*----* MuPAD 1.4.2 -- The Open Computer Algebra System /| /| *----* | Copyright (c) 1997 - 1999 by SciFace Software | *--|-* All rights reserved. |/ |/ *----* Licensed to: Nicolas M. Thiery for the MACS department >> read("mupadinit"): >> IC:=IR(Q,Cn(7)): Module GLIP version 0.3fix2 ready. Type GLIP::doc(); for usage information\ . >> IC::minimalGeneratingSet(); ==========================================================================\ ==== Computation of a minimal generating set using SAGBI+linear algebra. Version: $Id: PGrpIRng.mu,v 1.25 2000/10/10 21:27:08 nthiery Exp $ Date: mer oct 11 10:49:00 MDT 2000 Host: cox.Mines.EDU ==========================================================================\ ==== degreeBound: enhanced from the size of the group Constructing Minimal Generating Set at degree 0 No generators at degree 0 Constructing Minimal Generating Set at degree 1 Constructing the initial poset at degree 1 Looking for S-pairs by iterating through all 1 initial monomials . Statistics for degree 1: Date: mer oct 11 10:49:01 MDT 2000 Time: 90 ms Memory: 2180 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 1 -------------------------------------- [1, 0, 0, 0, 0, 0, 0] -------------------------------------- 1 130 2180416 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 2 Constructing the initial poset at degree 2 Looking for S-pairs by iterating through all 4 initial monomials .... Statistics for degree 2: Date: mer oct 11 10:49:01 MDT 2000 Time: 20 ms Memory: 2180 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 3 -------------------------------------- [1, 0, 0, 1, 0, 0, 0] [1, 0, 1, 0, 0, 0, 0] [1, 1, 0, 0, 0, 0, 0] -------------------------------------- 2 30 2180416 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 3 Constructing the initial poset at degree 3 Looking for S-pairs by iterating through all 12 initial monomials ............ Statistics for degree 3: Date: mer oct 11 10:49:01 MDT 2000 Time: 40 ms Memory: 2196 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 8 -------------------------------------- [1, 0, 1, 0, 1, 0, 0] [1, 1, 0, 0, 0, 1, 0] [1, 1, 0, 0, 1, 0, 0] [1, 1, 0, 1, 0, 0, 0] [1, 1, 1, 0, 0, 0, 0] [2, 0, 0, 0, 0, 0, 1] [2, 0, 0, 0, 0, 1, 0] [2, 0, 0, 0, 1, 0, 0] -------------------------------------- 3 50 2196800 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 4 Constructing the initial poset at degree 4 Looking for S-pairs by iterating through all 30 initial monomials ......................9:Snr+...6:Snr+..... Statistics for degree 4: Date: mer oct 11 10:49:01 MDT 2000 Time: 280 ms Memory: 2262 ko. S-Pairs: 2 (+ 0 normalf->0 + 0 reduction->0 + 3 non-lcm->0) Minimal generators: 12 -------------------------------------- [1, 1, 0, 1, 0, 1, 0] [1, 1, 0, 1, 1, 0, 0] [1, 1, 1, 0, 0, 1, 0] [1, 1, 1, 0, 1, 0, 0] [1, 1, 1, 1, 0, 0, 0] [2, 0, 0, 0, 0, 1, 1] [2, 0, 0, 0, 1, 0, 1] [2, 0, 0, 0, 1, 1, 0] [2, 0, 0, 1, 0, 0, 1] [2, 0, 0, 1, 0, 1, 0] [2, 0, 0, 1, 1, 0, 0] [2, 0, 1, 0, 0, 1, 0] -------------------------------------- 4 290 2262336 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 5 Constructing the initial poset at degree 5 Looking for S-pairs by iterating through all 66 initial monomials ..............53:Snr+.52:Snr+.51:Snr+...48:Snr+.47:Snr+.46:Snr+.45:Snr+..4\ 3:Snr+...40:Snr+..................22:Snr+......16:Snr+Snr+....12:Snr+...9:\ Snr+.....4:Snr+Snr+... Statistics for degree 5: Date: mer oct 11 10:49:03 MDT 2000 Time: 2 s 320 ms Memory: 2508 ko. S-Pairs: 16 (+ 0 normalf->0 + 0 reduction->0 + 12 non-lcm->0) Minimal generators: 12 -------------------------------------- [1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 0, 1, 0] [1, 1, 1, 1, 1, 0, 0] [2, 0, 0, 0, 1, 1, 1] [2, 0, 0, 1, 0, 1, 1] [2, 0, 0, 1, 1, 0, 1] [2, 0, 0, 1, 1, 1, 0] [2, 0, 0, 2, 0, 0, 1] [2, 0, 1, 0, 0, 1, 1] [2, 0, 1, 0, 1, 0, 1] [2, 0, 1, 0, 1, 1, 0] [2, 0, 1, 0, 2, 0, 0] -------------------------------------- 5 2330 2508096 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 6 Constructing the initial poset at degree 6 Looking for S-pairs by iterating through all 132 initial monomials ........125:Snr+..123:Snr+..121:Snr+......115:Snr+.....110:Snr+...107:Snr+\ .......100:Snr+...97:Snr+..95:Snr+....91:Snr+...88:Snr+...85:Snr+...82:Snr\ +......76:Snr+.....71:Snr+Snr+.70:Snr+Snr+.69:Snr+Snr+.68:Snr+Snr+.67:Snr+\ .66:Snr+.65:Snr+Snr+Snr+.64:Snr+.63:Snr+.62:Snr+Snr+Snr+.61:Snr+Snr+.60:Sn\ r+Snr+.59:Snr*.58:Snr*Snr*.57:Snr*Snr*.56:Snr*..54:Snr*Snr*.53:Snr*Snr*Snr\ *.......46:Snr*..........36:Snr*.35:Snr*......29:Snr*...26:Snr*.........17\ :Snr*.....12:Snr*Snr*...9:Snr*.....4:Snr*Snr*Snr*... Statistics for degree 6: Date: mer oct 11 10:49:17 MDT 2000 Time: 13 s 140 ms Memory: 2983 ko. S-Pairs: 36 (+ 0 normalf->0 + 23 reduction->0 + 75 non-lcm->0) Minimal generators: 6 -------------------------------------- [1, 1, 1, 1, 1, 1, 0] [2, 0, 0, 1, 1, 1, 1] [2, 0, 1, 0, 1, 1, 1] [2, 0, 1, 1, 0, 1, 1] [2, 0, 1, 1, 1, 0, 1] [2, 0, 1, 1, 1, 1, 0] -------------------------------------- 6 13140 2983232 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 7 Constructing the initial poset at degree 7 Looking for S-pairs by iterating through all 246 initial monomials ...................................212:Snr+Snr+...209:Snr+Snr+.208:Snr+...\ 205:Snr+..203:Snr+.202:Snr+..200:Snr+Snr+...197:Snr+Snr+.196:Snr+..194:Snr\ +..192:Snr+.191:Snr+Snr+...188:Snr+..186:Snr+.185:Snr+Snr+...182:Snr+...17\ 9:Snr+.178:Snr+Snr+.177:Snr+Snr+...174:Snr+Snr+....170:Snr+Snr+.169:Snr+..\ .166:Snr+Snr+Snr+.165:Snr+....................145:Snr+...142:Snr+...139:Sn\ r+..........129:Snr+Snr+Snr+.128:Snr+.127:Snr+.126:Snr+Snr+.125:Snr+....12\ 1:Snr+Snr+..119:Snr+...116:Snr+Snr+Snr+.115:Snr+Snr+Snr+....111:Snr+Snr+Sn\ r+....107:Snr+..105:Snr+.104:Snr+Snr+.103:Snr*....99:Snr*Snr*Snr*.98:Snr*.\ ..95:Snr*Snr*...92:Snr*Snr*...89:Snr*.88:Snr*Snr*Snr*.87:Snr*Snr*....83:Sn\ r*Snr*...80:Snr*Snr*Snr*.79:Snr*Snr*Snr*....75:Snr*...72:Snr*Snr*Snr*Snr*S\ nr*Snr*.71:Snr*Snr*Snr*Snr*Snr*.70:Snr*Snr*Snr*Snr*Snr*.69:Snr*Snr*Snr*.68\ :Snr*Snr*Snr*Snr*.67:Snr*Snr*Snr*.66:Snr*Snr*Snr*Snr*Snr*.65:Snr*Snr*Snr*S\ nr*Snr*Snr*.64:Snr*Snr*.63:Snr*Snr*Snr*Snr*Snr*Snr*.62:Snr*Snr*Snr*Snr*Snr\ *Snr*Snr*.61:Snr*Snr*.60:Snr*Snr*.59:Snr*Snr*Snr*.58:Snr*.................\ ..........31:Snr*..29:Snr*Snr*......23:Snr*....19:Snr*Snr*Snr*......13:Snr\ *Snr*Snr*..11:Snr*........3:Snr*Snr*.. Statistics for degree 7: Date: mer oct 11 10:50:16 MDT 2000 Time: 58 s 940 ms Memory: 4228 ko. S-Pairs: 63 (+ 0 normalf->0 + 97 reduction->0 + 233 non-lcm->0) Minimal generators: 6 -------------------------------------- [1, 1, 1, 1, 1, 1, 1] [2, 0, 1, 1, 1, 1, 1] [2, 0, 1, 2, 0, 1, 1] [2, 0, 2, 0, 2, 0, 1] [2, 1, 0, 2, 0, 2, 0] [2, 1, 1, 0, 2, 1, 0] -------------------------------------- 7 58950 4228416 #Stats: degree,time(ms),mem(bytes) Total time: 1 min 14 s 970 ms table( 1 = [[1, 0, 0, 0, 0, 0, 0]], 2 = [[1, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0]\ ], 3 = [[1, 0, 1, 0, 1, 0, 0], [1, 1, 0, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0, 0]\ , [1, 1, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 1], [2,\ 0, 0, 0, 0, 1, 0], [2, 0, 0, 0, 1, 0, 0]], 4 = [[1, 1, 0, 1, 0, 1, 0], [1, 1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 0]\ , [1, 1, 1, 0, 1, 0, 0], [1, 1, 1, 1, 0, 0, 0], [2, 0, 0, 0, 0, 1, 1], [2,\ 0, 0, 0, 1, 0, 1], [2, 0, 0, 0, 1, 1, 0], [2, 0, 0, 1, 0, 0, 1], [2, 0, 0\ , 1, 0, 1, 0], [2, 0, 0, 1, 1, 0, 0], [2, 0, 1, 0, 0, 1, 0]], 5 = [[1, 1, 1, 0, 1, 1, 0], [1, 1, 1, 1, 0, 1, 0], [1, 1, 1, 1, 1, 0, 0]\ , [2, 0, 0, 0, 1, 1, 1], [2, 0, 0, 1, 0, 1, 1], [2, 0, 0, 1, 1, 0, 1], [2,\ 0, 0, 1, 1, 1, 0], [2, 0, 0, 2, 0, 0, 1], [2, 0, 1, 0, 0, 1, 1], [2, 0, 1\ , 0, 1, 0, 1], [2, 0, 1, 0, 1, 1, 0], [2, 0, 1, 0, 2, 0, 0]], 6 = [[1, 1, 1, 1, 1, 1, 0], [2, 0, 0, 1, 1, 1, 1], [2, 0, 1, 0, 1, 1, 1]\ , [2, 0, 1, 1, 0, 1, 1], [2, 0, 1, 1, 1, 0, 1], [2, 0, 1, 1, 1, 1, 0]], 7 = [[1, 1, 1, 1, 1, 1, 1], [2, 0, 1, 1, 1, 1, 1], [2, 0, 1, 2, 0, 1, 1]\ , [2, 0, 2, 0, 2, 0, 1], [2, 1, 0, 2, 0, 2, 0], [2, 1, 1, 0, 2, 1, 0]] ) >> quit