*----* 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"): >> p:=5: >> IC:=ICpp(p): 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 1.23 2000/10/10 06:03:19 nthiery Exp $ Date: mar oct 10 00:17:22 MDT 2000 Host: lawson.Mines.EDU ==========================================================================\ ==== Constructing Minimal Generating Set at degree 0 No generators at degree 0 Constructing Minimal Generating Set at degree 1 Looking for S-pairs by iterating through all 1 initial monomials [1] Statistics for degree 1: Date: mar oct 10 00:17:22 MDT 2000 Time: 110 ms Memory: 2098 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 1 -------------------------------------- [1, 0, 0, 0, 0] -------------------------------------- 1 130 2098496 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 2 Looking for S-pairs by iterating through all 3 initial monomials [3][2][1] Statistics for degree 2: Date: mar oct 10 00:17:22 MDT 2000 Time: 20 ms Memory: 2098 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 2 -------------------------------------- [1, 0, 1, 0, 0] [1, 1, 0, 0, 0] -------------------------------------- 2 20 2098496 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 3 Looking for S-pairs by iterating through all 7 initial monomials [7][6][5][4][3][2][1] Statistics for degree 3: Date: mar oct 10 00:17:22 MDT 2000 Time: 20 ms Memory: 2114 ko. S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Minimal generators: 4 -------------------------------------- [1, 1, 0, 1, 0] [1, 1, 1, 0, 0] [2, 0, 0, 0, 1] [2, 0, 0, 1, 0] -------------------------------------- 3 30 2114880 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 4 Looking for S-pairs by iterating through all 14 initial monomials [14][13][12][11][10][9][8][7][6][5][4][3][2]Snr+[1] Statistics for degree 4: Date: mar oct 10 00:17:22 MDT 2000 Time: 150 ms Memory: 2196 ko. S-Pairs: 1 (+ 0 normalf->0 + 0 reduction->0 + 2 non-lcm->0) Minimal generators: 4 -------------------------------------- [1, 1, 1, 1, 0] [2, 0, 0, 1, 1] [2, 0, 1, 0, 1] [2, 0, 1, 1, 0] -------------------------------------- 4 150 2196800 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 5 Looking for S-pairs by iterating through all 26 initial monomials [26][25][24][23][22][21][20][19][18][17]Snr+[16]Snr+[15]Snr+[14][13]Snr+[1\ 2][11][10][9][8][7][6][5][4][3]Snr*[2][1] Statistics for degree 5: Date: mar oct 10 00:17:23 MDT 2000 Time: 400 ms Memory: 2229 ko. S-Pairs: 4 (+ 0 normalf->0 + 1 reduction->0 + 6 non-lcm->0) Minimal generators: 5 -------------------------------------- [1, 1, 1, 1, 1] [2, 0, 1, 1, 1] [2, 0, 2, 0, 1] [2, 1, 0, 1, 1] [2, 1, 0, 2, 0] -------------------------------------- 5 410 2229568 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 6 Looking for S-pairs by iterating through all 42 initial monomials [42][41][40][39][38][37]Snr+[36][35]Snr+[34][33][32][31][30]Snr+[29][28][2\ 7][26][25][24][23]Snr+[22]Snr+[21][20][19][18]Snr+[17][16][15][14][13]Snr*\ Snr*Snr*[12]Snr*Snr*[11]Snr*Snr*[10]Snr*[9][8][7][6][5][4]Snr*[3][2][1] Statistics for degree 6: Date: mar oct 10 00:17:24 MDT 2000 Time: 1 s 490 ms Memory: 2311 ko. S-Pairs: 6 (+ 0 normalf->0 + 9 reduction->0 + 28 non-lcm->0) Minimal generators: 3 -------------------------------------- [2, 1, 1, 2, 0] [2, 1, 2, 0, 1] [2, 2, 0, 1, 1] -------------------------------------- 6 1490 2311488 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 7 Looking for S-pairs by iterating through all 66 initial monomials [66][65][64][63][62][61][60][59][58][57][56][55][54][53][52][51][50][49][4\ 8][47]Snr+Snr+[46][45][44]Snr+[43]Snr+Snr+[42][41]Snr+[40][39]Snr+[38]Snr+\ Snr*[37][36][35][34]Snr+[33][32]Snr+Snr+[31][30][29][28][27][26][25][24]Sn\ r*[23][22][21][20][19][18]Snr*Snr*Snr*[17]Snr*[16][15][14]Snr*Snr*Snr*[13]\ [12][11]Snr*Snr*Snr*[10][9][8]Snr*Snr*[7]Snr*Snr*Snr*Snr*Snr*[6][5][4][3][\ 2][1] Statistics for degree 7: Date: mar oct 10 00:17:28 MDT 2000 Time: 4 s 100 ms Memory: 2409 ko. S-Pairs: 11 (+ 0 normalf->0 + 19 reduction->0 + 67 non-lcm->0) Minimal generators: 2 -------------------------------------- [2, 2, 0, 2, 1] [2, 2, 2, 0, 1] -------------------------------------- 7 4100 2409792 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 8 Looking for S-pairs by iterating through all 99 initial monomials [99][98][97][96][95][94][93][92][91][90][89][88][87][86][85][84]Snr+[83][8\ 2]Snr+[81][80][79][78][77][76][75][74]Snr+[73][72]Snr+[71][70][69][68][67]\ [66][65][64][63][62][61][60][59]Snr+Snr+[58][57][56][55][54][53][52][51][5\ 0]Snr+Snr+Snr+[49][48]Snr+Snr+[47]Snr+[46]Snr+Snr+Snr*[45][44]Snr*Snr*Snr*\ Snr*[43][42][41]Snr*Snr*Snr*[40]Snr*Snr*Snr*[39][38]Snr*Snr*Snr*Snr*Snr*[3\ 7][36]Snr*Snr*[35]Snr*Snr*Snr*[34]Snr*Snr*[33]Snr*[32]Snr*Snr*[31][30][29]\ [28][27][26][25]Snr*[24][23]Snr*[22][21][20]Snr*[19]Snr*[18][17]Snr*Snr*[1\ 6][15][14][13]Snr*Snr*Snr*[12]Snr*[11][10][9][8][7]Snr+Snr*[6]Snr*Snr*Snr*\ [5][4]Snr*Snr*Snr*Snr*[3][2][1] Statistics for degree 8: Date: mar oct 10 00:17:39 MDT 2000 Time: 10 s 940 ms Memory: 2655 ko. S-Pairs: 15 (+ 0 normalf->0 + 44 reduction->0 + 171 non-lcm->0) Minimal generators: 0 8 10940 2655552 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 9 Looking for S-pairs by iterating through all 143 initial monomials [143][142][141][140][139][138][137][136][135][134][133][132][131][130][129\ ][128][127][126][125][124][123][122][121][120][119][118][117][116][115][11\ 4][113][112][111][110][109][108][107][106][105][104]Snr+Snr+Snr+[103][102]\ [101]Snr+[100]Snr+Snr+Snr+[99][98]Snr+Snr+[97][96]Snr+Snr+[95]Snr+Snr+Snr+\ [94][93][92][91][90][89]Snr+Snr+[88][87][86]Snr+[85][84][83]Snr+Snr+[82]Sn\ r+[81][80][79][78][77]Snr*Snr*[76][75][74][73][72][71][70][69][68][67][66]\ [65]Snr*Snr*[64]Snr*[63][62][61][60]Snr*Snr*[59][58][57][56][55][54][53][5\ 2][51]Snr*[50][49][48][47]Snr*Snr*Snr*Snr*Snr*[46][45]Snr*[44][43]Snr*Snr*\ [42]Snr*Snr*Snr*Snr*Snr*Snr*[41][40]Snr*Snr*Snr*[39]Snr*Snr*Snr*Snr*Snr*[3\ 8]Snr*Snr*Snr*Snr*Snr*Snr*[37][36]Snr*Snr*[35][34]Snr*Snr*[33]Snr*Snr*[32]\ Snr*Snr*Snr*[31]Snr*Snr*Snr*Snr*Snr*[30]Snr*Snr*[29]Snr*Snr*Snr*Snr*Snr*Sn\ r*Snr*Snr*[28]Snr*Snr*[27][26][25][24]Snr*[23][22][21]Snr*[20][19][18]Snr*\ [17][16][15]Snr*[14][13]Snr*[12]Snr*Snr*Snr*[11][10][9]Snr*[8][7][6]Snr*Sn\ r*[5]Snr*[4][3][2]Snr*Snr*[1] Statistics for degree 9: Date: mar oct 10 00:18:05 MDT 2000 Time: 25 s 300 ms Memory: 2934 ko. S-Pairs: 20 (+ 0 normalf->0 + 76 reduction->0 + 310 non-lcm->0) Minimal generators: 0 9 25300 2934080 #Stats: degree,time(ms),mem(bytes) Constructing Minimal Generating Set at degree 10 Looking for S-pairs by iterating through all 201 initial monomials [201][200][199][198][197][196][195][194][193][192][191][190][189][188][187\ ][186][185][184][183][182][181][180][179][178][177][176][175][174][173][17\ 2][171][170][169][168][167][166]Snr+Snr+[165][164]Snr+Snr+[163][162][161][\ 160][159][158][157][156]Snr+[155][154]Snr+[153][152][151][150][149][148][1\ 47]Snr+[146][145][144][143][142][141][140][139][138][137][136][135][134][1\ 33][132][131][130][129][128][127][126]Snr+Snr+Snr+[125][124][123][122][121\ ][120][119][118][117]Snr+Snr+Snr+Snr+[116][115][114][113]Snr+Snr*Snr+[112]\ [111]Snr+Snr+[110][109]Snr+Snr+[108]Snr+Snr*Snr*Snr*[107][106][105]Snr*Snr\ *Snr*Snr*Snr*Snr*[104][103][102]Snr*Snr*Snr*Snr*Snr*[101]Snr*Snr*Snr*[100]\ [99]Snr*Snr*Snr*Snr*Snr*Snr*Snr*[98][97]Snr*Snr*[96]Snr*Snr*Snr*Snr*Snr*[9\ 5][94][93]Snr*[92][91][90]Snr*Snr*[89]Snr*[88][87][86][85][84]Snr*Snr*Snr*\ [83]Snr*Snr*Snr*Snr*[82]Snr*Snr*Snr*[81]Snr*Snr*[80][79]Snr*Snr*[78][77][7\ 6]Snr*[75]Snr*[74]Snr*[73][72][71][70][69][68][67][66][65][64][63][62][61]\ [60][59][58]Snr*Snr*Snr*Snr*[57][56][55][54][53][52]Snr*[51][50][49]Snr*Sn\ r*Snr*Snr*Snr*[48]Snr*Snr*Snr*Snr*Snr*[47]Snr*[46]Snr*Snr*Snr*[45][44][43]\ [42][41]Snr*Snr*Sn*Snr*[40]Snr*[39]Snr*Snr*[38][37][36][35]Snr*Snr*Snr*Snr\ *[34]Snr*[33][32][31]Snr*Snr*Snr*Snr*Snr*Snr*Snr*Snr*[30]Snr*Snr*Snr*Snr*S\ nr*[29][28]Snr*Snr*[27]Snr*Snr*Snr*Snr*Snr*Snr*Snr*[26]Snr*Snr*Snr*[25]Snr\ *Snr*Snr*Snr*[24]Snr*Snr*Snr*Snr*Snr*Snr*[23]Snr*Snr*Snr*Snr*Snr*Snr*Snr*S\ nr*[22]Snr*Sn*[21][20][19][18][17][16][15][14][13][12][11]Snr*Snr*[10][9][\ 8][7]Snr*[6]Snr*Snr*[5][4][3][2][1] Statistics for degree 10: Date: mar oct 10 00:19:05 MDT 2000 Time: 1 min 0 s 70 ms Memory: 3417 ko. S-Pairs: 21 (+ 2 normalf->0 + 132 reduction->0 + 678 non-lcm->0) Minimal generators: 0 10 60070 3417316 #Stats: degree,time(ms),mem(bytes) Total time: 1 min 42 s 670 ms table( 1 = [[1, 0, 0, 0, 0]], 2 = [[1, 0, 1, 0, 0], [1, 1, 0, 0, 0]], 3 = [[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [2, 0, 0, 0, 1], [2, 0, 0, 1, 0]]\ , 4 = [[1, 1, 1, 1, 0], [2, 0, 0, 1, 1], [2, 0, 1, 0, 1], [2, 0, 1, 1, 0]]\ , 5 = [[1, 1, 1, 1, 1], [2, 0, 1, 1, 1], [2, 0, 2, 0, 1], [2, 1, 0, 1, 1],\ [2, 1, 0, 2, 0]], 6 = [[2, 1, 1, 2, 0], [2, 1, 2, 0, 1], [2, 2, 0, 1, 1]], 7 = [[2, 2, 0, 2, 1], [2, 2, 2, 0, 1]] ) >> quit