Changeset 53ec64 in git for Singular/LIB/mprimdec.lib
- Timestamp:
- Mar 30, 2009, 3:49:52 PM (15 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 90adba8c39bf90d8c295b21a126ebc3b0e946470
- Parents:
- 3cc9dd65b81fdfcf2ee73067b26d8e81b3b7ed29
- File:
-
- 1 edited
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Singular/LIB/mprimdec.lib (modified) (21 diffs)
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Singular/LIB/mprimdec.lib
r3cc9dd r53ec64 1 // $Id: mprimdec.lib,v 1. 6 2006-07-25 17:54:27 Singular Exp $1 // $Id: mprimdec.lib,v 1.7 2009-03-30 13:49:52 dreyer Exp $ 2 2 /////////////////////////////////////////////////////////////////////////////// 3 3 // mprimdec.lib … … 10 10 // 11 11 // $Log: not supported by cvs2svn $ 12 // Revision 1.6 2006/07/25 17:54:27 Singular 13 // *hannes: Michael C. 14 // 12 15 // Revision 1.5 2005/04/28 09:22:17 Singular 13 16 // *hannes/lossen: new ring.lib … … 23 26 /////////////////////////////////////////////////////////////////////////////// 24 27 25 version="$Id: mprimdec.lib,v 1. 6 2006-07-25 17:54:27 Singular Exp $";28 version="$Id: mprimdec.lib,v 1.7 2009-03-30 13:49:52 dreyer Exp $"; 26 29 category="Commutative Algebra"; 27 30 … … 34 37 @*They also work in positive characteristic >> 0. 35 38 @*In small characteristic and for algebraic extensions, the 36 procedures cia Gianni Trage, Zacharias may not terminate.39 procedures via Gianni, Trager, Zacharias may not terminate. 37 40 38 41 PROCEDURES: … … 56 59 GTZopt(N[,check[,ann]]); a faster version of GTZmod 57 60 zeroOpt(N[,check[,ann]]); a faster version of zeroMod 58 clrSBmod(N); extracts an minimal SB from a SB59 minSatMod(N,I); minimal saturation of N w.r.t. I60 specialModulesEqual(N1,N2); checks for equality of standard bases of modules61 if N1 is contained in N2 or vice versa62 stdModulesEqual(N1,N2); checks for equality of standard bases63 modulesEqual(N1,N2); checks for equality of modules64 getData(N,l[,i]); extracts oldData and computes the remaining data65 61 "; 66 62 … … 134 130 // PrimdecA(N[,i]) 135 131 // computes a primary decomposition, not necessarily minimal, 136 // using a generalization of the algorithm of S chimoyama/Yokoyama,132 // using a generalization of the algorithm of Shimoyama/Yokoyama, 137 133 // suggested by Hans-Gerd Graebe, Leipzig 138 134 // [Hans-Gert Graebe, Minimal Primary Decompostion … … 145 141 RETURN: list l 146 142 a (not necessarily minimal) primary decomposition of N 147 computed by a generalized version of the algorithm of S chimoyama/Yokoyama,143 computed by a generalized version of the algorithm of Shimoyama/Yokoyama, 148 144 @*if i!=0 is given, the factorizing Groebner is used to compute the 149 145 isolated primes … … 375 371 RETURN: list l 376 372 a minimal primary decomposition of N 377 computed by an generalized version of the algorithm of S chimoyama/Yokoyama,378 @*if i=1 is given, the factorizing Groebner is used373 computed by an generalized version of the algorithm of Shimoyama/Yokoyama, 374 @*if i=1 is given, the factorizing Groebner basis algorithm is used internally. 379 375 EXAMPLE: example modDec; shows an example 380 376 " … … 464 460 RETURN: list l 465 461 the minimal primary decomposition of a zero-dimensional module N, 466 computed by a ge rnalized version of the algorithm of Gianni, Trager and Zacharias462 computed by a generalized version of the algorithm of Gianni, Trager and Zacharias 467 463 NOTE: if the parameter check is given, only components not containing check are computed 468 464 EXAMPLE: example zeroMod; shows an example … … 603 599 RETURN: list l 604 600 the minimal primary decomposition of the module N, 605 computed by a ge rnalized version of the algorithm of Gianny, Trager and Zacharias601 computed by a generalized version of the algorithm of Gianni, Trager and Zacharias 606 602 NOTE: if the parameter check is given, only components not containing check are computed 607 603 EXAMPLE: example GTZmod; shows an example … … 898 894 "USAGE: splitting(N[,check[, ann]]); modul N, module check, ideal ann 899 895 RETURN: (l, check) list l, module check 900 the elements of l consists of a triple with901 [1] of type module [2] and [3] of type ideal896 the elements of l consists of quadruples, where 897 [1] is of type module, [2], [3] and [4] are of type ideal, 902 898 s.th. the intersection of the modules is equal to the 903 899 zero-dimensional module N, furthermore l[j][3]=annil(l[j][1]) 900 and l[j][4] contains internal ideal data; 904 901 if l[j][2]!=0 then the module l[j][1] is primary 905 902 with associated prime l[j][2], and check=intersect(check, l[j][1]) is computed … … 1123 1120 proc primTest(ideal id, list #) 1124 1121 "USAGE: primTest(i[, p]); a zero-dimensional ideal i, irreducible poly p in i 1125 RETURN: if i neither is prime nor ishomogeneous then ideal(0) is returned,1126 else radical(i)1122 RETURN: if i is neither prime nor homogeneous then ideal(0) is returned, 1123 otherwise radical(i) 1127 1124 EXAMPLE: example primTest; shows an example 1128 1125 " … … 1320 1317 proc indSet (ideal @j) 1321 1318 "USAGE: indSet(i); i ideal 1322 RETURN: list with two entr ees1323 both are lists of new varstrings with the dependen d variables1319 RETURN: list with two entries 1320 both are lists of new varstrings with the dependent variables, 1324 1321 the independent set, the ordstring with the corresp. block ordering, 1325 1322 and the integer where the independent set starts in the varstring 1326 NOTE: the first entry gives the strings for all maximal independen dsets1327 the second gives the strings for the independen dsets,1323 NOTE: the first entry gives the strings for all maximal independent sets 1324 the second gives the strings for the independent sets, 1328 1325 which cannot be enhanced 1329 1326 EXAMPLE: example indSet; shows an example … … 1406 1403 the minimal primary decomposition of the module N, 1407 1404 computed by a generalized and optimized version of 1408 the algorithm of Giann y, Trager and Zacharias1405 the algorithm of Gianni, Trager and Zacharias 1409 1406 NOTE: if the parameter check is given, only components 1410 1407 not containing check are computed … … 1732 1729 the minimal primary decomposition of a zero-dimensional module N, 1733 1730 computed by a generalized and optimized version of the algorithm 1734 of Giann y, Trager and Zacharias1731 of Gianni, Trager and Zacharias 1735 1732 NOTE: if the parameter check is given, only components 1736 1733 not containing check are computed … … 1935 1932 ///////////////////////////////////////////////////////////////////////////// 1936 1933 1937 proc clrSBmod (module @N)1934 static proc clrSBmod (module @N) 1938 1935 "USAGE: clrSBmod(N); N module which is SB ordered by monomial ordering 1939 1936 RETURN: module = minimal SB … … 1990 1987 ///////////////////////////////////////////////////////////////////////////// 1991 1988 1992 proc minSatMod(module Nnew, ideal @h)1989 static proc minSatMod(module Nnew, ideal @h) 1993 1990 "USAGE: minSatMod(N, I); module N, ideal I 1994 1991 RETURN: list with 2 elements: … … 2121 2118 ///////////////////////////////////////////////////////////////////////////// 2122 2119 2123 proc specialModulesEqual( module k1, module k2)2120 static proc specialModulesEqual( module k1, module k2) 2124 2121 "USAGE: specialModulesEqual(N1, N2) N1, N2 standard bases of modules, 2125 2122 s.th. N1 is contained in N2 or vice versa … … 2235 2232 ///////////////////////////////////////////////////////////////////////////// 2236 2233 2237 proc stdModulesEqual(module k1, module k2)2234 static proc stdModulesEqual(module k1, module k2) 2238 2235 "USAGE: stdModulesEqual(N1, N2) N1, N2 standard bases of modules, 2239 2236 RETURN: int i … … 2280 2277 ///////////////////////////////////////////////////////////////////////////// 2281 2278 2282 proc modulesEqual( module @k, module @j)2279 static proc modulesEqual( module @k, module @j) 2283 2280 "USAGE: modulesEqual(N1, N2) N1, N2 modules, 2284 2281 RETURN: int i … … 2315 2312 } 2316 2313 2317 proc getData (module @N, list oldData, list #)2314 static proc getData (module @N, list oldData, list #) 2318 2315 "USAGE: getData(N, l[, noCheck]); module N, list l[, int noCheck] 2319 2316 RETURN: (ann, check, M, checked)
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