*----* 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(8,2,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end C/C++ Debugger interface is active. Debugger: 'ddd', Process: 22831 C/++ debugger name is set to ´gdb´Info: Computation of the invariant ring of the 2nd transitive permutation \ group on 8 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 20:50:10 CEST 2001 Host: giulia4.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 28 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [0, 4, 0, 0, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [8, 0, 0, 0, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 2, 0, 0, \ 0, 0] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 26 Info: degreeBound: enhancement from the size of the group: 6 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 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 20:50:13 CEST 2001 Info: Time: 20 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, 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 6 initial monomials ...... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 6 Skiped: 1 Char Col: 0 Mgs: 5 Info: 2 0 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 20:50:13 CEST 2001 Info: Time: 0 ms Info: Memory: 2829 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 5 Info: -------------------------------------- Info: [1, 0, 0, 0, 0, 0, 1, 0] Info: [1, 0, 0, 0, 1, 0, 0, 0] Info: [1, 0, 0, 1, 0, 0, 0, 0] Info: [1, 0, 1, 0, 0, 0, 0, 0] Info: [1, 1, 0, 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 15 initial monomials ............... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 15 Skiped: 6 Char Col: 0 Mgs: 9 Info: 3 10 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 20:50:14 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: 9 Info: -------------------------------------- Info: [1, 0, 1, 0, 1, 0, 0, 0] Info: [1, 0, 1, 1, 0, 0, 0, 0] Info: [1, 1, 0, 0, 0, 0, 1, 0] Info: [1, 1, 0, 0, 0, 1, 0, 0] Info: [1, 1, 0, 0, 1, 0, 0, 0] Info: [1, 1, 0, 1, 0, 0, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 0, 1] Info: [2, 0, 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 46 initial monomials ..........pp.pp.pp.p.pp...pp.pp..p...p..p....p................. Info: Applying Gauss Elimination [9:2][10:2][11:2][12:2][13:2].[16:2][17:2][19:2][22:2].[24:2][25:2][28:2][30:2].. Info: Extracting initial monomials that are not hit Info: Dim: 46 Skiped: 13 Char Col: 17 Mgs: 16 Info: 4 110 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 20:50:15 CEST 2001 Info: Time: 110 ms Info: Memory: 2895 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 16 Info: -------------------------------------- Info: [1, 0, 1, 0, 1, 0, 1, 0] Info: [1, 0, 1, 1, 0, 1, 0, 0] Info: [1, 1, 0, 0, 1, 0, 1, 0] Info: [1, 1, 0, 0, 1, 1, 0, 0] Info: [1, 1, 0, 1, 0, 0, 1, 0] Info: [1, 1, 0, 1, 0, 1, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 1] Info: [1, 1, 1, 0, 0, 0, 1, 0] Info: [1, 1, 1, 0, 0, 1, 0, 0] Info: [1, 1, 1, 0, 1, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 1, 1] Info: [2, 0, 0, 0, 0, 1, 0, 1] Info: [2, 0, 0, 0, 1, 0, 0, 1] Info: [2, 0, 0, 0, 1, 1, 0, 0] Info: [2, 0, 1, 0, 0, 0, 0, 1] Info: [2, 0, 1, 0, 0, 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 99 initial monomials .............pp..pp....pp..pp...pp..pp..pp..pp..pp.p..pp..p.p.p.p.p..p.ppp\ p.pppp.pp.ppp.p.p.ppp.pp.ppp..p.pp.ppp...p....p..p.pp.p.p....pp...........\ ................ Info: Applying Gauss Elimination [12:2][14:2][18:2][20:2][23:2][25:2][27:2][29:2].[31:2][32:3][34:2].[36:2][37:3][38:3][39:4][40:4]..[43:4][44:4][45:5][46:4].[48:3][49:6][50:5][51:6][52:5][53:2][54:7][55:4][56:7][57:3][58:7][59:6][61:8][62:2][64:2][65:9][66:2][67:10][68:7][70:6][71:2][72:2][73:5][74:5].[78:4][79:4][80:2][81:8][82:10][83:2][85:2][86:4][87:4]...... Info: Extracting initial monomials that are not hit Info: Dim: 99 Skiped: 26 Char Col: 65 Mgs: 8 Info: 5 370 3009889 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 20:50:17 CEST 2001 Info: Time: 370 ms Info: Memory: 3009 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 8 Info: -------------------------------------- Info: [1, 1, 1, 0, 0, 1, 1, 0] Info: [1, 1, 1, 0, 1, 1, 0, 0] Info: [1, 1, 1, 1, 0, 0, 0, 1] Info: [1, 1, 1, 1, 0, 0, 1, 0] Info: [1, 1, 1, 1, 0, 1, 0, 0] Info: [2, 0, 0, 1, 0, 1, 1, 0] Info: [2, 0, 1, 0, 0, 0, 1, 1] Info: [2, 0, 1, 0, 0, 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 222 initial monomials ...............................pp..pp...pp.p....p..pp....ppp..pppp...ppp..\ pppp..ppp..pppp.pp.ppp.ppp..pppp..........pppp..pppp..pppp..pppp.p.ppp.pp.\ pp.ppp..p.p.p.pp.pp.pp.ppp.pp.ppp..ppp.pp..ppp.....p..ppp.pp.p.ppp....pp.p\ p...p..p.pp.pp.pp.pp.p.p.pp.pp.pp..p.pp.pp..p.p..p..pp.pp.p.p.p.pp.pppppp.\ ppppp.ppppp.pp.pp.pppp.pppppp.p..pp..p.p.p.p.p..p.pp.ppp...p..p..p.p...p..\ p......p.p.p..p.p.p....p.p..p...p.....p.................. Info: Applying Gauss Elimination [30:2][32:2][35:2][36:2][40:2][42:3][46:3][48:4][51:3][53:4][55:3][57:4][58:3][59:3][60:6][62:4][63:3][72:4][74:4][76:4][78:4][79:4][80:4][81:7][82:2][83:4][84:3][85:2][86:3][87:3][88:2][89:3][90:2][91:4][92:2][93:4][94:3][95:4][96:7][98:4][99:3][103:2][104:6][105:4][106:8][107:2][108:4][109:4][110:4][111:5][112:2][113:7][114:4][116:2][117:3][118:3][119:6][120:12][121:9][122:14][123:3][124:5][125:7][126:9][127:10][128:14][129:7][130:10][131:19][132:15][133:6][134:15][135:16][136:8][137:19][138:5][139:18][140:6][141:20][142:4][143:6][144:15][145:16][146:26][147:21][148:4][149:29][150:8][151:18][152:13][153:22][154:8][155:4][156:18][157:9][158:11][159:8][160:15][161:11][162:38][163:22][164:34][165:14][166:33][167:34][168:8][169:29][170:10][171:13][172:8][173:10][174:42][175:37][176:3][177:41][178:17][179:11][180:34][181:7][182:3][183:6][184:4][185:10][186:2][187:2][188:3][189:17][190:17][191:41][192:45][193:48][194:42][195:38][196:24][197:43][198:2][199:38][200:16][201:50][202:36].[204:38][205:13][206:45][207:9][208:25][209:34][210:35][211:42][212:35][213:35][214:22][215:17][216:7][217:44][218:39][219:44][220:37][221:39]Info: Extracting initial monomials that are not hit Info: Dim: 222 Skiped: 63 Char Col: 159 Mgs: 0 Info: 6 1160 3272033 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 20:50:21 CEST 2001 Info: Time: 1 s 160 ms Info: Memory: 3272 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Updating the degreeBound to 5 which is optimal! Info: Total time: 2 s 50 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 20:50:22 CEST 2001 Host: giulia4.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms