Changeset 789d6f in git for Singular/LIB/schreyer.lib
 Timestamp:
 Dec 19, 2013, 2:52:39 PM (9 years ago)
 Branches:
 (u'jengelhdatetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '00e2e9c41af3fde1273eb3633f4c0c7c3db2579d')
 Children:
 b1645e52df1f9ba737d354f5a3f4bebff0aac7cd
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 4821a301f6cf9983952236a781877498075ab2e9
 gitauthor:
 Oleksandr Motsak <motsak@mathematik.unikl.de>20131219 14:52:39+01:00
 gitcommitter:
 Oleksandr Motsak <motsak@mathematik.unikl.de>20131219 17:09:18+01:00
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Singular/LIB/schreyer.lib
r4821a3 r789d6f 3 3 category="General purpose"; 4 4 info=" 5 LIBRARY: schreyer.lib Helpers for computing a Schreyer resolution in derham.lib5 LIBRARY: schreyer.lib Helpers for computing a Schreyer resolution in @code{derham.lib} 6 6 AUTHOR: Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.unikl.de} 7 KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy 7 8 8 9 PROCEDURES: 9 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 10 Sres(M,len) compute Schreyer resolution of module M of maximal length len 11 Ssyz(M) compute Schreyer resolution of module M of length 1 12 Scontinue(len) extend currently active resolution by (at most) len syszygies 13 14 14 NOTE: requires the dynamic or builtin module: syzextra 15 15 "; … … 394 394 "USAGE: Sres(module M, int len) 395 395 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 MRES396 PURPOSE: computes a Schreyer resolution of (basering^rank(M))/M with at most len syzygy modules 397 NOTE: input is a set of vectors M over a basering. The ring basering may be noncommutative. 398 @* If given len is zero then nvars(basering) + 1 is used instead. 399 @* Schreyer resolution is represented by a list of modules RES and a module MRES 400 400 belonging to a specially constructed ring, which is endowed with a Schreyer ordering. 401 401 @* The list of modules RES contains the images of maps (also called syzygies) subsituting the 402 402 computed beginning of a Schreyer free resolution of (baseRing^rank(M))/M. 403 403 @* The leading zero map RES[1] with rank(M) zero generators indicates that the image of 404 404 the first differential map is zero. The second map RES[2] is given by M, which indicates that 405 405 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) 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 @* Schreyer ordering extends an arbitrary starting module ordeing (defined by basering) 410 409 and is extended to higher syzygt modules using the following definition: 411 412 410 @* a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ), 411 @* where d(a) is the image of a under the differential (given by MRES), 413 412 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) + 1 413 @* Syzygies are given by Groebner bases with respect to corresponding Schreyer orderings. 415 414 EXAMPLE: example Sres; shows an example 416 415 "
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