*----* MuPAD 2.0.0 -- The Open Computer Algebra System /| /| *----* | Copyright (c) 1997 - 2000 by SciFace Software | *--|-* All rights reserved. |/ |/ *----* Licensed to: Nicolas M. Thiery >> read("testDegreeBounds.mu"): compTGroupF(6,6,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 6th transitive permutation \ group on 6 variables in characteristic 0. Info: Module GLIP version 0.4 ready. Type GLIP::doc(); for usage informati\ on. Info: ====================================================================\ ========== Info: Computation of a minimal generating set using SAGBI+linear algebra. Info: Version: $Id: comphead.mu,v 1.2 2001/03/21 17:51:40 nthiery Exp $ Date: Wed May 2 19:58:10 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 15 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [0, 3, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [2, 2, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [6, 0, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [4, 1, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 2, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 0, 0, 1] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 12 Info: Constructing a minimal generating set at degree 0 Info: No generators at degree 0 Info: Constructing a minimal generating set at degree 1 Info: Constructing the initial poset at degree 1 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 1 initial monomials . Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 1 Skiped: 0 Char Col: 0 Mgs: 1 Info: 1 20 2796897 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:58:11 CEST 2001 Info: Time: 30 ms Info: Memory: 2829 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [1, 0, 0, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 2 Info: Constructing the initial poset at degree 1 Info: Constructing the initial poset at degree 2 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 3 initial monomials ... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 3 Skiped: 1 Char Col: 0 Mgs: 2 Info: 2 0 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:58:11 CEST 2001 Info: Time: 0 ms Info: Memory: 2846 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 0, 0, 1, 0, 0] Info: [1, 1, 0, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 3 Info: Constructing the initial poset at degree 3 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 7 initial monomials ....... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 7 Skiped: 3 Char Col: 0 Mgs: 4 Info: 3 10 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:58:11 CEST 2001 Info: Time: 10 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 4 Info: -------------------------------------- Info: [1, 1, 0, 0, 1, 0] Info: [1, 1, 0, 1, 0, 0] Info: [1, 1, 1, 0, 0, 0] Info: [2, 0, 1, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 4 Info: Constructing the initial poset at degree 4 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 13 initial monomials .......pp...... Info: Applying Gauss Elimination [6:2]. Info: Extracting initial monomials that are not hit Info: Dim: 13 Skiped: 8 Char Col: 2 Mgs: 3 Info: 4 30 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:58:11 CEST 2001 Info: Time: 30 ms Info: Memory: 2878 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 3 Info: -------------------------------------- Info: [1, 1, 0, 1, 1, 0] Info: [1, 1, 1, 1, 0, 0] Info: [2, 0, 1, 0, 0, 1] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 5 Info: Constructing the initial poset at degree 5 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 23 initial monomials ......pp....pp.p..p.p.p.pp....pp... Info: Applying Gauss Elimination [5:2].[9:2]..[13:2][14:2][15:3][16:2].[19:2]. Info: Extracting initial monomials that are not hit Info: Dim: 23 Skiped: 9 Char Col: 12 Mgs: 2 Info: 5 90 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:58:11 CEST 2001 Info: Time: 90 ms Info: Memory: 2878 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 0] Info: [2, 0, 1, 1, 0, 1] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 6 Info: Constructing the initial poset at degree 6 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 41 initial monomials .........pp..p..p.p..p.p.ppp.pp.pp.....pp.pp..p.pp.p..p.pp.p.p.p...p.. Info: Applying Gauss Elimination [8:2][10:2][12:2][13:2][15:2][16:2][17:3][18:2][19:3][22:3][23:4][24:2][25:3][27:2][28:5][29:5][30:4][31:3][32:5][33:3][34:6][35:6][36:6][37:5][38:3]Info: Extracting initial monomials that are not hit Info: Dim: 41 Skiped: 14 Char Col: 25 Mgs: 2 Info: 6 160 2911585 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:58:12 CEST 2001 Info: Time: 160 ms Info: Memory: 2911 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 1] Info: [2, 0, 1, 2, 0, 1] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 7 Info: Constructing the initial poset at degree 7 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 63 initial monomials .................pp.......ppp.pp..p..p.p.p.p.p.pp.pp..p.p.pp..p.ppp.pppp.p\ ppp.pp.......pp.p.p.ppp....p.p.p..p Info: Applying Gauss Elimination [16:2].[23:3][24:2][26:2].[29:4][30:4].[32:3][33:5][34:3][36:2][37:2][38:6][39:4][40:6][41:3][42:4][43:8][44:4][47:5][48:7][49:3][51:5][52:3][53:8][54:10][55:10][56:10][57:7][58:4][59:5][60:9][61:2][62:8]Info: Extracting initial monomials that are not hit Info: Dim: 63 Skiped: 27 Char Col: 36 Mgs: 0 Info: 7 280 2977121 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:58:12 CEST 2001 Info: Time: 280 ms Info: Memory: 2977 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 8 Info: Constructing the initial poset at degree 8 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 98 initial monomials .......................pp..p....p.p..p.p.......p.ppp.ppp.ppp....p.....pppp\ .pppp.pp..p..p.p.p.p.p.p.p.p.p.p.p.pp.pppp.pp.ppp..p.p.pp.p.pp...pp.ppp.pp\ pp.pppp.....p.p.p.pp..p.p..p.p Info: Applying Gauss Elimination [22:2][24:2][28:2][29:2][31:2][32:2][39:2][40:3][41:3][42:4][46:2][49:3][50:4][51:4][52:5][53:4][55:3][57:2][58:3][59:4][60:4][61:6][62:6][63:7][64:4][65:4][66:5][67:4][68:6][69:13][70:9][71:9][73:2][74:2][75:10][76:16][77:12][78:17][79:8][80:2][81:3][82:11][83:20][85:5][86:10][87:10][88:4][89:17][90:14][91:24][92:13][93:21][94:15][95:11][96:21][97:17]Info: Extracting initial monomials that are not hit Info: Dim: 98 Skiped: 42 Char Col: 56 Mgs: 0 Info: 8 490 3059041 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:58:13 CEST 2001 Info: Time: 490 ms Info: Memory: 3059 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 9 Info: Constructing the initial poset at degree 9 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 146 initial monomials ........................................pp...........pppp.ppp..p.p....p.p.\ p.p.p.p.p..p.p.p.p.pp.pp.........pp..p.ppp.ppppp.ppppp.pppp.ppp....p......\ ppp.ppppp.ppp..p.p.p.p.p.p.p.pp.pp.pp.p.p.p.p.p.pp.pp..p..p.p.pppp.ppp.ppp\ pp.pp.p.p.p.p.pp.pp...pp.pp.ppp...p..p.p.p.p Info: Applying Gauss Elimination [39:2].[50:4][51:3][53:3][54:2].[59:6][60:6].[62:4][63:6][64:2][66:2][67:6].[69:3][70:3][71:3][80:7][81:5][82:5][83:3][84:5][85:9][86:6][87:7][91:2][94:7][95:10][96:9][97:3][98:10][99:8][101:2].[103:7][104:8][105:4][106:7][107:10][108:14][109:6][110:13][111:11][112:11][113:10][114:11][115:6][116:19][117:24][118:16][119:19][120:21][121:2][122:5][123:26][124:16][125:26][126:20][127:2][128:2][129:18][130:32][131:28][132:39][133:35][134:25][135:2][136:4][137:7][138:10][139:35][140:33][141:33][142:15][143:37][144:35][145:38]Info: Extracting initial monomials that are not hit Info: Dim: 146 Skiped: 67 Char Col: 79 Mgs: 0 Info: 9 790 3190113 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 9: Date: Wed May 2 19:58:14 CEST 2001 Info: Time: 790 ms Info: Memory: 3190 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 10 Info: Constructing the initial poset at degree 10 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 210 initial monomials ..................................................ppp..p...p....p.p..p.p..\ .....p............p.ppp.pppp.ppp....p.p.........ppppp.pppppp.ppp..p.p....p\ .p.p.p.p.p.p.p.p.p.p.p.p.p.p.p..p.p.p.p.p.p.p.pp.ppp.pppp.pppp.pppp......p\ ....pp.p.pp..p.ppp.pppp.pppppp.pppppp.pppppp.ppp....p......pp.pppp.pppp.p.\ p.p.p.pp.p.p..p.p.pp.pp.pppp.p.pp.p.p.p.p.p.ppp.p.ppp....p.pp.p.pppp.ppp.p\ .p.p.pp..p.pp..p.p.p Info: Applying Gauss Elimination [49:3][51:2][54:2][58:3][59:3][61:3][62:2][69:2][81:3][82:3][83:4][84:5][88:3][89:2][96:4][97:4][98:5][99:8][100:6][102:4][103:4][107:3][108:4][109:4][110:6][111:11][112:14][113:4][114:3][115:3][116:5][117:6][118:5][119:5][120:14][121:6][122:7][124:2][125:2][126:4][127:7][128:6][129:6][130:3][131:14][132:9][133:5][134:10][135:10][141:3][145:7][146:15][147:15][148:26][149:11][150:3][151:4][152:11][153:17][154:20][155:26][159:2][161:7][162:18][163:20][164:7][165:2][166:10][167:11][168:2][169:8][170:15][171:15][172:25][173:14][174:31][175:26][176:23][177:11][178:35][179:35][180:26][181:9][182:40][183:16][184:20][185:9][186:19][187:41][188:41][189:41][190:49][191:45][192:51][193:53][194:3][195:18][196:24][197:14][198:34][199:2][200:45][201:12][202:57][203:38][204:58][205:28][206:8][207:46][208:59][209:56]Info: Extracting initial monomials that are not hit Info: Dim: 210 Skiped: 99 Char Col: 111 Mgs: 0 Info: 10 1290 3468641 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 10: Date: Wed May 2 19:58:15 CEST 2001 Info: Time: 1 s 290 ms Info: Memory: 3468 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 11 Info: No generators at degree 11 Info: Constructing a minimal generating set at degree 12 Info: Constructing the initial poset at degree 11 Info: Constructing the initial poset at degree 12 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 408 initial monomials ..........................................................................\ .......................ppp..p...p.......p.p..p.p.......p.............p....\ ...............p.ppp.ppppp.ppp....p.p......p.........ppppppp.pppppppp.pppp\ p..p.p.p...p....p.p.p.p.p.p.p.p.p.p.p.p.p.p.p.p..p.p.p.p.p.p.p.p.p.p.p.p.p\ ............p.p.p.p.pp.ppp.ppppp.pppp.ppp.......p.p..........pp.p.pp..p.pp\ p.ppppp.pppppp.pppppppp.ppppppp.pppppp.pppp....p.p.p..........pppp.ppppppp\ p.pppppppp.pppp..p.p..p.p.p.p.p.p.p.p.p.pp.p.p.p.p.p.p.p.p.p.p.p.p.p.p.p.p\ .p.p.p.p.p.pp.pp.pppppp.ppp.pppp.ppppp.p.p.p.p.p.p.p.p.p.p.p.p.p.pp.p.pp.p\ p..p..p.p.ppp.pp.ppp.ppppppppp.ppppp.ppppppp.pppp.....p..p.p.pp.pp.pp.pp..\ .pp.ppp.ppp.pppppp.pppp.....pp.p.p.p.p.p.pp.p.ppp..p.ppp.p...p.pp.p.p.pp.p\ .p.pp..p.p.p.p.p.p Info: Applying Gauss Elimination [96:3][98:2][101:2][108:3][109:3][111:3][112:2][119:2][132:2][151:3][152:3][153:5][154:5][158:3][159:2][165:2][172:4][173:4][174:7][175:10][176:8][178:4][179:6][180:4][183:3][187:3][188:4][189:4][190:7][191:16][192:21][193:4][194:3][195:3][196:5][197:7][198:5][199:5][200:21][201:6][202:7][204:2][205:2][206:4][207:3][208:2][209:3][210:4][211:4][212:3][213:3][214:2][215:2][216:2][228:8][229:7][230:6][231:3][232:21][233:11][234:6][235:10][236:8][243:4][244:2][254:7][255:18][256:18][257:31][258:11][259:3][260:5][261:12][262:23][263:26][264:34][265:14][269:3][270:4][271:6][277:7][278:24][279:27][280:29][281:4][282:15][283:19][284:13][286:3][287:5][289:3][290:5][291:6][292:7][293:16][294:17][295:26][296:11][297:21][298:16][299:18][300:14][301:53][302:32][303:46][304:10][305:31][306:27][307:27][308:40][309:14][310:18][311:10][312:19][313:18][314:30][315:30][316:17][317:4][318:9][319:12][320:45][321:11][322:46][323:15][324:37][325:37][326:2][327:5][328:39][329:6][330:46][331:19][332:23][333:53][334:27][335:2][336:4][337:9][338:42][339:39][340:66][341:65][342:32][343:72][344:63][345:41][346:46][347:3][348:12][349:78][350:42][351:48][352:70][353:71][354:45][359:2][361:15][362:75][363:42][364:90][365:34][366:50][367:32][368:65][369:2][370:77][371:78][372:48][373:42][375:11][376:81][377:28][378:8][379:58][380:40][381:45][382:69][383:78][384:85][385:88][386:69][387:62][388:77][389:82][390:125][391:71][392:118][393:97][394:61][395:103][396:105][397:123][398:6][399:87][400:91][401:134][402:139][403:125][404:85][405:106][406:73][407:77]Info: Extracting initial monomials that are not hit Info: Dim: 408 Skiped: 205 Char Col: 203 Mgs: 0 Info: 12 3660 4042081 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 12: Date: Wed May 2 19:58:19 CEST 2001 Info: Time: 3 s 660 ms Info: Memory: 4042 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Updating the degreeBound to 6 which is optimal! Info: Total time: 7 s 300 ms Info: ====================================================================\ ========== Info: Computation of a minimal generating set using SAGBI+linear algebra. Info: Version: $Id: comphead.mu,v 1.2 2001/03/21 17:51:40 nthiery Exp $ Date: Wed May 2 19:58:19 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms