Changeset 6f2278 in git for Singular/LIB/fpalgebras.lib
- Timestamp:
- Feb 26, 2018, 2:54:56 PM (6 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- a2cd284766c6d39d5f8d6fb5b7f7f9ebf9d9cb02
- Parents:
- bf691c560475036d6c552dc0ec90b4d67f4c53c0
- File:
-
- 1 edited
-
Singular/LIB/fpalgebras.lib (modified) (18 diffs)
Legend:
- Unmodified
- Added
- Removed
-
Singular/LIB/fpalgebras.lib
rbf691c r6f2278 36 36 int isGroup = 0; 37 37 if (size(#) > 0) {isGroup = #[1];} 38 39 if (isGroup <= 0)38 39 if (isGroup != 0) 40 40 { 41 41 int baseringdef; 42 42 if (defined(basering)) // if a basering is defined, it should be saved for later use 43 {43 { 44 44 def save = basering; 45 45 baseringdef = 1; … … 121 121 122 122 proc baumslag(int m, int n, int d) 123 "USAGE: baumslag(m,n,d)123 "USAGE: baumslag(m,n,d) 124 124 RETURN: a ring containing an ideal I with the required relations 125 125 " … … 147 147 148 148 proc cgP1(int d) 149 " 150 p1 group with the following presentation 151 < x, y | [x, y] = 1 > 149 "USAGE: cgP1(d); d an integer 150 RETURN: ring 151 NOTE: - the ring contains the ideal I, which contains the required relations 152 @* - p1 group with the following presentation 153 @* < x, y | [x, y] = 1 > 154 @* -d gives the degreebound for the Letterplace ring 152 155 " 153 156 { … … 198 201 199 202 proc cgPM(int d) 200 " 201 pm group with the following presentation 202 < x, y, m | [x, y] = m^2 = 1, m^-1*x*m = x, m^-1*y*m = y^-1 > 203 "USAGE: cgPM(d); d an integer 204 RETURN: ring 205 NOTE: - the ring contains the ideal I, which contains the required relations 206 @* - pm group with the following presentation 207 @* < x, y, m | [x, y] = m^2 = 1, m^-1*x*m = x, m^-1*y*m = y^-1 > 208 @* - d gives the degreebound for the Letterplace ring 203 209 " 204 210 { … … 223 229 224 230 proc cgPG(int d) 225 " 226 pg group with the following presentation 227 < x, y, t | [x, y] = 1, t^2 = x, t^-1*y*t = y^-1 > 231 "USAGE: cgPG(d); d an integer 232 RETURN: ring 233 NOTE: - the ring contains the ideal I, which contains the required relations 234 @* - pg group with the following presentation 235 @* < x, y, t | [x, y] = 1, t^2 = x, t^-1*y*t = y^-1 > 236 @* - d gives the degreebound for the Letterplace ring 228 237 " 229 238 { … … 249 258 250 259 proc cgP2MM(int d) 251 " 252 p2mm group with the following presentation 253 < x, y, p, q | [x, y] = [p, q] = p^2 = q^2 = 1, p^-1*x*p = x, q^-1*x*q = x^-1, p^-1*y*p = y^-1, q^-1*y*q = y > 254 Note: More redundandent relations may be added to I 260 "USAGE: cgP2(d); d an integer 261 RETURN: ring 262 NOTE: - the ring contains the ideal I, which contains the required relations 263 @* - p2mm group with the following presentation 264 @* < x, y, p, q | [x, y] = [p, q] = p^2 = q^2 = 1, p^-1*x*p = x, q^-1*x*q = x^-1, p^-1*y*p = y^-1, q^-1*y*q = y > 265 @* - d gives the degreebound for the Letterplace ring 255 266 " 256 267 { … … 276 287 277 288 proc cgP2(int d) 278 " 279 p2 group with the following presentation 280 < x, y, m, t | [x, y] = t^2 = 1, m^2 = y, t^-1*x*t = x, m^-1*x*m = x^-1, t^-1*y*t = y^-1, t^-1*m*t = m^-1 > 289 "USAGE: cgP2(d); d an integer 290 RETURN: ring 291 NOTE: - the ring contains the ideal I, which contains the required relations 292 @* - p2 group with the following presentation 293 @* < x, y, m, t | [x, y] = t^2 = 1, m^2 = y, t^-1*x*t = x, m^-1*x*m = x^-1, t^-1*y*t = y^-1, t^-1*m*t = m^-1 > 294 @* - d gives the degreebound for the Letterplace ring 281 295 " 282 296 { … … 302 316 303 317 proc cgP2GG(int d) 304 " 305 p2gg group with the following presentation 306 < x, y, u, v | [x, y] = (u*v)^2 = 1, u^2 = x, v^2 = y, v^-1*x*v = x^-1, u^-1*y*u = y^-1 > 318 "USAGE: cgP2(d); d an integer 319 RETURN: ring 320 NOTE: - the ring contains the ideal I, which contains the required relations 321 @* - p2gg group with the following presentation 322 @* < x, y, u, v | [x, y] = (u*v)^2 = 1, u^2 = x, v^2 = y, v^-1*x*v = x^-1, u^-1*y*u = y^-1 > 323 @* - d gives the degreebound for the Letterplace ring 307 324 " 308 325 { … … 328 345 329 346 proc cgCM(int d) 330 " 331 cm group with the following presentation 332 < x, y, t | [x, y] = t^2 = 1, t^-1*x*t = x*y, t^-1*y*t = y^-1 > 347 "USAGE: cgCM(d); d an integer 348 RETURN: ring 349 NOTE: - the ring contains the ideal I, which contains the required relations 350 @* - cm group with the following presentation 351 @* < x, y, t | [x, y] = t^2 = 1, t^-1*x*t = x*y, t^-1*y*t = y^-1 > 352 @* - d gives the degreebound for the Letterplace ring 333 353 " 334 354 { … … 354 374 355 375 proc cgC2MM(int d) 356 " 357 c2mm group with the following presentation 358 < x, y, m, r | [x, y] = m^2 = r^2 = 1, m^-1*y*m = y^-1, m^-1*x*m = x*y, r^-1*y*r = y^-1, r^-1*x*r = x^-1, m^-1*r*m = r^-1 > 376 "USAGE: cgC2(d); d an integer 377 RETURN: ring 378 NOTE: - the ring contains the ideal I, which contains the required relations 379 @* - c2mm group with the following presentation 380 @* < x, y, m, r | [x, y] = m^2 = r^2 = 1, m^-1*y*m = y^-1, m^-1*x*m = x*y, r^-1*y*r = y^-1, r^-1*x*r = x^-1, m^-1*r*m = r^-1 > 381 @* - d gives the degreebound for the Letterplace ring 359 382 " 360 383 { … … 380 403 381 404 proc cgP4(int d) 382 " 383 p4 group with the following presentation 384 < x, y, r | [x, y] = r^4 = 1, r^-1*x*r = x^-1, r^-1*x*r = y > 405 "USAGE: cgP4(d); d an integer 406 RETURN: ring 407 NOTE: - the ring contains the ideal I, which contains the required relations 408 @* - p4 group with the following presentation 409 @* < x, y, r | [x, y] = r^4 = 1, r^-1*x*r = x^-1, r^-1*x*r = y > 410 @* - d gives the degreebound for the Letterplace ring 385 411 " 386 412 { … … 406 432 407 433 proc cgP4MM(int d) 408 " 409 p4mm group with the following presentation 410 < x, y, r, m | [x, y] = r^4 = m^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, m^-1*x*m = y, m^-1*r*m = r^-1 > 434 "USAGE: cgP4(d); d an integer 435 RETURN: ring 436 NOTE: - the ring contains the ideal I, which contains the required relations 437 @* - p4mm group with the following presentation 438 @* < x, y, r, m | [x, y] = r^4 = m^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, m^-1*x*m = y, m^-1*r*m = r^-1 > 439 @* - d gives the degreebound for the Letterplace ring 411 440 " 412 441 { … … 432 461 433 462 proc cgP4GM(int d) 434 " 435 p4gm group with the following presentation 436 < x, y, r, t | [x, y] = r^4 = t^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, t^-1*x*t = y, t^-1*r*t = x^-1*r^-1> 463 "USAGE: cgP4(d); d an integer 464 RETURN: ring 465 NOTE: - the ring contains the ideal I, which contains the required relations 466 @* - p4gm group with the following presentation 467 @* < x, y, r, t | [x, y] = r^4 = t^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, t^-1*x*t = y, t^-1*r*t = x^-1*r^-1> 468 @* - d gives the degreebound for the Letterplace ring 437 469 " 438 470 { … … 458 490 459 491 proc cgP3(int d) 460 " 461 p3 group with the following presentation 462 < x, y, r | [x, y] = r^3 = 1, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1> 492 "USAGE: cgP3(d); d an integer 493 RETURN: ring 494 NOTE: - the ring contains the ideal I, which contains the required relations 495 @* - p3 group with the following presentation 496 @* < x, y, r | [x, y] = r^3 = 1, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1> 497 @* - d gives the degreebound for the Letterplace ring 463 498 " 464 499 { … … 483 518 484 519 proc cgP31M(int d) 485 " 486 p31m group with the following presentation 487 < x, y, r, t | [x, y] = r^2 = t^2 = (t*r)^3 = 1, r^-1*x*r = x, t^-1*y*t = y, t^-1*x*t = x^-1*y, r^-1*y*r = x*y^-1 > 520 "USAGE: cgP3(d); d an integer 521 RETURN: ring 522 NOTE: - the ring contains the ideal I, which contains the required relations 523 @* - p31m group with the following presentation 524 @* < x, y, r, t | [x, y] = r^2 = t^2 = (t*r)^3 = 1, r^-1*x*r = x, t^-1*y*t = y, t^-1*x*t = x^-1*y, r^-1*y*r = x*y^-1 > 525 @* - d gives the degreebound for the Letterplace ring 488 526 " 489 527 { … … 511 549 512 550 proc cgP3M1(int d) 513 " 514 p3m1 group with the following presentation 515 < x, y, r, m | [x, y] = r^3 = m^2 = 1, m^-1*r*m = r^2, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1, m^-1*x*m = x^-1, m^-1*y*m = x^-1*y > 551 "USAGE: cgP3(d); d an integer 552 RETURN: ring 553 NOTE: - the ring contains the ideal I, which contains the required relations 554 @* - p3m1 group with the following presentation 555 @* < x, y, r, m | [x, y] = r^3 = m^2 = 1, m^-1*r*m = r^2, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1, m^-1*x*m = x^-1, m^-1*y*m = x^-1*y > 556 @* - d gives the degreebound for the Letterplace ring 516 557 " 517 558 { … … 537 578 538 579 proc cgP6(int d) 539 " 540 p6 group with the following presentation 541 < x, y, r | [x, y] = r^6 = 1, r^-1*x*r = y, r^-1*y*r = x^-1*y> 580 "USAGE: cgP6(d); d an integer 581 RETURN: ring 582 NOTE: - the ring contains the ideal I, which contains the required relations 583 @* - p6 group with the following presentation 584 @* < x, y, r | [x, y] = r^6 = 1, r^-1*x*r = y, r^-1*y*r = x^-1*y> 585 @* - d gives the degreebound for the Letterplace ring 542 586 " 543 587 { … … 563 607 564 608 proc cgP6MM(int d) 565 " 566 p6mm group with the following presentation 567 < x, y, r, m | [x, y] = r^6 = m^2 = 1, r^-1*y*r = x^-1*y, r^-1*x*r = y, m^-1*x*m = x^-1, m^-1*y*m = x^-1*y, m^-1*r*m = r^-1*y> 609 "USAGE: cgP6(d); d an integer 610 RETURN: ring 611 NOTE: - the ring contains the ideal I, which contains the required relations 612 @* - p6mm group with the following presentation 613 @* < x, y, r, m | [x, y] = r^6 = m^2 = 1, r^-1*y*r = x^-1*y, r^-1*x*r = y, m^-1*x*m = x^-1, m^-1*y*m = x^-1*y, m^-1*r*m = r^-1*y> 614 @* - d gives the degreebound for the Letterplace ring 568 615 " 569 616 {
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