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r36/xlog/INVBASE.LOG
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REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... % ***** Example 1 ***** g:=invbase{4*x^2 + x*y^2 - z +1/4, 2*x + y^2*z + 1/2, x^2*z - 1/2*x - y^2}; 3 2 3 2 g := {8*x*y*z - 2*x*y*z + 4*y - 4*y*z + 16*x*y + 17*y*z - 4*y, 4 2 2 2 8*y - 8*x*z - 256*y + 2*x*z + 64*z - 96*x + 20*z - 9, 3 2*y *z + 4*x*y + y, 3 2 2 2 8*x*z - 2*x*z + 4*y - 4*z + 16*x + 17*z - 4, 3 3 2 - 4*y*z - 8*y + 6*x*y*z + y*z - 36*x*y - 8*y, 2 2 2 4*x*y + 32*y - 8*z + 12*x - 2*z + 1, 2 2*y *z + 4*x + 1, 3 2 2 - 4*z - 8*y + 6*x*z + z - 36*x - 8, 2 2 2 8*x - 16*y + 4*z - 6*x - z} h:=invlex g; 6 5 4 3 2 h := {3976*x + 37104*z - 600*z + 2111*z + 122062*z + 232833*z - 680336*z + 288814, 2 6 5 4 3 2 1988*y - 76752*z + 1272*z - 4197*z - 251555*z - 481837*z + 1407741*z - 595666, 7 6 5 4 3 2 16*z - 8*z + z + 52*z + 75*z - 342*z + 266*z - 60} % ***** Example 2 ***** on trinvbase$ invtorder revgradlex,{x,y,z}$ g:=invbase{x^3 + y^2 + z - 3, y^3 + z^2 + x - 3, z^3 + x^2 + y - 3}; ---------- ORDER = 3 ---------- ---------- ORDER = 4 ---------- ---------- ORDER = 5 ---------- ---------- ORDER = 6 ---------- ---------- ORDER = 7 ---------- reductions = 77 zeros = 11 maxord = 7 order = 7 length = 13 D i m e n s i o n = 0 N u m b e r o f s o l u t i o n s = 27 2 2 3 2 2 2 2 2 2 2 2 2 g := {x *y *z - 3*x *y - x*y *z - x *z + x*y*z + x *y + 3*x*y + 3*x 2 - 3*x*y + y + z - 3, 2 3 2 2 2 2 2 x *y*z + x *y - 3*x *y - x*y*z + x*z + x + 3*x*y - 3*x, 2 3 2 2 2 2 2 2 x*y *z - 3*x*y - y *z - x*z + y*z - x + x*y + 3*y + 3*x - 3*y, 2 3 2 2 2 2 x *y + x *z - 3*x - y - z + 3, 2 3 2 2 2 x *z + x *y - x*y - 3*x - x*z + 3*x, 3 2 2 x*y*z + x*y - 3*x*y - y*z + z + x + 3*y - 3, 2 3 2 2 2 2 y *z + x *y - 3*y - z - x + 3, 3 2 2 x*y + x*z + x - 3*x, 3 2 x*z + x*y - y - 3*x - z + 3, 3 2 2 y*z + x *y + y - 3*y, 3 2 x + y + z - 3, 3 2 y + z + x - 3, 3 2 z + x + y - 3} h:=invlex g; h := { - 412373224241856640945111992285148*x 26 - 1449641911307232269543863070491*z 25 - 2168612583844782211565651535007*z 24 - 2847785553349083352614138977565*z 23 + 35576725674692081471990149502410*z 22 + 54428253744724168431241789131696*z 21 + 72399213723404842594731673129040*z 20 - 367271934803243933721304377312611*z 19 - 577412401939211224792461395441215*z 18 - 752437808233499373488146484648759*z 17 + 2023265153056028087298524971059780*z 16 + 3362763223678472034221124579531852*z 15 + 4206754352383617663824252489277347*z 14 - 6294684651757967009725536832231313*z 13 - 11645937803380007452970955449190202*z 12 - 13912359441969785881761771576274650*z 11 + 10813944944367254864931915957111635*z 10 + 24146769890624467199683669920316403*z 9 + 28253894162862384778437975597863994*z 8 - 9413195341759783675090699662838024*z 7 - 28732526014615244592092156992897700*z 6 - 34274801170918929476253738727746640*z 5 + 3129736563440111416048255862484824*z 4 + 17956474721641990844572020234799903*z 3 + 21526113174342847360723274047268152*z 2 + 795762450545743140366490379212137*z - 6078501600786528783018721470971548*z - 3909915395631179340911139035268300, - 412373224241856640945111992285148*y 26 + 3680069960199680647552580014011*z 25 + 4946533576928304373640222248439*z 24 + 6522058320833813074018729716109*z 23 - 91123955793021263648983859056246*z 22 - 122860148727246593163920662895892*z 21 - 161652285275223157884596590612424*z 20 + 962753147411097965886678769071203*z 19 + 1303906344577106971108666976068347*z 18 + 1646174502798616879170351863301227*z 17 - 5539016636709239326199213127901604*z 16 - 7732787650045519336370661934943044*z 15 - 9110016144563661988538140239320223*z 14 + 18612337918090152097453612706753413*z 13 + 27965492180063505085033283788513066*z 12 + 30440317356106139389125602029763822*z 11 - 36863224004805998790098755360970471*z 10 - 62542906673581589636380853858043447*z 9 - 64689461678563738668073440578715518*z 8 + 42623160090556250860454187465583768*z 7 + 83548043234053149543179359124170180*z 6 + 85865493477306743665317502795142584*z 5 - 27434780477528021937653276615015928*z 4 - 61602505785524913541319871156904287*z 3 - 62515628463318116801915981996829328*z 2 + 5925778048881538700551831705942583*z + 24088990130824351149845277501309728*z + 15820742036151533576971241715895080, 27 24 21 19 18 17 16 - z + 27*z - 317*z + 18*z + 2067*z + 50*z - 279*z 15 14 13 12 11 10 - 8156*z - 645*z + 1674*z + 20359*z + 3044*z - 4645*z 9 8 7 6 5 4 3 - 33644*z - 6288*z + 6388*z + 36936*z + 5925*z - 4957*z - 23187*z 2 - 4063*z + 4342*z + 5352} % ***** Example 3 (limited by the degree bound) ***** invtorder revgradlex,{x,z,y,t}$ k:=5$ on errcont$ invbase{x^(k+1)-y^(k-1)*z*t, x*z^(k-1)-y**k, x^k*y-z^k*t}; ---------- ORDER = 6 ---------- ---------- ORDER = 7 ---------- ---------- ORDER = 8 ---------- ---------- ORDER = 9 ---------- ---------- ORDER = 10 ---------- ---------- ORDER = 11 ---------- ---------- ORDER = 12 ---------- ---------- ORDER = 13 ---------- ---------- ORDER = 14 ---------- ---------- ORDER = 15 ---------- ---------- ORDER = 16 ---------- ---------- ORDER = 17 ---------- ---------- ORDER = 18 ---------- ---------- ORDER = 19 ---------- ---------- ORDER = 20 ---------- ---------- ORDER = 21 ---------- ***** Maximum degree bound exceeded. invtempbasis; 17 2 16 { - t*z + x *y , 13 3 11 - t*z + x *y , 9 4 6 - t*z + x *y , 4 6 - t*y *z + x , 5 5 - t*z + x *y, 4 5 x*z - y } end$ (TIME: invbase 1020 1020)