Tue Feb 10 12:26:42 2004 run on Linux

% *****  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 for test: 20 ms
