*----* 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(7,1,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 1st transitive permutation \ group on 7 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 19:58:54 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 21 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [7, 0, 0, 0, 0, 0, \ 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 0, 0, 0, \ 1] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 19 Info: degreeBound: enhancement from the size of the group: 7 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 2420065 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:58:55 CEST 2001 Info: Time: 20 ms Info: Memory: 2420 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, 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 4 initial monomials .... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 4 Skiped: 1 Char Col: 0 Mgs: 3 Info: 2 10 2420065 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:58:55 CEST 2001 Info: Time: 10 ms Info: Memory: 2420 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 3 Info: -------------------------------------- Info: [1, 0, 0, 1, 0, 0, 0] Info: [1, 0, 1, 0, 0, 0, 0] Info: [1, 1, 0, 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 12 initial monomials ............ Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 12 Skiped: 4 Char Col: 0 Mgs: 8 Info: 3 10 2420065 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:58:55 CEST 2001 Info: Time: 10 ms Info: Memory: 2420 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 8 Info: -------------------------------------- Info: [1, 0, 1, 0, 1, 0, 0] Info: [1, 1, 0, 0, 0, 1, 0] Info: [1, 1, 0, 0, 1, 0, 0] Info: [1, 1, 0, 1, 0, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 1] Info: [2, 0, 0, 0, 0, 1, 0] Info: [2, 0, 0, 0, 1, 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 30 initial monomials .........pp.pp.p.p...p.p.............. Info: Applying Gauss Elimination [8:2][9:2][10:2][11:2].... Info: Extracting initial monomials that are not hit Info: Dim: 30 Skiped: 10 Char Col: 8 Mgs: 12 Info: 4 80 2469217 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:58:55 CEST 2001 Info: Time: 80 ms Info: Memory: 2469 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 12 Info: -------------------------------------- Info: [1, 1, 0, 1, 0, 1, 0] Info: [1, 1, 0, 1, 1, 0, 0] Info: [1, 1, 1, 0, 0, 1, 0] Info: [1, 1, 1, 0, 1, 0, 0] Info: [1, 1, 1, 1, 0, 0, 0] Info: [2, 0, 0, 0, 0, 1, 1] Info: [2, 0, 0, 0, 1, 0, 1] Info: [2, 0, 0, 0, 1, 1, 0] Info: [2, 0, 0, 1, 0, 0, 1] Info: [2, 0, 0, 1, 0, 1, 0] Info: [2, 0, 0, 1, 1, 0, 0] Info: [2, 0, 1, 0, 0, 1, 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 66 initial monomials ...........pp.pp.pp...pp.pp.pp..pp.pp.pp..p.p..p..p.p.p.p..p.ppp.ppp.pp..p\ .pp.pp.......p....p.............. Info: Applying Gauss Elimination [10:2][11:2][12:2][15:2][16:2][17:2][19:2][20:2][21:2].[23:3][24:3].[26:3].[28:2][29:3][30:2][31:5][32:2][33:2][34:6][35:5][36:4][37:5][38:4][39:5][40:6][41:6][42:2][43:6][44:7][45:7][46:2][47:3][48:2][49:3][50:3][51:3].. Info: Extracting initial monomials that are not hit Info: Dim: 66 Skiped: 13 Char Col: 41 Mgs: 12 Info: 5 230 2518369 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:58:55 CEST 2001 Info: Time: 230 ms Info: Memory: 2518 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 12 Info: -------------------------------------- Info: [1, 1, 1, 0, 1, 1, 0] Info: [1, 1, 1, 1, 0, 1, 0] Info: [1, 1, 1, 1, 1, 0, 0] Info: [2, 0, 0, 0, 1, 1, 1] Info: [2, 0, 0, 1, 0, 1, 1] Info: [2, 0, 0, 1, 1, 0, 1] Info: [2, 0, 0, 1, 1, 1, 0] Info: [2, 0, 0, 2, 0, 0, 1] Info: [2, 0, 1, 0, 0, 1, 1] Info: [2, 0, 1, 0, 1, 0, 1] Info: [2, 0, 1, 0, 1, 1, 0] Info: [2, 0, 1, 0, 2, 0, 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 132 initial monomials .......................pp.pp.pp.pp.pp.pp.p...p.p.pp...pp.ppp.pppp..ppp.ppp\ .pppp.pp.pppp.ppp.pp.ppp..p.p.p.pp.pp.pp.pp.ppp.ppp.pp.ppp.ppp..pp..p.p.p.\ pp..pp.pp..pp.....p....p.pp.pp.pp..p.pp.pp..p.p..p..p.pp.p..p.pppp.ppp..p.\ pp....p.p..........p............ Info: Applying Gauss Elimination [22:2][23:2][24:2][25:2][26:2][27:2][28:2][31:2][32:2][33:3][36:2][37:3][38:4][40:3][41:3][42:4][43:3][44:5][45:6][46:3][47:6][48:3][49:2][50:3][51:4][52:3][53:3][54:2][55:4][56:4][57:4][58:3][59:6][60:6][61:5][62:7][63:3][64:2][65:3][66:4][67:3][68:4][69:7][70:7][71:4][72:7][73:4][74:4][75:5][76:7][77:10][78:5][79:4][80:4][81:5][82:9][83:9][84:13][85:17][86:6][87:11][88:13][89:17][90:5][91:15][92:21][93:7][94:20][95:17][96:12][97:25][98:18][99:12][100:27][101:32][102:32][103:10][104:38][105:31][106:19][107:30][108:21][109:23][110:26][111:23][112:34][113:34][114:32][115:12][116:21][117:31][118:17][119:28][120:27][121:18][122:20][123:11][124:17][125:11]Info: Extracting initial monomials that are not hit Info: Dim: 132 Skiped: 27 Char Col: 99 Mgs: 6 Info: 6 620 2682209 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:58:56 CEST 2001 Info: Time: 620 ms Info: Memory: 2682 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 6 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 1, 0] Info: [2, 0, 0, 1, 1, 1, 1] Info: [2, 0, 1, 0, 1, 1, 1] Info: [2, 0, 1, 1, 0, 1, 1] Info: [2, 0, 1, 1, 1, 0, 1] Info: [2, 0, 1, 1, 1, 1, 0] 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 246 initial monomials ............................................pp..pp.pp.pp.ppp..........pp.p\ p.pp.ppp.ppp.ppp.....ppp.ppp.ppp.ppp.ppp.ppp..pp.pp.pp.pppp.pp..pp.pp..p.p\ .p.p.p...p.p.pppp..p.p.pppp.pp.pp.ppp.pp.ppp..p.p.p.ppp.pppp.pp.ppp.ppppp.\ ppppppp.pppp.ppppppp.ppppppp.pppp.pppppp..p.pp.pp.pppp.pppp.pppppppp.ppppp\ p.pppp.pppppp...p.pp.pp.pppp...p..p.p.p.p.p.pp.pp.pp.ppp.ppp..pp..p.p.pp.p\ pp.ppp.pppp.pppp..ppp...p.p..ppp....p..p.p..p.....pp..........p.p.p..p.ppp\ p.pppp..p.ppp..p..p.p..p.pp..p.......pp.p..p.pp....p.p..p.ppp.............\ ..... Info: Applying Gauss Elimination [43:2][45:2][46:2][47:2][48:3][58:2][59:2][60:2][61:3][62:3][63:3][68:3][69:3][70:3][71:3][72:3][73:3].[75:3][76:3][77:3][78:4][79:3].[81:3][82:3].[84:3][85:4][86:2][87:4][88:4][91:2][92:3][93:7][95:3][96:3][97:8][98:4][99:5][100:8][101:4][102:10][103:3][104:2][105:2][106:2][107:4][108:6][109:2][110:3][111:5][112:8][113:5][114:8][115:11][116:5][117:13][118:6][119:4][120:6][121:4][122:6][123:8][124:10][125:13][126:8][127:13][128:8][129:3][130:9][131:11][132:8][133:17][134:10][135:3][136:6][137:10][138:3][139:4][140:5][141:5][142:8][143:9][144:12][145:11][146:16][147:18][148:11][149:12][150:5][151:4][152:13][153:9][154:7][155:17][156:13][157:13][158:15][159:20][160:10][161:2][162:11][163:14][164:37][165:50][166:10][167:10][168:18][169:4][170:5][171:9][172:11][173:14][174:23][175:8][176:24][177:18][178:38][179:42][180:13][181:11][182:17][183:16][184:13][185:9][186:16][187:18][188:12][189:24][190:18][191:21][192:29][193:33][194:43][195:69][196:73][197:20][198:59][199:100][200:30][201:47][202:31][203:28][204:46][205:23][206:47][207:82][208:38][209:101][210:24][211:35][212:98][213:98][214:94][215:43][216:100][217:102][218:34][219:97][220:55][221:37][222:82][223:97][224:94][225:58][226:105][227:107][228:106][229:104][230:106][232:105][233:100][234:80][235:97][237:66][238:83][239:35][240:75][242:80]Info: Extracting initial monomials that are not hit Info: Dim: 246 Skiped: 60 Char Col: 180 Mgs: 6 Info: 7 1510 3026273 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:58:58 CEST 2001 Info: Time: 1 s 510 ms Info: Memory: 3452 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 6 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 1, 1] Info: [2, 0, 1, 1, 1, 1, 1] Info: [2, 0, 1, 2, 0, 1, 1] Info: [2, 0, 2, 0, 2, 0, 1] Info: [2, 1, 0, 2, 0, 2, 0] Info: [2, 1, 1, 0, 2, 1, 0] Info: -------------------------------------- Info: Total time: 2 s 900 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 19:58:58 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms