@@ -1,411 +1,411 @@ -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) +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)