*----* 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(6,4,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 4th 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 19:57:49 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, 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: degreeBound: enhancement from the degrees of the primary invariants:\ 13 Info: degreeBound: enhancement from the size of the group: 9 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 2813281 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:57:50 CEST 2001 Info: Time: 40 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 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:57:50 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: 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 8 initial monomials ........ Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 8 Skiped: 3 Char Col: 0 Mgs: 5 Info: 3 20 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:57:50 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: 5 Info: -------------------------------------- Info: [1, 1, 0, 0, 0, 1] 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 14 initial monomials .......pp....... Info: Applying Gauss Elimination [6:2]. Info: Extracting initial monomials that are not hit Info: Dim: 14 Skiped: 9 Char Col: 2 Mgs: 3 Info: 4 20 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:57:50 CEST 2001 Info: Time: 20 ms Info: Memory: 2846 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 26 initial monomials ......pp...p..pp.p..p.p.p.p.pp....pp.p... Info: Applying Gauss Elimination [5:2][8:2].[10:2]..[14:2][15:2].[17:3][18:2].[21:2].. Info: Extracting initial monomials that are not hit Info: Dim: 26 Skiped: 9 Char Col: 15 Mgs: 2 Info: 5 70 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:57:50 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: 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 48 initial monomials ..........pp..p..p.p..p.p.p.ppp.pp.ppp...p....pp.pp..p.pp.p.p.p.pp.p.p.p.p\ .p.p...p.. Info: Applying Gauss Elimination [9:2][11:2][13:2][14:2][16:2][17:2][18:2][19:3][20:2][21:4][24:3][25:3][26:3][27:3][28:2][29:3][31:2][32:5][33:4][34:5][35:3][36:5][37:5][38:4][39:4][40:2][41:4][42:7][43:3][44:6][45:3].Info: Extracting initial monomials that are not hit Info: Dim: 48 Skiped: 15 Char Col: 32 Mgs: 1 Info: 6 190 2927969 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:57:51 CEST 2001 Info: Time: 190 ms Info: Memory: 2927 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- 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 76 initial monomials ...................pp.......p..ppp.pp..p..p.p.p.p.p.p.pp.pp..p.p.p.p.p.pp.\ .p.ppp.pppp.ppppp.pp.p...p......pp.p.p.ppp.p....p.p.p.p..p Info: Applying Gauss Elimination [18:2][25:2].[27:3][28:2][30:2].[33:4][34:4]..[37:4][38:5][39:3][41:2][42:4][43:4][44:5].[46:6][47:4][48:5][49:3][50:4][51:7][52:4][53:5].[57:5][58:5][59:7][60:3][62:5][63:3][64:11][65:10][66:11][67:10][68:11][69:3][70:4][71:7][72:11][73:9][74:6][75:11]Info: Extracting initial monomials that are not hit Info: Dim: 76 Skiped: 30 Char Col: 46 Mgs: 0 Info: 7 320 2993505 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:57:51 CEST 2001 Info: Time: 320 ms Info: Memory: 2993 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 121 initial monomials ...........................pp..p....p.p..p.p.p.........pp.p.ppp.ppp.pppp..\ ..p.p....pp....pppp.pppp.pp..p..p.p.p.p.p.p.p.p.p.p.p.p.p.p.pp.ppp.pp.pppp\ .pp..p.p.p.p.p..pp.p.pp...pp.ppp.ppppp.pppp.p......p.p.p.pp..p.pp...p.p Info: Applying Gauss Elimination [26:2][28:2][32:2][33:2][35:2][36:2][37:2][46:3][47:2][48:3][49:4][50:5][54:2][55:5][59:4][60:5][61:3][62:3][63:4][64:5][65:3][67:3][69:2][70:4][71:6][72:6][73:6][74:6][75:6][76:7][77:6][78:5][79:3][80:3][81:4][82:4][83:6][84:12][85:13][86:12][87:7][89:2].[91:2][92:6][93:6][94:12][95:14][96:16][97:14][98:16][99:10][100:2][101:3][102:17][103:20][104:17][106:15][107:5][108:10][109:9][110:4][111:17][112:10][113:23][114:15][115:26][116:28][117:18][118:15][119:8][120:16]Info: Extracting initial monomials that are not hit Info: Dim: 121 Skiped: 49 Char Col: 72 Mgs: 0 Info: 8 590 3124577 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:57:52 CEST 2001 Info: Time: 590 ms Info: Memory: 3124 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 187 initial monomials ................................................pp........pp.....p..pppp.p\ pp..p.p....p.p.p.p.p.p.p.p..p.p.p.p.p.p.p.pp.p......pp......ppp.pp.p.pp..p\ .ppp.ppppp.pppppp.pppp.pppp....p.p.....pp.....ppp.ppppp.ppp..p.p.p.p.p.p.p\ .p.pp.pp.pp.p.p.p.p.p.p.p.p.p.p.p.pp.pp..p..p.p.pppp.ppp.ppppp.ppp.pp.p.p.\ p.p...p.p.pp.pp...pp.pp.ppp.p...p..p.p.p.p.p Info: Applying Gauss Elimination [47:2][55:2][60:3].[62:4][63:3][65:3][66:2].[71:6][72:6][73:2].[75:4][76:6][77:3][79:2][80:4][81:6][82:7][83:2].[85:3][86:4][87:2][93:4][99:5][100:4][101:2][102:7][103:5][104:5][105:3][106:7][107:9][108:7][109:8][113:2][114:12][115:8][119:4][120:12][121:7][122:9][123:5][124:3][125:10][126:8][128:2].[130:6][131:9][132:5][133:8][134:14][135:17][136:8][137:16][138:8][139:12][140:11].[142:9][143:9][144:12][145:11][146:11][147:11][148:2][149:7][150:23][151:26][152:22][153:22][154:20][155:2][156:5][157:20][158:17][159:28][160:22][161:28][162:25][163:12][164:2].[166:21][167:23][168:22][169:39][170:28][171:45][172:40][173:29][174:2][175:4][176:7][177:29][178:10][179:12][180:45][181:40][182:30][183:19][184:34][185:27][186:27]Info: Extracting initial monomials that are not hit Info: Dim: 187 Skiped: 80 Char Col: 107 Mgs: 0 Info: 9 1010 3321185 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 9: Date: Wed May 2 19:57:53 CEST 2001 Info: Time: 1 s 10 ms Info: Memory: 3321 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: 2 s 750 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 19:57:53 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms