158 159 160 161 162 163 164 165 166 167 168 x , x , x , x , x , x , x , x , x , x , x , x , 169 170 171 172 173 174 175 176 177 178 179 180 x , x , x , x , x , x , x , x , x , x , x , x , 181 182 183 184 185 186 187 188 189 190 191 192 x , x , x , x , x , x , x , x , x , x , x , x , 193 194 195 196 197 198 199 200 201 202 203 204 x , x , x , x , x , x , x , x , x , x , x , x , 205 206 207 208 209 210 211 212 213 214 215 216 x , x , x , x , x , x , x , x , x , x , x , x , 217 218 219 220 221 222 223 224 225 226 227 228 x , x , x , x , x , x , x , x , x , x , x , x , 229 230 231 232 233 234 235 236 237 238 239 240 x , x , x , x , x , x , x , x , x , x , x , x , 241 242 243 244 245 246 247 248 249 250 251 252 x , x , x , x , x , x , x , x , x , x , x , x , 253 254 255 256 257 258 259 260 261 262 263 264 x , x , x , x , x , x , x , x , x , x , x , x , 265 266 267 268 269 270 271 272 273 274 275 276 x , x , x , x , x , x , x , x , x , x , x , x , 277 278 279 280 281 282 283 284 285 286 287 288 x , x , x , x , x , x , x , x , x , x , x , x , 289 290 291 292 293 294 295 296 297 298 299 300 x , x , x , x , x , x , x , x , x , x , x , x , 301 302 303 304 305 306 307 308 309 310 311 312 x , x , x , x , x , x , x , x , x , x , x , x , 313 314 315 316 317 318 319 320 321 322 323 324 x , x , x , x , x , x , x , x , x , x , x , x , 325 326 327 328 329 330 331 332 333 334 335 336 x , x , x , x , x , x , x , x , x , x , x , x , 337 338 339 340 341 342 343 344 345 346 347 348 x , x , x , x , x , x , x , x , x , x , x , x , 349 350 351 352 353 354 355 356 357 358 359 360 x , x , x , x , x , x , x , x , x , x , x , x , 361 362 363 364 365 366 367 368 369 370 371 372 x , x , x , x , x , x , x , x , x , x , x , x , 373 374 375 376 377 378 379 380 381 382 383 384 x , x , x , x , x , x , x , x , x , x , x , x , 385 386 387 388 389 390 391 392 393 394 395 396 x , x , x , x , x , x , x , x , x , x , x , x , 397 398 399 400 401 402 403 404 405 406 407 408 x , x , x , x , x , x , x , x , x , x , x , x , 409 410 411 412 413 414 415 416 417 418 419 420 x , x , x , x , x , x , x , x , x , x , x , x , 421 422 423 424 425 426 427 428 429 430 431 432 x , x , x , x , x , x , x , x , x , x , x , x , 433 434 435 436 437 438 439 440 441 442 443 444 x , x , x , x , x , x , x , x , x , x , x , x , 445 446 447 448 449 450 451 452 453 454 455 456 x , x , x , x , x , x , x , x , x , x , x , x , 457 458 459 460 461 462 463 464 465 466 467 468 x , x , x , x , x , x , x , x , x , x , x , x , 469 470 471 472 473 474 475 476 477 478 479 480 x , x , x , x , x , x , x , x , x , x , x , x , 481 482 483 484 485 486 487 488 489 490 491 492 x , x , x , x , x , x , x , x , x , x , x , x , 493 494 495 496 497 498 499 500 501 502 2 x , x , x , x , x , x , x , x - z, x - x z, x - x z, 503 3 504 4 505 5 506 6 507 7 x - x z, x - x z, x - x z, x - x z, x - x z, 508 8 509 9 510 10 511 11 512 12 x - x z, x - x z, x - x z, x - x z, x - x z, 513 13 514 14 515 15 516 16 517 17 x - x z, x - x z, x - x z, x - x z, x - x z, 518 18 519 19 520 20 521 21 522 22 x - x z, x - x z, x - x z, x - x z, x - x z, 523 23 524 24 525 25 526 26 527 27 x - x z, x - x z, x - x z, x - x z, x - x z, 528 28 529 29 530 30 531 31 532 32 x - x z, x - x z, x - x z, x - x z, x - x z, 533 33 534 34 535 35 536 36 537 37 x - x z, x - x z, x - x z, x - x z, x - x z, 538 38 539 39 540 40 541 41 542 42 x - x z, x - x z, x - x z, x - x z, x - x z, 543 43 544 44 545 45 546 46 547 47 x - x z, x - x z, x - x z, x - x z, x - x z, 548 48 549 49 550 50 551 51 552 52 x - x z, x - x z, x - x z, x - x z, x - x z, 553 53 554 54 555 55 556 56 557 57 x - x z, x - x z, x - x z, x - x z, x - x z, 558 58 559 59 560 60 561 61 562 62 x - x z, x - x z, x - x z, x - x z, x - x z, 563 63 564 64 565 65 566 66 567 67 x - x z, x - x z, x - x z, x - x z, x - x z, 568 68 569 69 570 70 571 71 572 72 x - x z, x - x z, x - x z, x - x z, x - x z, 573 73 574 74 575 75 576 76 577 77 x - x z, x - x z, x - x z, x - x z, x - x z, 578 78 579 79 580 80 581 81 582 82 x - x z, x - x z, x - x z, x - x z, x - x z, 583 83 584 84 585 85 586 86 587 87 x - x z, x - x z, x - x z, x - x z, x - x z, 588 88 589 89 590 90 591 91 592 92 x - x z, x - x z, x - x z, x - x z, x - x z, 593 93 594 94 595 95 596 96 597 97 x - x z, x - x z, x - x z, x - x z, x - x z, 598 98 599 99 600 100 601 101 602 102 x - x z, x - x z, x - x z, x - x z, x - x z, 603 103 604 104 605 105 606 106 607 107 x - x z, x - x z, x - x z, x - x z, x - x z, 608 108 609 109 610 110 611 111 612 112 x - x z, x - x z, x - x z, x - x z, x - x z, 613 113 614 114 615 115 616 116 617 117 x - x z, x - x z, x - x z, x - x z, x - x z, 618 118 619 119 620 120 621 121 622 122 x - x z, x - x z, x - x z, x - x z, x - x z, 623 123 624 124 625 125 626 126 627 127 x - x z, x - x z, x - x z, x - x z, x - x z, 628 128 629 129 630 130 631 131 632 132 x - x z, x - x z, x - x z, x - x z, x - x z, 633 133 634 134 635 135 636 136 637 137 x - x z, x - x z, x - x z, x - x z, x - x z, 638 138 639 139 640 140 641 141 642 142 x - x z, x - x z, x - x z, x - x z, x - x z, 643 143 644 144 645 145 646 146 647 147 x - x z, x - x z, x - x z, x - x z, x - x z, 648 148 649 149 650 150 651 151 652 152 x - x z, x - x z, x - x z, x - x z, x - x z, 653 153 654 154 655 155 656 156 657 157 x - x z, x - x z, x - x z, x - x z, x - x z, 658 158 659 159 660 160 661 161 662 162 x - x z, x - x z, x - x z, x - x z, x - x z, 663 163 664 164 665 165 666 166 667 167 x - x z, x - x z, x - x z, x - x z, x - x z, 668 168 669 169 670 170 671 171 672 172 x - x z, x - x z, x - x z, x - x z, x - x z, 673 173 674 174 675 175 676 176 677 177 x - x z, x - x z, x - x z, x - x z, x - x z, 678 178 679 179 680 180 681 181 682 182 x - x z, x - x z, x - x z, x - x z, x - x z, 683 183 684 184 685 185 686 186 687 187 x - x z, x - x z, x - x z, x - x z, x - x z, 688 188 689 189 690 190 691 191 692 192 x - x z, x - x z, x - x z, x - x z, x - x z, 693 193 694 194 695 195 696 196 697 197 x - x z, x - x z, x - x z, x - x z, x - x z, 698 198 699 199 700 200 701 201 702 202 x - x z, x - x z, x - x z, x - x z, x - x z, 703 203 704 204 705 205 706 206 707 207 x - x z, x - x z, x - x z, x - x z, x - x z, 708 208 709 209 710 210 711 211 712 212 x - x z, x - x z, x - x z, x - x z, x - x z, 713 213 714 214 715 215 716 216 717 217 x - x z, x - x z, x - x z, x - x z, x - x z, 718 218 719 219 720 220 721 221 722 222 x - x z, x - x z, x - x z, x - x z, x - x z, 723 223 724 224 725 225 726 226 727 227 x - x z, x - x z, x - x z, x - x z, x - x z, 728 228 729 229 730 230 731 231 732 232 x - x z, x - x z, x - x z, x - x z, x - x z, 733 233 734 234 735 235 736 236 737 237 x - x z, x - x z, x - x z, x - x z, x - x z, 738 238 739 239 740 240 741 241 742 242 x - x z, x - x z, x - x z, x - x z, x - x z, 743 243 744 244 745 245 746 246 747 247 x - x z, x - x z, x - x z, x - x z, x - x z, 748 248 749 249 750 250 751 251 752 252 x - x z, x - x z, x - x z, x - x z, x - x z, 753 253 754 254 755 255 756 256 757 257 x - x z, x - x z, x - x z, x - x z, x - x z, 758 258 759 259 760 260 761 261 762 262 x - x z, x - x z, x - x z, x - x z, x - x z, 763 263 764 264 765 265 766 266 767 267 x - x z, x - x z, x - x z, x - x z, x - x z, 768 268 769 269 770 270 771 271 772 272 x - x z, x - x z, x - x z, x - x z, x - x z, 773 273 774 274 775 275 776 276 777 277 x - x z, x - x z, x - x z, x - x z, x - x z, 778 278 779 279 780 280 781 281 782 282 x - x z, x - x z, x - x z, x - x z, x - x z, 783 283 784 284 785 285 786 286 787 287 x - x z, x - x z, x - x z, x - x z, x - x z, 788 288 789 289 790 290 791 291 792 292 x - x z, x - x z, x - x z, x - x z, x - x z, 793 293 794 294 795 295 796 296 797 297 x - x z, x - x z, x - x z, x - x z, x - x z, 798 298 799 299 800 300 801 301 802 302 x - x z, x - x z, x - x z, x - x z, x - x z, 803 303 804 304 805 305 806 306 807 307 x - x z, x - x z, x - x z, x - x z, x - x z, 808 308 809 309 810 310 811 311 812 312 x - x z, x - x z, x - x z, x - x z, x - x z, 813 313 814 314 815 315 816 316 817 317 x - x z, x - x z, x - x z, x - x z, x - x z, 818 318 819 319 820 320 821 321 822 322 x - x z, x - x z, x - x z, x - x z, x - x z, 823 323 824 324 825 325 826 326 827 327 x - x z, x - x z, x - x z, x - x z, x - x z, 828 328 829 329 830 330 831 331 832 332 x - x z, x - x z, x - x z, x - x z, x - x z, 833 333 834 334 835 335 836 336 837 337 x - x z, x - x z, x - x z, x - x z, x - x z, 838 338 839 339 840 340 841 341 842 342 x - x z, x - x z, x - x z, x - x z, x - x z, 843 343 844 344 845 345 846 346 847 347 x - x z, x - x z, x - x z, x - x z, x - x z, 848 348 849 349 850 350 851 351 852 352 x - x z, x - x z, x - x z, x - x z, x - x z, 853 353 854 354 855 355 856 356 857 357 x - x z, x - x z, x - x z, x - x z, x - x z, 858 358 859 359 860 360 861 361 862 362 x - x z, x - x z, x - x z, x - x z, x - x z, 863 363 864 364 865 365 866 366 867 367 x - x z, x - x z, x - x z, x - x z, x - x z, 868 368 869 369 870 370 871 371 872 372 x - x z, x - x z, x - x z, x - x z, x - x z, 873 373 874 374 875 375 876 376 877 377 x - x z, x - x z, x - x z, x - x z, x - x z, 878 378 879 379 880 380 881 381 882 382 x - x z, x - x z, x - x z, x - x z, x - x z, 883 383 884 384 885 385 886 386 887 387 x - x z, x - x z, x - x z, x - x z, x - x z, 888 388 889 389 890 390 891 391 892 392 x - x z, x - x z, x - x z, x - x z, x - x z, 893 393 894 394 895 395 896 396 897 397 x - x z, x - x z, x - x z, x - x z, x - x z, 898 398 899 399 900 400 901 401 902 402 x - x z, x - x z, x - x z, x - x z, x - x z, 903 403 904 404 905 405 906 406 907 407 x - x z, x - x z, x - x z, x - x z, x - x z, 908 408 909 409 910 410 911 411 912 412 x - x z, x - x z, x - x z, x - x z, x - x z, 913 413 914 414 915 415 916 416 917 417 x - x z, x - x z, x - x z, x - x z, x - x z, 918 418 919 419 920 420 921 421 922 422 x - x z, x - x z, x - x z, x - x z, x - x z, 923 423 924 424 925 425 926 426 927 427 x - x z, x - x z, x - x z, x - x z, x - x z, 928 428 929 429 930 430 931 431 932 432 x - x z, x - x z, x - x z, x - x z, x - x z, 933 433 934 434 935 435 936 436 937 437 x - x z, x - x z, x - x z, x - x z, x - x z, 938 438 939 439 940 440 941 441 942 442 x - x z, x - x z, x - x z, x - x z, x - x z, 943 443 944 444 945 445 946 446 947 447 x - x z, x - x z, x - x z, x - x z, x - x z, 948 448 949 449 950 450 951 451 952 452 x - x z, x - x z, x - x z, x - x z, x - x z, 953 453 954 454 955 455 956 456 957 457 x - x z, x - x z, x - x z, x - x z, x - x z, 958 458 959 459 960 460 961 461 962 462 x - x z, x - x z, x - x z, x - x z, x - x z, 963 463 964 464 965 465 966 466 967 467 x - x z, x - x z, x - x z, x - x z, x - x z, 968 468 969 469 970 470 971 471 972 472 x - x z, x - x z, x - x z, x - x z, x - x z, 973 473 974 474 975 475 976 476 977 477 x - x z, x - x z, x - x z, x - x z, x - x z, 978 478 979 479 980 480 981 481 982 482 x - x z, x - x z, x - x z, x - x z, x - x z, 983 483 984 484 985 485 986 486 987 487 x - x z, x - x z, x - x z, x - x z, x - x z, 988 488 989 489 990 490 991 491 992 492 x - x z, x - x z, x - x z, x - x z, x - x z, 993 493 994 494 995 495 996 496 997 497 x - x z, x - x z, x - x z, x - x z, x - x z, 998 498 999 499 1000 500 2 x - x z, x - x z, x - x z + z + y, 1001 501 2 x - x z + x z + x y] > > time()-st; 208.797