*----* 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(6,9,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 9th 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 19:58:37 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, 0, 2, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [6, 0, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [3, 0, 1, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [2, 2, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 0, 0, 1] Info: secondaryInvariantsSeries: working on cycletype, [0, 3, 0, 0, 0, 0] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 14 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 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:58:38 CEST 2001 Info: Time: 30 ms Info: Memory: 2846 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 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:58:38 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, 0, 1, 0, 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 10 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:58:38 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: 2 Info: -------------------------------------- Info: [1, 0, 1, 0, 1, 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 [4:2]. Info: Extracting initial monomials that are not hit Info: Dim: 10 Skiped: 6 Char Col: 2 Mgs: 2 Info: 4 30 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:58:38 CEST 2001 Info: Time: 30 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, 1, 0, 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 [11:2]. Info: Extracting initial monomials that are not hit Info: Dim: 15 Skiped: 12 Char Col: 2 Mgs: 1 Info: 5 20 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:58:39 CEST 2001 Info: Time: 20 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 27 initial monomials .............pp.....p.p.p..p.pp.p... Info: Applying Gauss Elimination [12:2][17:2][18:2].[21:2][22:2][23:3][24:2]Info: Extracting initial monomials that are not hit Info: Dim: 27 Skiped: 17 Char Col: 8 Mgs: 2 Info: 6 80 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:58:39 CEST 2001 Info: Time: 80 ms Info: Memory: 2895 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, 2, 1, 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 38 initial monomials ....................pp..p..p....pp.pp...p.p.p.pp...p Info: Applying Gauss Elimination [19:2][21:2]..[27:2][28:2].[32:3][33:2][34:4][35:2][37:2]Info: Extracting initial monomials that are not hit Info: Dim: 38 Skiped: 26 Char Col: 12 Mgs: 0 Info: 7 110 2911585 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:58:39 CEST 2001 Info: Time: 110 ms Info: Memory: 2911 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 60 initial monomials .........................pp.p.........p.p.p.p..p..p.p.pp.pp.....pp..pp..p.\ pp..p.p.p.p Info: Applying Gauss Elimination [24:2][25:2][34:2][35:2][36:2][37:2][39:2].[42:2][43:3][44:4][45:3][49:2][51:4][53:2][54:4][55:3][56:4][57:4][58:2][59:2]Info: Extracting initial monomials that are not hit Info: Dim: 60 Skiped: 39 Char Col: 21 Mgs: 0 Info: 8 210 2977121 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:58:39 CEST 2001 Info: Time: 210 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 9 Info: Constructing the initial poset at degree 9 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 84 initial monomials ..............................................pp...pp..........p.p.p.p.p.p\ ..p.p.ppp..p.p.p.pp......pp..p.p.p.p Info: Applying Gauss Elimination [45:2][48:2][58:2][59:2][60:2].[62:2][63:2][65:2][66:2][67:4].[70:4][71:4][72:5].[78:2][80:3][81:2][82:4][83:2]Info: Extracting initial monomials that are not hit Info: Dim: 84 Skiped: 63 Char Col: 21 Mgs: 0 Info: 9 290 3026273 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 9: Date: Wed May 2 19:58:40 CEST 2001 Info: Time: 290 ms Info: Memory: 3026 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 123 initial monomials .....................................................................pp.pp\ .p.pp...p..........pp.ppp..pp..........p.p.p.p.pp.p.p..p.p.p.pp..p.p.p.ppp\ .pp...pp..p.p.p.p Info: Applying Gauss Elimination [68:2][69:2][70:2][71:3][72:2]..[84:2][85:4][87:2][97:2][98:5][99:2][100:3][101:4][102:6].[104:2][105:4][106:2][107:2][108:3][110:6][111:4][112:6][113:5][114:8][115:4][117:2][119:2][120:5][121:9][122:5]Info: Extracting initial monomials that are not hit Info: Dim: 123 Skiped: 90 Char Col: 33 Mgs: 0 Info: 10 470 3091809 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 10: Date: Wed May 2 19:58:40 CEST 2001 Info: Time: 470 ms Info: Memory: 3091 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 166 initial monomials ..........................................................................\ ...pp.p.........................p.p.p.p...p..p.p.p.p..pp.p.p.pp.pp..p..p..\ .......pp...pp.ppp.........p.p.p.p.p.p.pp..p.p.p.ppp..p.pp..pp.p...p Info: Applying Gauss Elimination [76:2][77:2][102:2][103:2][104:2][105:2][108:2].[111:2][112:2][113:2][115:3][116:2][117:2][118:3][119:3][121:3][122:3][123:2][132:2][135:3][136:3].[146:3][147:2][148:5][149:4][150:6][151:7][152:6][153:2][154:4][155:2][156:4][158:8][159:9][160:9][161:8][162:8][165:8]Info: Extracting initial monomials that are not hit Info: Dim: 166 Skiped: 126 Char Col: 40 Mgs: 0 Info: 11 660 3206497 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 11: Date: Wed May 2 19:58:41 CEST 2001 Info: Time: 660 ms Info: Memory: 3206 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 233 initial monomials ..........................................................................\ .......................................................pp.pp.p....ppp.p...\ ........................p.p.p.p..p.p.p.p.pp.p.p..p.p.p..p.p.p.p.pp.p.p.pp.\ .p.p.pp.pp..............pppp..pp.......p.p.p.p.pp.p.p.p.p.p.p.pp..p.p.p.p.\ .p Info: Applying Gauss Elimination [128:2][129:2][130:2][134:3][135:2][162:2][163:2][164:3][165:2][167:2][168:3][169:2][170:2][171:3][172:2][173:2][175:2][176:4][177:3].[180:2][181:4][182:3][183:7][184:2][185:3][186:4][187:2][188:6][189:6][190:7][191:7][192:7][205:6][207:9][214:7][215:2][216:7][217:2][218:8][219:9][220:11][221:8][222:11][223:2][224:2][225:8][226:8][227:2][228:2][229:12][230:9][232:9]Info: Extracting initial monomials that are not hit Info: Dim: 233 Skiped: 180 Char Col: 53 Mgs: 0 Info: 12 1000 3353953 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 12: Date: Wed May 2 19:58:42 CEST 2001 Info: Time: 1 s 0 ms Info: Memory: 3353 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 13 Info: Constructing the initial poset at degree 13 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 305 initial monomials ..........................................................................\ ..........................................................................\ ..................................pp.pp.p.pp..p...p............p.....p.pp.\ pp.ppp.p.p.ppp.............................p.p.p.p.p.p.p.p.p.p.p.p.p.p.p..\ p.p.p.p.p.pp..p.p.p.p.p.p.ppp.p.p.pp.p.pp.........ppp....pp.....p.p.pp..p.\ p.p.p.p.p.p.p Info: Applying Gauss Elimination [181:2][182:2][183:2][184:2][186:2][187:2]..[201:2][206:2][207:2][208:2][209:4].[211:2][212:3].[242:5][243:2][244:3][245:3][246:7][247:2][248:2].[250:4][251:5][252:3].[254:2].[257:2][258:2][259:4][260:6][261:4][262:3].[265:3][266:6][267:6][268:5][269:8][270:9][271:5][272:8][273:8][274:10][275:11][276:5][284:3][288:4][293:4][294:9][295:12][296:10][297:8][298:7][299:14][300:2][301:10][302:8][303:2][304:13]Info: Extracting initial monomials that are not hit Info: Dim: 305 Skiped: 241 Char Col: 64 Mgs: 0 Info: 13 1410 3583329 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 13: Date: Wed May 2 19:58:44 CEST 2001 Info: Time: 1 s 410 ms Info: Memory: 3583 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 14 Info: Constructing the initial poset at degree 14 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 410 initial monomials ..........................................................................\ ..........................................................................\ ...................................................pp.p.ppp.p.p...........\ ........p.....................................p.p.p.p.p..p.p.p.p...p..p.p.\ p.p..p.pp.p..p.p.p.ppp.pp..p.pp.pp.p.pp...p.................pp.p.pp.p..p..\ p.pp.pppp.p.pp..........................p.p.p.p.p.p.p.p.p.ppp.p.p.p..p.p.p\ .p.p.p.p.p.p..p.p.p.p.pppp.p.p.pp..p.p.p.p.pp.pp....pp......pp..p...p.p.p.\ p.p.p.p.p.p Info: Applying Gauss Elimination [198:2][199:2][200:3][201:2][202:2][221:2][258:3][259:2][260:2][261:3][262:2][264:2][265:2][266:2][267:3][270:3].[273:2][274:2][275:3][277:2][278:4][279:4][281:3][282:2][283:2][284:5][285:8][286:4][287:3][288:5][289:5][290:3][291:3][292:4][293:5][294:2][311:2][312:3][313:7][314:2][316:3][318:3][319:5][320:6][321:3][322:3][348:5].[350:6][351:11][352:5][353:6][354:6][355:3][356:10][357:8][358:9].[360:6][361:5][362:8][363:7][364:10][365:6][366:3][367:2][368:3][369:2].[372:5][373:7][374:2][375:11][376:11][377:10][378:3][379:5][380:4][381:6][382:17][383:11][384:17][385:19][386:14][387:12][390:2][396:3][398:2][401:14][402:20][403:14][404:20][405:21][406:12][407:20][408:3][409:4]Info: Extracting initial monomials that are not hit Info: Dim: 410 Skiped: 312 Char Col: 98 Mgs: 0 Info: 14 2280 3927393 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 14: Date: Wed May 2 19:58:46 CEST 2001 Info: Time: 2 s 280 ms Info: Memory: 3927 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 110 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 19:58:47 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms