*----* 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(5,3,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 3rd transitive permutation \ group on 5 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 19:57:00 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 10 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [1, 2, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [1, 0, 0, 1, 0] Info: secondaryInvariantsSeries: working on cycletype, [5, 0, 0, 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 0, 1] 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 30 2796897 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Wed May 2 19:57:00 CEST 2001 Info: Time: 40 ms Info: Memory: 2813 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] 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 2 initial monomials .. Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 2 Skiped: 1 Char Col: 0 Mgs: 1 Info: 2 10 2813281 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Wed May 2 19:57:00 CEST 2001 Info: Time: 10 ms Info: Memory: 2813 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [1, 1, 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 3 initial monomials ... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 3 Skiped: 2 Char Col: 0 Mgs: 1 Info: 3 10 2813281 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Wed May 2 19:57:00 CEST 2001 Info: Time: 10 ms Info: Memory: 2813 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [1, 1, 1, 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 6 initial monomials ...... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 6 Skiped: 4 Char Col: 0 Mgs: 2 Info: 4 0 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Wed May 2 19:57:00 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, 1, 1, 1, 0] Info: [2, 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 9 initial monomials ......... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 9 Skiped: 7 Char Col: 0 Mgs: 2 Info: 5 10 2829665 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Wed May 2 19:57:01 CEST 2001 Info: Time: 10 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, 1, 1, 1, 1] Info: [2, 2, 0, 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 14 initial monomials .............. Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 14 Skiped: 13 Char Col: 0 Mgs: 1 Info: 6 10 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Wed May 2 19:57:01 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: 1 Info: -------------------------------------- Info: [2, 2, 1, 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 20 initial monomials ...............pp...p.p.p Info: Applying Gauss Elimination [14:2].... Info: Extracting initial monomials that are not hit Info: Dim: 20 Skiped: 14 Char Col: 5 Mgs: 1 Info: 7 40 2878817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Wed May 2 19:57:01 CEST 2001 Info: Time: 40 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: [3, 2, 0, 0, 2] Info: -------------------------------------- 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 30 initial monomials ...................pp.p.p.pp.p..p..pp..p.p Info: Applying Gauss Elimination [18:2][19:2][20:2][21:2][22:2][23:2][24:2].[26:2]... Info: Extracting initial monomials that are not hit Info: Dim: 30 Skiped: 18 Char Col: 12 Mgs: 0 Info: 8 80 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Wed May 2 19:57:01 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: 0 Info: Updating the degreeBound to 7 which is optimal! Info: Total time: 640 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 19:57:01 CEST 2001 Host: giulia3.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: Total time: 0 ms