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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)
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