Changeset 33694c in git for Singular/LIB/schreyer.lib
 Timestamp:
 Dec 19, 2013, 2:34:22 PM (10 years ago)
 Branches:
 (u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
 Children:
 1966e4f1761815810664e4021de885a45ad57a25
 Parents:
 ec896331e6b7d2d8e1e5007a0322eb8424cd90cd
 gitauthor:
 Oleksandr Motsak <motsak@mathematik.unikl.de>20131219 14:34:22+01:00
 gitcommitter:
 Oleksandr Motsak <motsak@mathematik.unikl.de>20131219 14:35:31+01:00
 File:

 1 edited
Legend:
 Unmodified
 Added
 Removed

Singular/LIB/schreyer.lib
rec89633 r33694c 3 3 category="General purpose"; 4 4 info=" 5 LIBRARY: schreyer.lib Helpers for working with the Schreyer induced ordering5 LIBRARY: schreyer.lib Helpers for computing a Schreyer resolution in derham.lib 6 6 AUTHOR: Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.unikl.de} 7 7 8 8 PROCEDURES: 9 Sres(M,l ) Schreyer resolution of module M of maximal length l10 Ssyz(M) Schreyer resolution of module M of length 111 Scontinue(l ) continue the resolution computation by most l steps12 13 KEYWORDS: syzygy; Schreyer induced ordering; Schreyer free resolution14 NOTE: requires the dynamic module: syzextra9 Sres(M,len) compute Schreyer resolution of module M of maximal length len 10 Ssyz(M) compute Schreyer resolution of module M of length 1 11 Scontinue(len) extend currently active resolution by (at most) len syszygies 12 13 KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy 14 NOTE: requires the dynamic or builtin module: syzextra 15 15 "; 16 16 … … 329 329 330 330 proc Scontinue(int l) 331 "USAGE: Scontinue(l) 332 RETURN: nothing, instead it changes RES and MRES variables in the current ring 333 PURPOSE: computes further (at most l) syzygies 334 NOTE: must be used within a ring returned by Sres or Ssyz. RES and MRES are 335 explained in Sres 331 "USAGE: Scontinue(int len) 332 RETURN: nothing, instead it changes the currently active resolution 333 PURPOSE: extends the currently active resolution by at most len syzygies 334 NOTE: must be used within a ring returned by Sres or Ssyz 336 335 EXAMPLE: example Scontinue; shows an example 337 336 " … … 361 360 362 361 proc Ssyz(module M) 363 "USAGE: Ssyz( M)364 RETURN: ring, containing a list of modules RES and a module MRES365 PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)366 NOTE: The output is explained in Sres362 "USAGE: Ssyz(module M) 363 RETURN: ring, containing a Schreyer resolution 364 PURPOSE: computes a Schreyer resolution of M of length 1 365 NOTE: the output is explained in Sres 367 366 EXAMPLE: example Ssyz; shows an example 368 367 " … … 393 392 394 393 proc Sres(module M, int l) 395 "USAGE: Sres(M, l) 396 RETURN: ring, containing a list of modules RES and a module MRES 397 PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer 398 induced ordering with gen(i) > gen(j) if i > j, provided both gens 399 are from the same syzygy level. 400 NOTE: RES contains the images of maps subsituting the beginning of the 401 Schreyer free resolution of baseRing^r/M, while MRES is a sum of 402 these images in a big free sum, containing all the syzygy modules. 403 The syzygy modules are shifted so that gen(i) correspons to MRES[i]. 404 The leading zero module RES[0] indicates the fact that coker of the 405 first map is zero. The number of zeroes inducates the rank of input. 406 NOTE: If l == 0 then l is set to be nvars(basering) + 1 394 "USAGE: Sres(module M, int len) 395 RETURN: ring, containing a Schreyer resolution 396 PURPOSE: computes a Schreyer resolution of (basering^rank(M))/M with at most len syzygy modules, 397 computed with respect to a Schreyer (induced) ordering. 398 NOTE: Input is a set of vectors M over a basering. basering may be noncommutative. 399 NOTE: Schreyer resolution is represented by a list of modules RES and a module MRES 400 belonging to a specially constructed ring, which is endowed with a Schreyer ordering. 401 The list of modules RES contains the images of maps (also called syzygies) subsituting the 402 computed beginning of a Schreyer free resolution of (baseRing^rank(M))/M. 403 The leading zero map RES[1] with rank(M) zero generators indicates that the image of 404 the first differential map is zero. The second map RES[2] is given by M, which indicates that 405 the resolution is of (baseRing^rank(M))/M is being computed. 406 The module MRES is a direct sum of modules from RES and comprises all computed differential maps. 407 Syzygies are shifted so that gen(i) is mapped to MRES[i] under the differential. 408 Syzygies are given by Groebner bases with respect to corresponding Schreyer orderings. 409 NOTE: Schreyer ordering extends an arbitrary starting module ordeing (defined by basering) 410 and is extended to higher syzygt modules using the following definition: 411 a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ), 412 where d(a) is the image of a under the differential (given by MRES), 413 and comp(a) is the mod. component, for any module terms a and b. 414 NOTE: If len == 0 then len is set to be nvars(basering) + 1 407 415 EXAMPLE: example Sres; shows an example 408 416 "
Note: See TracChangeset
for help on using the changeset viewer.