*----* 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(6,13,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 13th 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 19:57:30 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, [1, 1, 1, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 2, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [4, 1, 0, 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, [0, 3, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 0, 0, 1] Info: secondaryInvariantsSeries: working on cycletype, [0, 1, 0, 1, 0, 0] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 8 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 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:57:31 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, 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 10 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:57:31 CEST 2001 Info: Time: 10 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, 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 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:57:31 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: 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 20 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:57:31 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: 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 30 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:57:31 CEST 2001 Info: Time: 30 ms Info: Memory: 2895 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 26 initial monomials .............pp.....p.p.p.p.pp.p... Info: Applying Gauss Elimination [12:2][17:2][18:2].[20:2][21:2][22:3][23:2]Info: Extracting initial monomials that are not hit Info: Dim: 26 Skiped: 17 Char Col: 8 Mgs: 1 Info: 6 90 2927969 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:57:32 CEST 2001 Info: Time: 90 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: [1, 1, 1, 1, 1, 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 37 initial monomials ....................pp...p....pp.pp...p.p.p.pp...p Info: Applying Gauss Elimination [19:2]..[26:2][27:2].[31:3][32:2][33:4][34:2][36:2]Info: Extracting initial monomials that are not hit Info: Dim: 37 Skiped: 26 Char Col: 11 Mgs: 0 Info: 7 120 2944353 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:57:32 CEST 2001 Info: Time: 120 ms Info: Memory: 2944 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 57 initial monomials ........................pp.p.........p.p.p..p..p.pp.pp.....pp..pp..p.pp..p\ .p.p.p Info: Applying Gauss Elimination [23:2][24:2][33:2][34:2][35:2][37:2][39:2][40:3][41:4][42:3][46:2][48:4][50:2][51:4][52:3][53:4][54:4][55:2][56:2]Info: Extracting initial monomials that are not hit Info: Dim: 57 Skiped: 38 Char Col: 19 Mgs: 0 Info: 8 230 2977121 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:57:32 CEST 2001 Info: Time: 230 ms Info: Memory: 2977 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: 1 s 0 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 19:57:32 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms