*----* 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(6,8,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 8th 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 19:58:29 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, [2, 0, 0, 1, 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, [0, 0, 2, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 3, 0, 0, 0, 0] 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 30 2796897 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:58:30 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 10 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:58:30 CEST 2001 Info: Time: 10 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 5 initial monomials ..... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 5 Skiped: 3 Char Col: 0 Mgs: 2 Info: 3 0 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:58:30 CEST 2001 Info: Time: 0 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 1, 0, 1, 0, 0] Info: [1, 1, 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 10 initial monomials ......pp.... Info: Applying Gauss Elimination [5:2]. Info: Extracting initial monomials that are not hit Info: Dim: 10 Skiped: 6 Char Col: 2 Mgs: 2 Info: 4 20 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:58:30 CEST 2001 Info: Time: 20 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 1, 0, 1, 1, 0] Info: [1, 1, 1, 1, 0, 0] 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 15 initial monomials ...........pp.... Info: Applying Gauss Elimination [10:2]. Info: Extracting initial monomials that are not hit Info: Dim: 15 Skiped: 12 Char Col: 2 Mgs: 1 Info: 5 30 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:58:31 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: 1 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 0] 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 29 initial monomials .................pp...pp...p.p.p.p..p. Info: Applying Gauss Elimination [16:2][19:2].[22:2][23:2][24:2][25:2].. Info: Extracting initial monomials that are not hit Info: Dim: 29 Skiped: 17 Char Col: 9 Mgs: 3 Info: 6 70 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:58:31 CEST 2001 Info: Time: 70 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, 1, 1, 1, 1] Info: [2, 2, 1, 0, 1, 0] Info: [3, 2, 0, 0, 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 41 initial monomials .......................ppp.p..pp.....pp.p...p.p.pp..p.p.p Info: Applying Gauss Elimination [22:3][23:2][25:2]..[30:2][31:2][34:2][35:2][36:3][37:3].[39:2][40:2]Info: Extracting initial monomials that are not hit Info: Dim: 41 Skiped: 26 Char Col: 14 Mgs: 1 Info: 7 120 2911585 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:58:31 CEST 2001 Info: Time: 120 ms Info: Memory: 2911 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [3, 2, 0, 0, 1, 1] Info: -------------------------------------- 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 68 initial monomials ..............................pp.pp....p.....p.p..p.p.p.p..p.pppp.pp..p..p\ ..p....pp..p.p.pp..p.p.p Info: Applying Gauss Elimination [29:2][30:2][34:2][39:2][40:2][42:2][43:2][44:2][45:2].[47:2][48:5][49:4][50:3][51:3][53:2][54:2][55:2][59:4][61:4][62:3][63:3][64:4][65:4][66:2][67:4]Info: Extracting initial monomials that are not hit Info: Dim: 68 Skiped: 41 Char Col: 26 Mgs: 1 Info: 8 260 2977121 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:58:31 CEST 2001 Info: Time: 260 ms Info: Memory: 2977 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [3, 2, 0, 1, 1, 1] Info: -------------------------------------- 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 98 initial monomials ............................................pp...pp..p..p.p.p...p.pp.p...p\ p.pp.pp.......p.p.p.p.pp.pp..p.p.p.pp...p.p.p.pp.pp.pp..p.p....p.p.p.p Info: Applying Gauss Elimination [43:2][46:2][48:2]..[51:2][52:2].[56:3][57:3][60:2][61:2][62:2][69:2][70:2].[72:4][73:6][74:3][75:4][76:2][77:2][78:5][79:5][80:3][81:4][82:4][83:5][84:3][85:6][86:6][87:8][88:8][89:2][90:2][94:5][95:6][96:5][97:7]Info: Extracting initial monomials that are not hit Info: Dim: 98 Skiped: 58 Char Col: 39 Mgs: 1 Info: 9 430 3059041 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 9: Date: Wed May 2 19:58:32 CEST 2001 Info: Time: 430 ms Info: Memory: 3059 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [3, 2, 0, 2, 1, 1] Info: -------------------------------------- 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 147 initial monomials ....................................................pp...p................\ ...p.p.....p.p.pp..p.ppp.pppp.ppp....pp.pp.ppp.....p.p.pp.pp.p...p.pp.p.pp\ .....pp.....p.p.pp.pp....p.p.pp.p.pp.p.p.p.p..p.pp..p.p.p.pp.pp.p..p.p.p Info: Applying Gauss Elimination [51:2][54:2][73:2][74:2][79:2][80:2][81:3][83:2][84:3][85:5][86:5][87:3][90:3][91:2][92:6][93:3].[95:5][96:3][97:4][98:4][99:4][100:5][101:7][104:4][105:5][106:4][107:7][112:5].[118:7][119:10][120:11][121:9][122:4][123:8][124:6][125:5][126:11][127:8][128:12]..[131:3][132:11][133:7][134:12][135:13][136:14][137:3][138:3][139:2][140:10][141:12].[144:10][145:15][146:15]Info: Extracting initial monomials that are not hit Info: Dim: 147 Skiped: 89 Char Col: 58 Mgs: 0 Info: 10 720 3157345 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 10: Date: Wed May 2 19:58:33 CEST 2001 Info: Time: 720 ms Info: Memory: 3157 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: Constructing the initial poset at degree 11 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 202 initial monomials ..........................................................................\ ...................pp.p.....pp.pp.pp.pp.p..p...p......p............p.p.p.p\ .p.p.p.p.p.p.p.p.p.p.ppp.pppp.ppp.p.p.p.ppp.pppp.ppppp...p...p.p.p.ppp..p.\ p...p.p.pp.pp.p.pp...p.p.p.pp...p...p.p.p.p.pp.p.pp...p.p.p.pp.p.p.p.pp.pp\ ..p.p.p.p Info: Applying Gauss Elimination [92:2][93:2][98:2][99:2][100:2][101:2][102:2][104:2][107:3][113:2][125:3][126:2].[128:2][129:3].[131:2][132:2][133:2][134:2][135:2].[137:3][138:3][139:6][140:6][141:8][142:5][143:2][144:3][145:6][146:6][147:10][148:9][149:4][150:12][151:9][153:2][154:3][155:2][156:6][157:7][158:2][159:5][160:11][161:9][162:2][163:6][164:11][165:13][166:12][167:13][170:2][171:4][172:10][173:14][176:2][179:12][180:5][181:12][182:15][183:15][184:15][185:18][186:20][187:7][188:5][189:15][190:6][191:17].[193:16][194:8][195:21][196:23][197:17][198:4][199:8][200:12][201:22]Info: Extracting initial monomials that are not hit Info: Dim: 202 Skiped: 122 Char Col: 80 Mgs: 0 Info: 11 1120 3370337 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 11: Date: Wed May 2 19:58:34 CEST 2001 Info: Time: 1 s 130 ms Info: Memory: 3386 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 12 Info: Constructing the initial poset at degree 12 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 291 initial monomials ..........................................................................\ .............pp....p..........................p............p...p...p..p.p.\ ....pp.ppp......pp...p..p.p.p...p.p.pp.p.....pp.pp.ppp.pp.pp.....pp.pp.pp.\ ppp.pp.p..p...p.p......p..........p.p.p.p.p.p.p.ppp.pp.pp.p.p.p.pp.p..p.p.\ .p.p.pp.p.p..p.p.ppp.pppp.pppp.pp..pppp.p.p.p.pp.p.ppppp..pp.ppp.p...p.p.p\ p..p.p....p.p.p.p.pp.pp...p.p.p...p.p..p.p.p.p.pp..p.p.p.pp.p.p.p.p.p.p.p.\ p Info: Applying Gauss Elimination [86:2][90:2][116:2][128:2][131:2][134:2][136:2][137:2][142:3][143:4][149:4][152:2][153:3][154:3][155:5][156:4][159:3][160:2][161:4][162:3][167:2][168:5][169:3][170:4][171:7][176:2][177:2][178:2][179:3][180:5][181:5][183:2][186:3][187:6][193:3][203:2][204:5][205:5][206:3][207:7][208:6][209:9][210:7][211:7][212:4][213:5][214:3][215:9][216:6][217:6][218:4][219:2][220:2][222:6][223:11][224:12][225:10][226:8][227:10][228:3][229:5][230:18][231:12][232:15][233:18][234:10][235:21][236:18][237:2][238:4][239:5][240:3][241:12][242:22][243:7][244:19][245:19][246:14][247:27][248:2][249:2][250:4][251:14][252:2][253:5][254:18][255:26][257:4][258:5][259:16][260:9][261:26][262:15][265:3][266:3][267:17][270:17][271:23][272:21][273:23][274:16][275:25][276:19][277:32][278:32][279:29][280:34][281:5][282:19][283:33][284:2][285:21][286:28][287:32][288:37][289:21][290:37]Info: Extracting initial monomials that are not hit Info: Dim: 291 Skiped: 174 Char Col: 117 Mgs: 0 Info: 12 1810 3648865 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 12: Date: Wed May 2 19:58:36 CEST 2001 Info: Time: 1 s 810 ms Info: Memory: 3648 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Updating the degreeBound to 9 which is optimal! Info: Total time: 5 s 80 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 19:58:36 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms