*----* 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(6,1,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 1st 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 19:57:10 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, 3, 0, 0, 0, 0] 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, [0, 0, 0, 0, 0, 1] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 14 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 10 2403681 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:57:10 CEST 2001 Info: Time: 10 ms Info: Memory: 2403 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 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 2403681 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:57:10 CEST 2001 Info: Time: 10 ms Info: Memory: 2403 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] 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 10 initial monomials .......... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 10 Skiped: 4 Char Col: 0 Mgs: 6 Info: 3 20 2420065 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:57:10 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: 6 Info: -------------------------------------- Info: [1, 0, 1, 0, 1, 0] Info: [1, 1, 0, 0, 1, 0] Info: [1, 1, 0, 1, 0, 0] Info: [1, 1, 1, 0, 0, 0] Info: [2, 0, 0, 0, 0, 1] Info: [2, 0, 0, 0, 1, 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 22 initial monomials ........pp.pp.p...p......... Info: Applying Gauss Elimination [7:2][8:2][9:2]... Info: Extracting initial monomials that are not hit Info: Dim: 22 Skiped: 10 Char Col: 6 Mgs: 6 Info: 4 40 2436449 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:57:11 CEST 2001 Info: Time: 40 ms Info: Memory: 2436 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 6 Info: -------------------------------------- Info: [1, 1, 0, 1, 1, 0] Info: [1, 1, 1, 0, 1, 0] Info: [1, 1, 1, 1, 0, 0] Info: [2, 0, 0, 0, 1, 1] Info: [2, 0, 0, 1, 0, 1] Info: [2, 0, 0, 1, 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 42 initial monomials ..........pp.pp...pp.pp..pp.pp..p..p.p.p..p.ppp.ppp..p.pp....p...p.... Info: Applying Gauss Elimination [9:2][10:2][13:2][14:2][16:2][17:2].[19:3].[21:2][22:3][23:4][24:2][25:2][26:5][27:4][28:2][29:2][30:6][31:4][32:3]..[35:3]..[38:2]. Info: Extracting initial monomials that are not hit Info: Dim: 42 Skiped: 12 Char Col: 28 Mgs: 2 Info: 5 120 2452833 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:57:11 CEST 2001 Info: Time: 120 ms Info: Memory: 2452 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, 0, 1, 1, 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 80 initial monomials ...................pp.pp.pp.p...p.pp...pp.pppp..ppp.pppp.pp.ppp..p.p.p.pp.\ pp.pp.ppp.p.ppp....p..pp....p.pp.pp..p.pp..p..p.pp..p.pppp..p..p....p.... Info: Applying Gauss Elimination [18:2][19:2][20:2][21:2][24:2][25:3][28:2][29:4][31:3][32:4][33:3][34:6][35:3][36:2][37:3][38:2][39:3][40:2][41:3][42:4][43:2][44:6][45:3][48:2][49:6][50:8][51:4][52:4][53:4][54:5][55:12][56:10][57:9][58:9][59:11][60:14][61:6][62:9][63:13][64:13][65:9][66:11][67:18][68:16][69:7][70:17][71:8][72:9][73:10][74:14][75:2][76:15][77:6]Info: Extracting initial monomials that are not hit Info: Dim: 80 Skiped: 25 Char Col: 53 Mgs: 2 Info: 6 310 2518369 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:57:11 CEST 2001 Info: Time: 310 ms Info: Memory: 2518 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, 0, 1, 1, 1, 1] Info: -------------------------------------- Info: Total time: 830 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 19:57:11 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms