*----* 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(9,2,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end C/C++ Debugger interface is active. Debugger: 'ddd', Process: 11148 C/++ debugger name is set to ´gdb´Info: Computation of the invariant ring of the 2nd transitive permutation \ group on 9 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: Thu May 3 20:20:22 CEST 2001 Host: giulia2.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 36 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [9, 0, 0, 0, 0, 0, \ 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 3, 0, 0, 0, \ 0, 0, 0] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 34 Info: degreeBound: enhancement from the size of the group: 5 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 10 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Thu May 3 20:20:23 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: 1 Info: -------------------------------------- Info: [1, 0, 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 5 initial monomials ..... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 5 Skiped: 1 Char Col: 0 Mgs: 4 Info: 2 10 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Thu May 3 20:20:23 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: 4 Info: -------------------------------------- Info: [1, 0, 0, 0, 1, 0, 0, 0, 0] Info: [1, 0, 0, 1, 0, 0, 0, 0, 0] Info: [1, 0, 1, 0, 0, 0, 0, 0, 0] Info: [1, 1, 0, 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 21 initial monomials ..................... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 21 Skiped: 5 Char Col: 0 Mgs: 16 Info: 3 20 2846049 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Thu May 3 20:20:23 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: 16 Info: -------------------------------------- Info: [1, 0, 0, 0, 1, 1, 0, 0, 0] Info: [1, 0, 0, 1, 0, 0, 1, 0, 0] Info: [1, 0, 1, 0, 0, 0, 0, 1, 0] Info: [1, 0, 1, 0, 0, 0, 1, 0, 0] Info: [1, 0, 1, 0, 0, 1, 0, 0, 0] Info: [1, 1, 0, 0, 0, 0, 0, 0, 1] Info: [1, 1, 0, 0, 0, 0, 0, 1, 0] Info: [1, 1, 0, 0, 0, 0, 1, 0, 0] Info: [1, 1, 0, 0, 0, 1, 0, 0, 0] Info: [1, 1, 0, 0, 1, 0, 0, 0, 0] Info: [1, 1, 0, 1, 0, 0, 0, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 0, 0, 1] Info: [2, 0, 0, 0, 0, 0, 0, 1, 0] Info: [2, 0, 0, 0, 0, 0, 1, 0, 0] Info: [2, 0, 0, 0, 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 55 initial monomials ...........pp.pp.pp.p.p.p...p.p.p.p....p............................. Info: Applying Gauss Elimination [10:2][11:2][12:2][13:2][14:2][15:2][18:2][19:2][20:2][21:2][23:2][25:2][28:2]. Info: Extracting initial monomials that are not hit Info: Dim: 55 Skiped: 17 Char Col: 14 Mgs: 24 Info: 4 130 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Thu May 3 20:20:24 CEST 2001 Info: Time: 130 ms Info: Memory: 2895 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 24 Info: -------------------------------------- Info: [1, 1, 0, 0, 0, 1, 0, 0, 1] Info: [1, 1, 0, 0, 1, 0, 0, 1, 0] Info: [1, 1, 0, 0, 1, 0, 1, 0, 0] Info: [1, 1, 0, 0, 1, 1, 0, 0, 0] Info: [1, 1, 0, 1, 0, 0, 0, 1, 0] Info: [1, 1, 0, 1, 0, 0, 1, 0, 0] Info: [1, 1, 0, 1, 0, 1, 0, 0, 0] Info: [1, 1, 0, 1, 1, 0, 0, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 0, 1] Info: [1, 1, 1, 0, 0, 0, 0, 1, 0] Info: [1, 1, 1, 0, 0, 0, 1, 0, 0] Info: [1, 1, 1, 0, 0, 1, 0, 0, 0] Info: [1, 1, 1, 0, 1, 0, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 0, 1, 1] Info: [2, 0, 0, 0, 0, 0, 1, 0, 1] Info: [2, 0, 0, 0, 0, 0, 1, 1, 0] Info: [2, 0, 0, 0, 0, 1, 0, 0, 1] Info: [2, 0, 0, 0, 0, 1, 0, 1, 0] Info: [2, 0, 0, 0, 0, 1, 1, 0, 0] Info: [2, 0, 0, 0, 1, 0, 0, 0, 1] Info: [2, 0, 0, 0, 1, 0, 0, 1, 0] Info: [2, 0, 0, 0, 1, 0, 1, 0, 0] Info: [2, 0, 0, 1, 0, 0, 0, 0, 1] Info: [2, 0, 0, 1, 0, 1, 0, 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 143 initial monomials ..............pp.pp.pp.pp....pp.pp.pp.pp...pp.pp.pp.pp..pp.pp.pp.pp..p.p.p\ ..p.p..p..p.p.p.p.p.p.p.p.ppp.ppp.ppp.ppp.ppp.pp.p.ppp.pp.ppp.pp.p.p.ppp.p\ p.pp.p....p.......p.p.p....p.pp.p..pp.p.p..........p....p.p..........p....\ ..................... Info: Applying Gauss Elimination [13:2][14:2][15:2][16:2][20:2][21:2][22:2][23:2][26:2][27:2][28:2][29:2][31:2][32:2][33:2][34:2].[36:3][37:3][38:3].[40:3][41:3].[43:3].[45:3][46:3][47:3][48:5][49:5][50:5].[52:4][53:7][54:7][55:6][56:7][57:6][58:5][59:4][60:7][61:7][62:6][63:6][64:5][65:4][66:6][67:6][68:7][69:5][70:3][71:12][72:12][73:7][74:3][75:12][76:3][77:3][78:2][79:10][80:4][81:4].[83:9][84:10][85:4][86:12][87:11][88:6][89:7][90:5][91:12][92:12][93:7][94:4][95:10][96:10][97:12][98:4][99:3][100:9][101:2].[103:9][104:3][105:9][106:6][107:8][108:6][109:8][110:4][111:4][112:3][114:3][116:4].... Info: Extracting initial monomials that are not hit Info: Dim: 143 Skiped: 19 Char Col: 100 Mgs: 24 Info: 5 610 3091809 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Thu May 3 20:20:25 CEST 2001 Info: Time: 610 ms Info: Memory: 3091 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 24 Info: -------------------------------------- Info: [1, 1, 0, 1, 1, 0, 0, 1, 0] Info: [1, 1, 0, 1, 1, 0, 1, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 1, 1] Info: [1, 1, 1, 0, 0, 0, 1, 0, 1] Info: [1, 1, 1, 0, 0, 0, 1, 1, 0] Info: [1, 1, 1, 0, 0, 1, 0, 0, 1] Info: [1, 1, 1, 0, 1, 0, 0, 1, 0] Info: [1, 1, 1, 0, 1, 0, 1, 0, 0] Info: [1, 1, 1, 0, 1, 1, 0, 0, 0] Info: [1, 1, 1, 1, 0, 0, 0, 0, 1] Info: [1, 1, 1, 1, 0, 0, 0, 1, 0] Info: [1, 1, 1, 1, 0, 0, 1, 0, 0] Info: [1, 1, 1, 1, 0, 1, 0, 0, 0] Info: [2, 0, 0, 0, 0, 0, 1, 1, 1] Info: [2, 0, 0, 0, 0, 1, 0, 1, 1] Info: [2, 0, 0, 0, 0, 1, 1, 0, 1] Info: [2, 0, 0, 0, 0, 1, 1, 1, 0] Info: [2, 0, 0, 0, 1, 0, 0, 1, 1] Info: [2, 0, 0, 0, 1, 0, 1, 0, 1] Info: [2, 0, 0, 0, 1, 0, 1, 1, 0] Info: [2, 0, 0, 0, 1, 1, 0, 0, 1] Info: [2, 0, 0, 0, 1, 1, 0, 1, 0] Info: [2, 0, 0, 1, 0, 0, 1, 0, 1] Info: [2, 0, 0, 1, 0, 1, 0, 0, 1] Info: -------------------------------------- Info: Total time: 1 s 200 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: Thu May 3 20:20:25 CEST 2001 Host: giulia2.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms