Changeset dcad76 in git


Ignore:
Timestamp:
Feb 27, 2018, 2:51:59 PM (5 years ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a657104b677b4c461d018cbf3204d72d34ad66a9')
Children:
617c8e724541d5f5c39e8ee6708e0e2d8905d332
Parents:
1cc42d37189567a882e48c99e9fb011e6ba56bdc0277c5dd6af4f887925e06b299068d0c17f5d324
git-author:
Hans Schoenemann <hannes@mathematik.uni-kl.de>2018-02-27 14:51:59+01:00
git-committer:
GitHub <noreply@github.com>2018-02-27 14:51:59+01:00
Message:
Merge pull request #857 from jgmbenoit/debian/4.1.1+ds-1/lintian/spelling

correct spelling errors as detected by lintian
Files:
8 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/arr.lib

    r1cc42d rdcad76  
    13401340            after a tranformation x -> Tx + c we have the arrangement has the matrix representation
    13411341            [AT^-1|b+AT^-1c] such that [AT^-1]_v = I and [b+AT^-1c]_v = 0;
    1342 NOTE:       algorith performs a base change if H_k is homogenous (i.e. has no)
     1342NOTE:       algorithm performs a base change if H_k is homogenous (i.e. has no)
    13431343            constant term and an affine transformation otherwise
    13441344            Ax+b = 0, Transformation x = Ty+c: AT^-1y + AT^-1c + b = 0

  • Singular/LIB/schreyer.lib

    r0277c5 rdcad76  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="version schreyer.lib 4.1.1.0 Dec_2017 "; // $Id$
     2version="version schreyer.lib 4.1.1.1 Feb_2018 "; // $Id$
    33category="General purpose";
    44info="
    5 LIBRARY: schreyer.lib Schreyer resolution computations and helpers for derham.lib
     5LIBRARY: schreyer.lib helpers for derham.lib
    66AUTHOR:  Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.uni-kl.de}
    77KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy
    … …  
    5555
    5656PROCEDURES:
    57   s_res(M,l)   compute Schreyer resolution via LiftTree method from [BMSS]
    5857  Sres(M,l)    helper for computing Schreyer resolution
    5958  Ssyz(M)      helper for computing Schreyer resolution of module M of length 1
    6059  Scontinue(l) helper for extending currently active resolution
    61   SSres(M,l)    helper2 for computing Schreyer resolution
    62   SSsyz(M)      helper2 for computing Schreyer resolution of module M of length 1
    63   SScontinue(l) helper2 for extending currently active resolution
    64 
    65 SEE ALSO: syz, sres, lres, res
     60
     61SEE ALSO: syz, sres, lres, res, fres
    6662";
    6763
    … …  
    121117  return (list(G, II));
    122118}
    123 
    124 static proc splitSyzGB( module J, int c )
    125 {
    126   module JJ; vector v, vv; int i;
    127 
    128   for( i = ncols(J); i > 0; i-- )
    129   {
    130     v = J[i];
    131 
    132     vv = 0;
    133 
    134     while(   Syzextra::leadcomp(v) <= c )
    135     {
    136       vv = vv + lead(v);
    137       v  = v  - lead(v);
    138     }
    139 
    140     J[i] = vv;
    141     JJ[i] = v;
    142   }
    143 
    144   J = simplify(J, 2);
    145   JJ = simplify(JJ, 2);
    146 
    147   return (list(J, JJ));
    148 }
    149 
    150119
    151120static proc Sinit(module M)
    … …  
    302271}
    303272
    304 proc Ssyz(module M)
    305 "USAGE:  Ssyz(module M)
    306 RETURN:  ring, containing a Schreyer resolution
    307 PURPOSE: computes a Schreyer resolution of M of length 1 (see the library overview)
    308 SEE ALSO: Sres
    309 EXAMPLE: example Ssyz; shows an example
    310 "
    311 {
    312   def S = Sinit(M); setring S;
    313 
    314   Sstep(); // NOTE: what if M is zero?
    315 
    316   return (S);
    317 }
    318 example
    319 { "EXAMPLE:"; echo = 2;
    320   ring r;
    321   module M = maxideal(1); M;
    322   def S = Ssyz(M); setring S; S;
    323   "Only the first syzygy: ";
    324   RES;
    325   MRES; // Note gen(i)
    326   kill S;
    327   setring r; kill M;
    328 
    329   module M = 0;
    330   def S = Ssyz(M); setring S; S;
    331   "Only the first syzygy: ";
    332   RES;
    333   MRES;
    334 }
    335 
    336273proc Sres(module M, int l)
    337274"USAGE:  Sres(module M, int len)
    … …  
    377314}
    378315
    379 
    380 
    381316// ================================================================== //
    382317
    383 
    384 LIB "general.lib"; // for sort
    385 
    386 static proc MySort(def M)
    387 " Sorts the given ideal or module wrt >_{(c, ds)}  (.<.<.<.<) "
    388 {
    389   if( typeof( attrib(basering, "DEBUG") ) == "int" )
    390   {
    391     int @DEBUG = attrib(basering, "DEBUG");
    392   } else
    393   {
    394     int @DEBUG = 0; // !system("with", "ndebug");
    395   }
    396 
    397   if( typeof( attrib(basering, "KERCHECK") ) == "int" )
    398   {
    399     int @KERCHECK = attrib(basering, "KERCHECK");
    400   } else
    401   {
    402     int @KERCHECK = @DEBUG;
    403   }
    404 
    405   def @N = M;
    406 
    407   if( size(M) > 0 )
    408   {
    409     Syzextra::Sort_c_ds(@N);
    410 
    411     if( @KERCHECK )
    412     {
    413       def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed?
    414       def @M = M;
    415       @M = M[iv];
    416 
    417       // 0^th syz. property
    418       if( (size(@N) + size(@M)) > 0 )
    419       {
    420         if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 )
    421         {
    422           "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
    423 
    424           "@M:"; @M;
    425           "@N:"; @N;
    426 
    427           "module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ): ";
    428           module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) );
    429 
    430           "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
    431         }
    432       }
    433     }
    434   }
    435 
    436   return (@N);
    437 }
    438 
    439 
    440 /* static */
    441 proc SSinit(def M)
    442 {
    443 //  rtimer, "***TIMESNAP0 for SSinit: on level: [",-1,"] :: t: ", timer, ", r: ", rtimer;
    444   if( (typeof(M) != "module") && (typeof(M) != "ideal") )
    445   {
    446     ERROR("Sorry: need an ideal or a module for input");
    447   }
    448   def @save = basering;
    449 
    450   int @DEBUG = 0; // !system("with", "ndebug");
    451 
    452   if( typeof( attrib(SSinit, "DEBUG") ) == "int" )
    453   {
    454     @DEBUG = attrib(SSinit, "DEBUG");
    455   }
    456 
    457   int @SYZCHECK = 0; // @DEBUG;
    458 
    459   if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" )
    460   {
    461     @SYZCHECK = attrib(SSinit, "SYZCHECK");
    462   }
    463 
    464   int @KERCHECK = 0; // @DEBUG;
    465 
    466   if( typeof( attrib(SSinit, "KERCHECK") ) == "int" )
    467   {
    468     @KERCHECK = attrib(SSinit, "KERCHECK");
    469   }
    470 
    471   int @IGNORETAILS = 0;
    472 
    473   if( typeof( attrib(SSinit, "IGNORETAILS") ) == "int" )
    474   {
    475     @IGNORETAILS = attrib(SSinit, "IGNORETAILS");
    476   }
    477 
    478   int @TREEOUTPUT = 0;
    479 
    480   if( typeof( attrib(SSinit, "TREEOUTPUT") ) == "int" )
    481   {
    482     @TREEOUTPUT = attrib(SSinit, "TREEOUTPUT");
    483   }
    484 
    485   int @RINGCHANGE = 0;
    486 
    487   if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
    488   {
    489     @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
    490   }
    491 
    492   def opts = option(get);
    493   option(redSB); option(redTail);
    494     M = simplify(interred(groebner(M)), 1 + 2 + 4 + 32); // NOTE: we require interreduced GB for input
    495   option(set, opts); kill opts;
    496 
    497 //  int @IS_A_SB = attrib(M, "isSB");  if( !@IS_A_SB )  {  } else  {  }
    498 // attrib(M, "isSB", 1);
    499 
    500   if( @IGNORETAILS )
    501   {
    502     M = lead(M);
    503   }
    504 
    505   def @N = MySort(M); // TODO: replace with inplace sorting!!!
    506   def LEAD = lead(@N);
    507 
    508   if( @KERCHECK )
    509   {
    510     def @LEAD = lead(M);
    511 
    512     // sort wrt neg.deg.rev.lex!
    513     intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed!
    514 
    515     M = M[iv_ds]; // sort M wrt ds on current leading terms
    516     @LEAD = @LEAD[iv_ds];
    517 
    518     if( size(module( matrix(@N) - matrix(M) )) > 0 )
    519     {
    520       "M:"; M;
    521       "@N:"; @N;
    522 
    523       "module( matrix(@N) - matrix(M) ): ";
    524       module( matrix(@N) - matrix(M) );
    525 
    526       "ERROR: wrong sorting (in SSnit): @N != M!!!";
    527     }
    528 
    529     if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 )
    530     {
    531       "LEAD:"; LEAD;
    532       "@LEAD:"; @LEAD;
    533 
    534       "module( matrix(@LEAD) - matrix(LEAD) ): ";
    535       module( matrix(@LEAD) - matrix(LEAD) );
    536 
    537       "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!";
    538     }
    539 
    540   }
    541 
    542   M = @N;
    543 
    544   def TAIL =   Syzextra::Tail(M);
    545 
    546   int @RANK = nrows(M); int @SIZE = ncols(M);
    547 
    548   intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements
    549 
    550   // TODO: what about real modules? weighted ones?
    551 
    552   if( @RINGCHANGE )
    553   {
    554     list @l = ringlist(@save);
    555     int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]);
    556     // NOTE: @wdeg will be ignored anyway :(
    557     @l[3] = list(list("C", @z), list("lp", @wdeg));
    558     kill @z, @m, @wdeg; // since these vars are ring independent!
    559     def S = ring(@l); // --  Syzextra::MakeInducedSchreyerOrdering(1);
    560     kill @l;
    561     setring S; // ring with an easy divisibility test ("C, lex") // or not!???
    562   } else
    563   { def S = basering; }
    564 
    565   // Setup the leading syzygy^{-1} module to zero:
    566   module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0));
    567 
    568   if( !@RINGCHANGE )
    569   {
    570     if( defined(RES) )  { kill RES; }
    571     if( defined(MRES) ) { kill MRES; }
    572     if( defined(LRES) ) { kill LRES; }
    573     if( defined(TRES) ) { kill TRES; }
    574   }
    575 
    576   module MRES = Z;
    577 
    578   list RES;  RES[1] = Z;
    579   list LRES; LRES[1] = Z;
    580   list TRES; TRES[1] = Z;
    581 
    582   if( !defined(M) )
    583   {
    584     def M = imap(@save, M);
    585   }
    586 
    587   module F = freemodule(@RANK); intvec @V = deg(F[1..@RANK]); kill F;
    588 
    589   attrib(M, "isHomog", @V);
    590   attrib(M, "isSB", 1);
    591   attrib(M, "degrees", @DEGS);
    592 
    593   if( !defined(LEAD) )
    594   {
    595     def LEAD = imap(@save, LEAD);
    596   }
    597 
    598   attrib(LEAD, "isHomog", @V);
    599   attrib(LEAD, "isSB", 1);
    600 
    601   if( !defined(TAIL) )
    602   {
    603     def TAIL = imap(@save, TAIL);
    604   }
    605 
    606   if( @SYZCHECK )
    607   {
    608     // 0^th syz. property
    609     if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 )
    610     {
    611       transpose( transpose(M) * transpose(MRES) );
    612       "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!";
    613     }
    614   }
    615 
    616   RES [size(RES)+1] = M; // list of all syzygy modules
    617   LRES[size(LRES)+1] = LEAD; // list of all syzygy modules
    618   TRES[size(TRES)+1] = TAIL; // list of all syzygy modules
    619 
    620   MRES = MRES, M; //?
    621 
    622   attrib(MRES, "isHomog", @V);
    623 
    624 //  attrib(S, "InducionStart", @RANK);
    625 
    626 
    627   if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" )
    628   {
    629     attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") );
    630   } else
    631   {
    632     attrib(S, "LEAD2SYZ", 0);
    633   }
    634 
    635   if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" )
    636   {
    637     attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") );
    638   } else
    639   {
    640     attrib(S, "TAILREDSYZ", 1);
    641   }
    642 
    643   if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" )
    644   {
    645     attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") );
    646   } else
    647   {
    648     attrib(S, "HYBRIDNF", 0);
    649   }
    650 
    651   if( typeof( attrib(SSinit, "NOCACHING") ) == "int" )
    652   {
    653     attrib(S, "NOCACHING", attrib(SSinit, "NOCACHING") );
    654   } else
    655   {
    656     attrib(S, "NOCACHING", 0);
    657   }
    658 
    659 
    660   // maybe resetting existing ring attributes!
    661   attrib(S, "DEBUG", @DEBUG);
    662   attrib(S, "SYZCHECK", @SYZCHECK);
    663   attrib(S, "KERCHECK", @KERCHECK);
    664   attrib(S, "IGNORETAILS", @IGNORETAILS);
    665   attrib(S, "TREEOUTPUT", @TREEOUTPUT);
    666   attrib(S, "SYZNUMBER", 0);
    667 
    668   export RES;
    669   export MRES;
    670   export LRES;
    671   export TRES;
    672 
    673 //  rtimer, "***TIMESNAP1 for SSinit: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
    674 
    675   return (S);
    676 }
    677 example
    678 { "EXAMPLE:"; echo = 2;
    679   ring R = 0, (w, x, y, z), dp;
    680 
    681   def M = maxideal(1);
    682   def S = SSinit(M); setring S; S;
    683 
    684   "Only the first initialization: ";
    685   RES; LRES; TRES;
    686   MRES;
    687 
    688   kill S; setring R; kill M;
    689 
    690   ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
    691   def S = SSinit(M); setring S; S;
    692 
    693   "Only the first initialization: ";
    694   RES; LRES; TRES;
    695   MRES;
    696 
    697   kill S; setring R; kill M;
    698 }
    699 
    700 
    701 LIB "poly.lib"; // for lcm
    702 
    703 
    704 
    705 // -------------------------------------------------------- //
    706 
    707 /// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz?
    708 
    709 /// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ?
    710 
    711 // TODO: store m * @tail -.-^-.-^-.--> ?
    712 static proc SSTraverseTail(poly m, def @tail, def L, def T, list #)
    713 {
    714   if( typeof( attrib(basering, "DEBUG") ) == "int" )
    715   {
    716     int @DEBUG = attrib(basering, "DEBUG");
    717   } else
    718   {
    719     int @DEBUG = 0; // !system("with", "ndebug");
    720   }
    721 
    722   if( typeof( attrib(basering, "KERCHECK") ) == "int" )
    723   {
    724     int @KERCHECK = attrib(basering, "KERCHECK");
    725   } else
    726   {
    727     int @KERCHECK = @DEBUG;
    728   }
    729 
    730   if( typeof(#[1]) == "module" )
    731   {
    732     vector ss =   Syzextra::TraverseTail(m, @tail, L, T, #[1]);
    733   } else
    734   {
    735     vector ss =   Syzextra::TraverseTail(m, @tail, L, T);
    736   }
    737 
    738   if( @KERCHECK )
    739   {
    740     vector s = 0;
    741 
    742     def @l, @p;
    743     @p = @tail;
    744 
    745   // iterate tail-terms in ANY order!
    746     while( size(@p) > 0 )
    747     {
    748       @l = lead(@p);
    749       s = s + SSReduceTerm(m, @l, [0], L, T, #); // :(
    750       @p = @p - @l;
    751     }
    752 
    753     if( s != ss )
    754     {
    755       "ERROR in   Syzextra::TraverseTail => old: ", s, " != ker: ", ss;
    756       "m: ", m;
    757       "@tail: ", @tail;
    758       L; T; #;
    759     }
    760   }
    761 
    762   return (ss);
    763 }
    764 
    765 // -------------------------------------------------------- //
    766 
    767 // -------------------------------------------------------- //
    768 
    769 // module (N, LL, TT) = SSComputeSyzygy(L, T);
    770 // Compute Syz(L ++ T) = N = LL ++ TT
    771 
    772 // resolution/syzygy step:
    773 /* static */
    774 proc SSstep()
    775 {
    776 //  rtimer, "***TIMESNAP0 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
    777 
    778   int @DEBUG = attrib(basering, "DEBUG");
    779   int @SYZCHECK = attrib(basering, "SYZCHECK");
    780 
    781 /*
    782   // is initial weights are all zeroes!
    783   def L =  lead(M);
    784   intvec @V = deg(M[1..ncols(M)]);  @W;  @V;  @W = @V;  attrib(L, "isHomog", @W);
    785     Syzextra::SetInducedReferrence(L, @RANK, 0);
    786 */
    787 
    788 //  def L =  lead(MRES);
    789 //  @W = @W, @V;
    790 //  attrib(L, "isHomog", @W);
    791 
    792 
    793   // General setting:
    794 //    Syzextra::SetInducedReferrence(MRES, 0, 0); // limit: 0!
    795   int @l = size(RES);
    796 
    797   def M =  RES[@l];
    798 
    799   def L = LRES[@l];
    800   def T = TRES[@l];
    801 
    802 
    803   //// TODO: wrong !!!!!
    804   int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?!
    805 
    806 
    807 
    808 /*
    809   if( @RANK !=  nrows(M) )
    810   {
    811     type(MRES);
    812     @RANK;
    813     type(M);
    814     pause();
    815   }
    816 */
    817 
    818   intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V;
    819 
    820   // TODO: N  = SYZ( M )!!!
    821   module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/);
    822 
    823   // shift syz.comp by @RANK:
    824   module Z;
    825   Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL);   LL = transpose(Z);
    826   Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT);   TT = transpose(Z);
    827   Z = 0; Z[@RANK] = 0; Z = Z, transpose(N);     N = transpose(Z);
    828 
    829 
    830   if( @SYZCHECK )
    831   {
    832     if( size(N) > 0 )
    833     {
    834       // next syz. property
    835       if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 )
    836       {
    837         "MRES", MRES;
    838 
    839         "N: "; N;
    840 
    841         "LL:"; LL;
    842         "TT:"; TT;
    843 
    844         "RANKS: ", @RANK;
    845 
    846         "transpose( transpose(N) * transpose(MRES) ) != 0!!!";
    847         transpose( transpose(N) * transpose(MRES) );
    848 
    849         "transpose(N) * transpose(MRES): ";
    850         transpose(N) * transpose(MRES);
    851       }
    852     }
    853   }
    854 
    855   attrib(N, "isHomog", @V);
    856 
    857   // TODO: correct the following:
    858   intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :(
    859 
    860 
    861   attrib(N, "degrees", @DEGS);
    862 
    863    RES[@l + 1] = N; // list of all syzygy modules
    864   LRES[@l + 1] = LL; // list of all syzygy modules
    865   TRES[@l + 1] = TT; // list of all syzygy modules
    866 
    867   MRES = MRES, N;
    868 
    869   attrib(MRES, "isHomog", @V);
    870 
    871 //  L = L, lead(N);  attrib(basering, "InducionLeads", L);
    872 
    873   int ss = attrib(basering, "SYZNUMBER");
    874   attrib(basering, "SYZNUMBER", ss + 1 );
    875 
    876 //  rtimer, "***TIMESNAP1 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
    877 }
    878 
    879 /* static */
    880 proc SScontinue(int l)
    881 "USAGE:  SScontinue(l)
    882 RETURN:  nothing, instead it changes RES and MRES variables in the current ring
    883 PURPOSE: computes further (at most l) syzygies
    884 NOTE:    must be used within a ring returned by Sres or Ssyz. RES and MRES are
    885          explained in Sres
    886 EXAMPLE: example Scontinue; shows an example
    887 "
    888 {
    889 //  rtimer, "***TIMESNAP0 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
    890 
    891   /// TODO!
    892 //  def data =   Syzextra::GetInducedData();
    893 
    894   if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */
    895   {
    896     ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz");
    897   }
    898   for (;  (l != 0) && (size(RES[size(RES)]) > 0); l-- )
    899   {
    900     SSstep();
    901   }
    902 
    903 //  rtimer, "***TIMESNAP1 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
    904 
    905 }
    906 example
    907 { "EXAMPLE:"; echo = 2;
    908   ring r;
    909   module M = maxideal(1); M;
    910   def S = SSsyz(M); setring S; S;
    911   "Only the first syzygy: ";
    912   RES; MRES;
    913   "More syzygies: ";
    914   SScontinue(10);
    915   RES; MRES;
    916 }
    917 
    918 /* static */
    919 proc SSsyz(def M)
    920 "USAGE:  SSsyz(M)
    921 RETURN:  ring, containing a list of modules RES and a module MRES
    922 PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)?
    923 NOTE:    The output is explained in Sres
    924 EXAMPLE: example Ssyz; shows an example
    925 "
    926 {
    927   if( (typeof(M) != "module") && (typeof(M) != "ideal") )
    928   {
    929     ERROR("Sorry: need an ideal or a module for input");
    930   }
    931 
    932   def SS = SSinit(M); setring SS;
    933 
    934   SSstep(); // NOTE: what if M is zero?
    935 
    936   return (SS);
    937 }
    938 example
    939 { "EXAMPLE:"; echo = 2;
    940   ring r;
    941 
    942 /*  ideal M = 0;
    943   def S = SSsyz(M); setring S; S;
    944   "Only the first syzygy: ";
    945   RES; LRES; TRES;
    946   MRES;
    947 
    948   kill S; setring r; kill M;
    949 */
    950 
    951   ideal M = maxideal(1); M;
    952 
    953   def S = SSres(M, 0); setring S; S;
    954   MRES;
    955   print(_);
    956   RES;
    957 
    958   kill S; setring r; kill M;
    959 
    960   kill r;
    961 
    962   ring R = 0, (w, x, y, z), dp;
    963   ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
    964 
    965   def S = SSres(M, 0); setring S; S;
    966   "";
    967   LRES;
    968   "";
    969   TRES;
    970   "";
    971   MRES;
    972   print(_);
    973   RES;
    974 }
    975 
    976 /* static */
    977 proc SSres(def M, int l)
    978 "USAGE:  SSres(I, l)
    979 RETURN:  ring, containing a list of modules RES and a module MRES
    980 PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer
    981          induced ordering with gen(i) > gen(j) if i > j, provided both gens
    982          are from the same syzygy level.???
    983 NOTE:    RES contains the images of maps subsituting the beginning of the
    984          Schreyer free resolution of baseRing^r/M, while MRES is a sum of
    985          these images in a big free sum, containing all the syzygy modules.
    986          The syzygy modules are shifted so that gen(i) correspons to MRES[i].
    987          The leading zero module RES[0] indicates the fact that coker of the
    988          first map is zero. The number of zeroes inducates the rank of input.
    989 NOTE:    If l == 0 then l is set to be nvars(basering) + 1
    990 EXAMPLE: example SSres; shows an example
    991 "
    992 {
    993   if( (typeof(M) != "module") && (typeof(M) != "ideal") )
    994   {
    995     ERROR("Sorry: need an ideal or a module for input");
    996   }
    997 /*
    998   "KERCHECK: ", attrib(SSinit, "KERCHECK");
    999   "SYZCHECK: ", attrib(SSinit, "SYZCHECK");
    1000   "DEBUG: ", attrib(SSinit, "DEBUG");
    1001   "HYBRIDNF: ", attrib(SSinit, "HYBRIDNF");
    1002   "TAILREDSYZ: ", attrib(SSinit, "TAILREDSYZ");
    1003   "LEAD2SYZ: ", attrib(SSinit, "LEAD2SYZ");
    1004 */
    1005 
    1006   def SS = SSinit(M); setring SS;
    1007 /*
    1008   "KERCHECK: ", attrib(SS, "KERCHECK");
    1009   "SYZCHECK: ", attrib(SS, "SYZCHECK");
    1010   "DEBUG: ", attrib(SS, "DEBUG");
    1011   "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
    1012   "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
    1013   "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
    1014   "";
    1015   "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
    1016   "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
    1017 */
    1018   if (l == 0)
    1019   {
    1020     l = nvars(basering) + 2; // not really an estimate...?!
    1021   }
    1022 
    1023   SSstep(); l = l - 1;
    1024 
    1025   SScontinue(l);
    1026 /*
    1027   "KERCHECK: ", attrib(SS, "KERCHECK");
    1028   "SYZCHECK: ", attrib(SS, "SYZCHECK");
    1029   "DEBUG: ", attrib(SS, "DEBUG");
    1030   "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
    1031   "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
    1032   "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
    1033   "";
    1034   "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
    1035   "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
    1036 */
    1037   return (SS);
    1038 }
    1039 example
    1040 { "EXAMPLE:"; echo = 2;
    1041   ring r;
    1042   module M = maxideal(1); M;
    1043   def S = SSres(M, 0); setring S; S;
    1044   RES;
    1045   MRES;
    1046 }
    1047 
    1048 static proc SRES_betti2(SRES SR, def a)
    1049 {
    1050   def R = SR.r; setring R;
    1051   return ( betti(SR.rsltn, a) );
    1052 }
    1053 
    1054 static proc SRES_betti1(SRES SR)
    1055 {
    1056   def R = SR.r; setring R;
    1057   return ( betti(SR.rsltn) );
    1058 }
    1059 
    1060 static proc SRES_print(SRES SR)
    1061 {
    1062   def R = SR.r; setring R;
    1063   "Schreyer resolution: ";
    1064   SR.rsltn; //  print ();
    1065   "over the ring: "; R;
    1066 }
    1067 
    1068 static proc SRES_minres(SRES SR)
    1069 {
    1070   def save = basering;
    1071   SRES S;
    1072   def R = SR.r; S.r = R;
    1073   setring R;
    1074   S.rsltn = minres(SR.rsltn); // in target ring :(
    1075   return (S);
    1076 }
    1077 
    1078 
    1079 // cannot be automatically used via overloading :(
    1080 static proc SRES_list(def SR)
    1081 "USAGE:  SRES_list(resolution)
    1082 RETURN:  list
    1083 PURPOSE: convert given resolution to a list
    1084 NOTE:    result is over basering
    1085 SEE ALSO: s_res, resolution
    1086 EXAMPLE: example s_res; shows an example
    1087 "
    1088 {
    1089   if( typeof(SR) != "SRES" )
    1090   {
    1091     list @@@L = SR;
    1092     return (@@@L);
    1093   }
    1094 
    1095   def save = basering;
    1096   def R = SR.r;
    1097 
    1098 //    if( 0 )  // ( save == R ) // TODO: not implemented :(((
    1099 //    {      list L = SR.rsltn;      return (L);    }
    1100 
    1101   setring R;
    1102 
    1103   list @@@L = SR.rsltn;
    1104   setring save;
    1105   return (imap( R, @@@L ));
    1106 }
    1107 
    1108318static proc mod_init()
    1109319{
    1110320  load("syzextra.so");
    1111 
    1112   if( 1 ) // !defined(Syzextra) )
    1113   {
    1114     // TODO: SSres - return SRESOLUTION?
    1115     newstruct("SRES","ring r,resolution rsltn"); // http://www.singular.uni-kl.de/Manual/latest/sing_179.htm#SEC218
    1116     system("install","SRES","print",SRES_print, 1);
    1117     system("install","SRES","betti",SRES_betti1, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
    1118     system("install","SRES","betti",SRES_betti2, 2); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
    1119     system("install","SRES","minres",SRES_minres, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_344.htm#SEC383
    1120 //    system("install","SRES","list", SRES_list, 1); // will never work :(((
    1121 //    system("install","SRES","string",SRES_string, 1);
    1122   }
    1123 }
    1124 
    1125 
    1126 static proc testallSexamples()
    1127 {
    1128   example Ssyz;
    1129   example Scontinue;
    1130   example Sres;
    1131 }
    1132 
    1133 static proc testallSSexamples()
    1134 {
    1135   example SSsyz;
    1136   example SScontinue;
    1137   example SSres;
    1138 }
    1139 example
    1140 { "EXAMPLE:"; echo = 2;
    1141   testallSexamples();
    1142   testallSSexamples();
    1143 }
    1144 
    1145 static proc  StartResTesting(list #)
    1146 {
    1147   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1148 
    1149   if( defined(@save_res_list) )
    1150   { ERROR("Sorry: existing global variable @save_res_list - run StopAddResTesting before another Start!!!"); }
    1151 
    1152   string @save_res_desc = string(#);
    1153 
    1154   if( !@treeout )
    1155   {
    1156     ">>>>>>>>> {{{{{{{{{ STARTING TESTING ('" + @save_res_desc + "') :::::::::::: ";
    1157   } else
    1158   {
    1159     "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
    1160   }
    1161 
    1162   list @save_res_list = list();
    1163   export @save_res_list;
    1164   export @save_res_desc;
    1165 }
    1166 
    1167 static proc  StopResTesting()
    1168 {
    1169   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1170 
    1171   if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
    1172   { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }
    1173 
    1174   if( !defined(@save_res_list) || !defined(@save_res_desc) )
    1175   { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }
    1176 
    1177   int i, j;
    1178   int f = 0;
    1179   def m, mm;
    1180 
    1181   if( !@treeout )
    1182   {
    1183   for (i = size(@save_res_list); i > 0; i--)
    1184   {
    1185     "Total Time: ", @save_res_list[i][5], ", Res: ", @save_res_list[i][6], ", Minimal Betti: ", @save_res_list[i][5] - @save_res_list[i][6], ",        ", @save_res_list[i][1], "   :with:    ", @save_res_list[i][2];
    1186   }
    1187 
    1188   }
    1189 
    1190   for (i = size(@save_res_list); i > 1; i--)
    1191   {
    1192     m = @save_res_list[i][4];
    1193 
    1194     for (j = i-1; j > 0; j--)
    1195     {
    1196       mm = @save_res_list[j][4];
    1197       if( (nrows(m) != nrows(mm)) || (ncols(m) != ncols(mm)) )
    1198       {
    1199         "ERROR: SIZE(Betti[j: ", j, "]) != SIZE(Betti[i: ", i, "]):";
    1200         "j: ", j;
    1201         print( @save_res_list[j][4], "betti");
    1202         print(@save_res_list[j]);
    1203 
    1204         "i: ", i;
    1205         print( @save_res_list[i][4], "betti");
    1206         print(@save_res_list[i]);
    1207 
    1208         f = 1;
    1209 
    1210       } else
    1211       {
    1212         if( m != mm )
    1213         {
    1214           "ERROR: Betti[j: ", j, "] != Betti[i: ", i, "]:";
    1215           "j: ", j;
    1216           print( @save_res_list[j][4], "betti");
    1217           print(@save_res_list[j]);
    1218 
    1219           "i: ", i;
    1220           print( @save_res_list[i][4], "betti");
    1221           print(@save_res_list[i]);
    1222 
    1223           f = 1;
    1224         };
    1225       };
    1226 
    1227     };
    1228 
    1229   };
    1230 
    1231   if( f )
    1232   {
    1233     print(@save_res_list);
    1234     "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
    1235 
    1236     "ERROR: There were some wrong betti numbers... ";
    1237   } else
    1238   {
    1239     if( !@treeout )
    1240     {
    1241       "BETTI: "; print( @save_res_list[1][4], "betti");
    1242     }
    1243   }
    1244 
    1245   kill @save_res_list;
    1246 
    1247   if( !@treeout )
    1248   {
    1249     "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
    1250   } else
    1251   {
    1252 //    "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
    1253     "] },";
    1254   }
    1255   kill @save_res_desc;
    1256 }
    1257 
    1258 static proc StartAddResTest(string method, string desc)
    1259 {
    1260   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1261 
    1262   if( !defined(@save_res_list) )
    1263   { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }
    1264 
    1265   if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
    1266   { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }
    1267 
    1268 
    1269   def @save_opts = option(get); export @save_opts;
    1270   def @save_method = method; export @save_method;
    1271   def @save_desc = desc; export @save_desc;
    1272 
    1273   if( !@treeout )
    1274   {
    1275     "< START RES TEST{{{ ", @save_method, ", with:", @save_desc, " ... ";
    1276   } else
    1277   {
    1278 //    Print("{ \"RESOLUTION: HYBRIDNF:%d, TAILREDSYZ: %d, LEAD2SYZ: %d, IGNORETAILS: %d\": [\n",
    1279 //       attributes.__HYBRIDNF__, attributes.__TAILREDSYZ__, attributes.__LEAD2SYZ__, attributes.__IGNORETAILS__);
    1280     " { \"RESOLUTION: " + @save_method + ", with: " + @save_desc + "\": [";
    1281   }
    1282 }
    1283 
    1284 
    1285 static proc StopAddResTest(def RR, intmat S, int @t, int @m)
    1286 {
    1287   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1288 
    1289   if( !(defined(@save_opts) && defined(@save_method) && defined(@save_desc)) )
    1290   { ERROR("Sorry: no global variables - run StartAddResTest beforehand!!!"); }
    1291 
    1292   list @l = list(@save_method, @save_desc, option(get), S, @t, @m);
    1293 
    1294 //  RR,
    1295 //  print(S, "betti");
    1296 
    1297   if( !@treeout )
    1298   {
    1299     "> -STOP RES TEST}}} ", @save_method, ", with:", @save_desc, ", Timer:", @t; option();
    1300   } else
    1301   {
    1302     " ] },";
    1303   }
    1304 
    1305 
    1306   option(set, @save_opts); kill @save_opts;
    1307 
    1308   kill @save_method; kill @save_desc;
    1309 
    1310   @save_res_list[1 + size(@save_res_list)] = @l;
    1311 }
    1312 
    1313 
    1314 static proc SCheck(def S)
    1315 {
    1316   setring S; // for checking...
    1317 
    1318   module M = MRES;
    1319   if( ncols(M) < nrows(M) )
    1320   {
    1321     M[nrows(M)] = 0;
    1322   } else
    1323   {
    1324     M = transpose(M);
    1325     if( ncols(M) < nrows(M) )
    1326     {
    1327       M[nrows(M)] = 0;
    1328     }
    1329     M = transpose(M);
    1330   }
    1331 
    1332   if( nrows(M) != ncols(M) )
    1333   {
    1334     "ERROR: non-square M!!!";
    1335   }
    1336 
    1337   if( size(module( M*M )) > 0 )
    1338   {
    1339     "ERROR: module( M*M ) != 0!!!";
    1340     module( M*M );
    1341 
    1342     "MRES': "; M; print(M);
    1343 
    1344   }
    1345 //  "MRES': "; M; print(M);
    1346 
    1347   if( size(RES[1]) != 0 )
    1348   {
    1349     "ERROR: wrong starting zero module!!!";
    1350   }
    1351 
    1352 //  RES;
    1353 /*
    1354   MRES;
    1355   RES;
    1356   "";
    1357   LRES;
    1358   "";
    1359   TRES;
    1360 */
    1361 }
    1362 
    1363 //// TODO: SSres(0) fails..!!!??
    1364 static proc TestSSres(def I)
    1365 {
    1366   def save = basering;
    1367   int @t,@m,r,rr,i;
    1368   string name =
    1369     "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
    1370     ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
    1371     ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));
    1372 
    1373   int @PROFILE = attrib(SSinit, "PROFILE");
    1374   if(@PROFILE){ string @prof = "SSres_" + @save_res_desc + "_" + name + ".prof"; }
    1375 
    1376   StartAddResTest(
    1377    "SSres",
    1378    "minres + betti(,1) + mods: {" + name + "}"
    1379   );
    1380 
    1381   option(redSB); option(redTail);
    1382   timer=0;rtimer=0;def R=SSres(I,0);@m=rtimer;
    1383   setring R;module M;list @l=list();@l[size(RES)-1]=list();r=nrows(RES[1]);for(i=2;i<=size(RES);i++){M=RES[i];rr=nrows(M);if((r>0)&&(size(M)>0)&&(r<rr)){M=transpose(M);M=M[(r+1)..ncols(M)];M=transpose(M);RES[i]=M;};r=rr;@l[i-1] = M;};resolution RR=@l;RR=minres(RR);def S=betti(RR,1);@t=rtimer;
    1384   SCheck(R);
    1385   StopAddResTest(RR, S, @t,@m);
    1386   kill S, RR; setring save; kill R;
    1387 }
    1388 
    1389 
    1390 // Further recognized switches are the following attributes of @code{Schreyer::SSinit} procedure:
    1391 // LEAD2SYZ, TAILREDSYZ, HYBRIDNF, DEBUG, ...
    1392 
    1393 proc s_res(def I, int l)
    1394 "USAGE:  s_res(ideal/module M, int len)
    1395 RETURN:  resolution object over basering
    1396 PURPOSE: compute a non-minimal Schreyer free resolution of M of length at most len via the LiftTree algorithm described in [BMSS].
    1397 NOTE:    If given len is zero then nvars(basering) + 1 is used instead.
    1398 @* This functions is not related to the helpers from this library. This procedure works in only in commutative case.
    1399 @* One can switch on computation protocol and statistic (depending on the build) by setting the @code{prot} option.
    1400 SEE ALSO: sres, lres, Sres
    1401 EXAMPLE: example s_res; shows an example
    1402 "
    1403 {
    1404   def @save = basering;
    1405 
    1406   int @RINGCHANGE = 0;
    1407 
    1408   if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
    1409   {
    1410     @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
    1411   }
    1412 
    1413   def R=SSinit(I);
    1414   if( @RINGCHANGE ){ setring R; }
    1415 
    1416   int @l = size(RES);
    1417   def rsltn =   Syzextra::ComputeResolution(RES[@l], LRES[@l], TRES[@l], l);
    1418 
    1419   if( !@RINGCHANGE )
    1420   {
    1421     return (rsltn); // ret
    1422   }
    1423 
    1424   SRES ret; ret.r = R; ret.rsltn = rsltn;
    1425   return (ret);
    1426 }
    1427 example
    1428 { "EXAMPLE:"; echo = 2;
    1429   ring R;
    1430   module M = maxideal(1); M;
    1431   s_res(M, 0); // Koszul complex
    1432   list rs = _; // get syzygies
    1433   print(betti(rs, 0), "betti"); // non-minimal betties
    1434   print(minres(rs));
    1435   print(betti(rs, 1), "betti"); //minimal betties
    1436 }
    1437 
    1438 /* static */
    1439 proc s_res_bm(def I)
    1440 {
    1441   def @save = basering;
    1442 
    1443   int @RINGCHANGE = 0;
    1444 
    1445   if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
    1446   {
    1447     @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
    1448   }
    1449   int t,tt,sum;
    1450 
    1451 t=rtimer;def R=SSinit(I);tt=rtimer;
    1452 
    1453   "%% Setup(SSinit) TIME:", tt - t; // if(@prot){ } ?
    1454   int sum = (tt-t);
    1455 
    1456   if( @RINGCHANGE ){ setring R; }
    1457 
    1458   int @l = size(RES);
    1459   module N, L, T, LL, TT;
    1460   L = LRES[@l];
    1461   T = TRES[@l];
    1462 
    1463 
    1464   int ss = attrib(basering, "SYZNUMBER");
    1465 
    1466   while ( 1 )
    1467   {
    1468 //  SSstep():
    1469 t=rtimer;(N,LL,TT)=SSComputeSyzygy(L,T);tt=rtimer;
    1470 
    1471     @l = @l + 1;
    1472     "%% SSstep[",@l-2, "] TIME:", tt - t;  // if(@prot){ } ?
    1473     sum = sum + (tt-t);
    1474 
    1475     if( (size(LL) == 0) || (size(N) == 0) ) { break; }
    1476     L = LL; T = TT; RES[@l] = N; // LRES[@l] = LL; TRES[@l] = TT;
    1477 
    1478     ss = ss + 1; attrib(basering, "SYZNUMBER", ss );
    1479   }
    1480 
    1481   "%% Whole Resolution (with "+string(@l)+"syzygies) TIME:", sum;  // if(@prot){ } ?
    1482   resolution rsltn = list(RES[2..size(RES)]);
    1483 
    1484   if( !@RINGCHANGE )
    1485   {
    1486     return (rsltn); // ret
    1487   }
    1488 
    1489   SRES ret; ret.r = R; ret.rsltn = rsltn;
    1490   return (ret);
    1491 }
    1492 
    1493 
    1494 static proc s_syz(def I)
    1495 {
    1496   def R=SSinit(I); setring R;
    1497   int @l = size(RES); //   def M =  RES[@l];
    1498   module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(LRES[@l], TRES[@l]);
    1499   SSYZ ret; ret.r = R; ret.szg = N; // Schreyer::  Syzextra::ComputeResolution(RES[2], LRES[2], TRES[2], 0);
    1500   return (ret);
    1501 }
    1502 
    1503 static proc TestSSSres(def I)
    1504 {
    1505   def save = basering;
    1506   int @t,@m,r,rr,i;
    1507   string name =
    1508     "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
    1509     ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
    1510     ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));
    1511 
    1512   int @PROFILE = attrib(SSinit, "PROFILE");
    1513   if(@PROFILE){ string @prof = "SSSres_" + @save_res_desc + "_" + name + ".prof"; }
    1514 
    1515   StartAddResTest(
    1516    "SSSres",
    1517    "minres + betti(,1) + mods: {" + name + "}"
    1518   );
    1519 
    1520   option(redSB); option(redTail);
    1521   timer=0;rtimer=0;def R=SSinit(I);setring R;def RR=  Syzextra::ComputeResolution(RES[2], LRES[2], TRES[2], 0);
    1522 @m=rtimer;
    1523 RR=minres(RR); def S=betti(RR,1);@t=rtimer;
    1524   SCheck(R);
    1525   StopAddResTest(RR, S, @t,@m);
    1526   kill S, RR; setring save; kill R;
    1527 }
    1528 
    1529 
    1530 static proc TestSres(def I)
    1531 {
    1532   def save = basering;
    1533   int @t,r,rr,i,@m;
    1534   StartAddResTest(
    1535   "Sres",
    1536   "minres + betti(,1)"
    1537   );
    1538   option(redSB); option(redTail);
    1539   timer=0;rtimer=0;def R=Sres(I,0);@m=rtimer;setring R;module M;list @l=list();@l[size(RES)-1]=list();r=nrows(RES[1]);for(i=2;i<=size(RES);i++){M=RES[i];rr=nrows(M);if((r>0)&&(size(M)>0)&&(r<rr)){M=transpose(M);M=M[(r+1)..ncols(M)];M=transpose(M);RES[i]=M;};r=rr;@l[i-1] = M;};resolution RR=@l;RR=minres(RR);def S=betti(RR,1);@t=rtimer;
    1540   SCheck(R);
    1541   StopAddResTest(RR, S, @t,@m);
    1542   kill S, RR; setring save; kill R;
    1543 }
    1544 
    1545 
    1546 static proc Testsres(def M)
    1547 {
    1548   int @t,@m;
    1549   StartAddResTest("sres", "no minres + betti(,1)");
    1550   option(redSB);option(redTail);
    1551   timer=0;rtimer=0;def RR=sres(groebner(M),0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
    1552   StopAddResTest(RR, S, @t,@m); kill S, RR;
    1553 }
    1554 
    1555 static proc Testlres(def M)
    1556 {
    1557   int @t,@m;
    1558   StartAddResTest("lres", "no minres + betti(,1)");
    1559   option(redSB);option(redTail);
    1560   timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
    1561   StopAddResTest(RR, S, @t,@m); kill S, RR;
    1562 
    1563   StartAddResTest("lres", "minres + betti()");
    1564   option(redSB);option(redTail);
    1565   timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(minres(RR));@t=rtimer;
    1566   StopAddResTest(RR, S, @t,@m);
    1567   kill S, RR;
    1568 }
    1569 
    1570 
    1571 static proc Testnres(def M)
    1572 {
    1573   int @t,@m;
    1574   StartAddResTest("nres", "no minres + betti(,1)");
    1575 
    1576   option(redSB); option(redTail);
    1577   timer=0;rtimer=0;def RR=nres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
    1578 
    1579   StopAddResTest(RR, S, @t,@m); kill S, RR;
    1580 }
    1581 
    1582 static proc TestSSresAttribs(def M, list #)
    1583 {
    1584   M = groebner(M);
    1585 
    1586   StartResTesting(#);
    1587 
    1588   attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
    1589   attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);
    1590 
    1591  // WRONG???! LEAD2SYZ?
    1592 //  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
    1593 //  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);
    1594 
    1595   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1596   if( !@treeout )
    1597   {
    1598    Testlres(M); Testnres(M);
    1599 //   Testsres(M); //   TestSres(M); // too long for the last medium test :(
    1600   }
    1601 
    1602   StopResTesting();
    1603 }
    1604 
    1605 static proc TestSSresAttribs2tr(def M, list #)
    1606 {
    1607   M = groebner(M);
    1608 
    1609   StartResTesting(#);
    1610 
    1611   attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
    1612   Testlres(M);
    1613 
    1614   StopResTesting();
    1615 }
    1616 
    1617 static proc testSimple(list #)
    1618 {
    1619   def DEBUG = 0;
    1620   if(size(#) > 0) { DEBUG = #[1]; }
    1621 
    1622   def TREE = 0;
    1623   if(size(#) > 1) { TREE = #[2]; }
    1624 
    1625   system("--min-time", "0.01");
    1626   system("--ticks-per-sec", 100);
    1627 
    1628 //  option(prot);
    1629 
    1630   // TODO: only for now!!
    1631   attrib(SSinit, "DEBUG", (DEBUG > 0) );
    1632   attrib(SSinit, "SYZCHECK", (DEBUG > 0) );
    1633   attrib(SSinit, "KERCHECK", (DEBUG > 0) );
    1634 
    1635   attrib(SSinit, "TREEOUTPUT", TREE);
    1636   attrib(SSinit, "PROFILE", 0);
    1637   attrib(SSinit, "IGNORETAILS", 0); // not only frame
    1638 
    1639   attrib(SSinit, "NOCACHING", 0);
    1640 
    1641   int @treeout = attrib(SSinit, "TREEOUTPUT");
    1642 
    1643   if( @treeout)
    1644   {
    1645     monitor("SimpleTests.json", "o");
    1646     "{ \"SimpleTests\": [";
    1647   } else { option(prot); }
    1648 
    1649 
    1650   ring r; ideal M = maxideal(1);
    1651   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1652   kill r;
    1653 
    1654   ring r = 0, (a, b, c, d), lp; ideal M = maxideal(1);
    1655   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1656   kill r;
    1657 
    1658   ring R = 0, (w, x, y, z), dp;
    1659   ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
    1660   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1661   kill R;
    1662 
    1663 
    1664   ring r = 0, (a, b, c, d, e, f), dp; ideal M = maxideal(1);
    1665   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1666   kill r;
    1667 
    1668 
    1669   ring r = 0, (x, y), lp; ideal M = x2, xy, y2;  // Schreyer conterexample???
    1670   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1671   kill r;
    1672 
    1673   ring r = 0, (x, y, z, t), dp; ideal M = homog(xy + y2 +x + 2y -1, t), homog(xz - x -y -z -2, t), homog(yz +1, t);  // TODO: seg. fault?
    1674   TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
    1675   kill r;
    1676 
    1677 
    1678   ring AGR = (101), (a, b, c, d), dp;
    1679   // simple: AGR@101n3d002s004%1:
    1680   ideal M = c*d, b*d, a*d, c^2-d^2, b*c, a*c, b^2-d^2, a*b, a^2-d^2;
    1681   TestSSresAttribs(M, "simple: AGR@101n3d002s004%1");
    1682 
    1683   // medium: AGR@101n3d004s009%1;
    1684   M = a*b+7*a*c-16*b*c-27*a*d+37*b*d-2*c*d, d^3, c*d^2, b*d^2, a*d^2, c^2*d, b*c*d, a*c*d, b^2*d, a^2*d, c^3, b*c^2, a*c^2, b^2*c, a^2*c, b^3, a^3;
    1685   TestSSresAttribs(M, "medium: AGR@101n3d004s009%1");
    1686 
    1687   kill AGR;
    1688 
    1689 
    1690   string Name = "bordiga"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;
    1691   ideal I = -x2y+26/17xy2+70/17y3+96/121x2z+63/82xyz+115/11y2z-8114xz2-40/79yz2+16/125z3+3023x2u-123/70xyu+3395y2u-81/119xzu-23/66yzu+3626z2u+18/53xu2+111/58yu2-34/39zu2+53/40u3-94/17x2v-10/19xyv+81/88y2v-91/33xzv-9967yzv-103/4z2v-26/109xuv+69/97yuv+92/17zuv-19/96u2v+10/21xv2+6147yv2+32/113zv2-79/82uv2-77/51v3,4347x2y-9017xy2+11327y3+18/79x2z-93/43xyz-35/47y2z+14704xz2+10727yz2-1764z3-612x2u+20/107xyu-103/89y2u-39/2xzu+2345yzu+10251z2u-9984xu2-10299yu2+113/118zu2+37/91u3+2/31x2v+9552xyv-47/100y2v-3242xzv+113/27yzv-11271z2v-13/79xuv+15917yuv+5/114zuv+103/119u2v-21/55xv2-59/19yv2+101/68zv2-7817uv2-112/29v3,7228x2y-111/113xy2+5913y3+6/43x2z-11251xyz+27/121y2z+97/96xz2-7398yz2-97/114z3+38/15x2u+5005xyu-41/126y2u-61/116xzu+89/9yzu-4087z2u+26/15xu2-92/103yu2+21/68zu2-4027u3+97/91x2v+5150xyv-4/47y2v-2310xzv+7307yzv-77/86z2v+30/83xuv+413yuv-50zuv-103/106u2v+105/73xv2-109/98yv2+59/63zv2+715uv2+963v3,x3+3487x2y-9744xy2-13276y3-15213x2z-118/51xyz+101/104y2z+2754xz2+9111yz2-17/94z3+11136x2u-43/82xyu-9/41y2u-7306xzu-6839yzu+5692z2u-14682xu2+37/80yu2-85/97zu2-6186u3+34/15x2v+84/109xyv+5086y2v+27/112xzv-3/40yzv+19/120z2v+11222xuv+38/55yuv-24/83zuv+15814u2v-111/61xv2+49/44yv2+125/81zv2+1933uv2-19/71v3;
    1692   TestSSresAttribs(I, Name);
    1693   kill @p, Name, R;
    1694 
    1695   string Name = "rat.d8.g6"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;
    1696   ideal I = -19/125x2y2-87/119xy3-97/21y4+36/53x2yz+2069xy2z-59/50y3z-65/33x2z2-14322xyz2+79/60y2z2-9035xz3-14890yz3+87/47z4-23/48x2yu+45/44xy2u+1972y3u+79/118x2zu-5173xyzu+115/121y2zu+1239xz2u-115/17yz2u-15900z3u-78/95x2u2+67/101xyu2-12757y2u2+12752xzu2+68/21yzu2+103/90z2u2-12917xu3+97/92yu3-24/49zu3-13/79u4-51/61x2yv-3103xy2v+77/117y3v+73/115x2zv-79/33xyzv+123/110y2zv+11969xz2v-31/95yz2v-123/95z3v-105/124x2uv+12624xyuv+2/63y2uv+6579xzuv+13/62yzuv+4388z2uv-12747xu2v-26/105yu2v-78/61zu2v-125/53u3v-5/71xyv2+62/77y2v2+21/44xzv2-9806yzv2+3/91z2v2+361xuv2+568yuv2+2926zuv2+53/38u2v2-14523yv3+2082zv3+113/115uv3,108/73x2y2+4028xy3+38/43y4-1944x2yz+39/80xy2z+8/109y3z+52/27x2z2+103/45xyz2+5834y2z2+63/101xz3+107/80yz3+1178z4-1/6x2yu+78/25xy2u-21/43y3u+50/71x2zu-14693xyzu+15074y2zu+9/103xz2u-7396yz2u-14493z3u+93/25x2u2+61/4xyu2-11306y2u2-79/81xzu2+59/82yzu2-5/106z2u2+89/71xu3-34/11yu3+15/103zu3-115/52u4-54/65x2yv+67/16xy2v-7/68y3v-10/13x2zv+32/85xyzv+1/91y2zv+107/118xz2v+7594yz2v-98/103z3v+9919x2uv-965xyuv+53/34y2uv+119/11xzuv-3400yzuv-8329z2uv+75/98xu2v-24yu2v+55/87zu2v-82/71u3v-73/115x2v2+85/19xyv2-213y2v2-7704xzv2-15347yzv2+14960z2v2+15065xuv2-125/17yuv2+32/83zuv2-14/73u2v2-21/44xv3+79/2yv3-61/32zv3+46/119uv3-2082v4,9/20x2y2+113/71xy3-88/65y4+9983x2yz-6722xy2z+87/68y3z+1893x2z2+65/32xyz2+51/55y2z2-102/53xz3+58/5yz3-7187z4-96/7x2yu-14/87xy2u-3532y3u+95/54x2zu+19/65xyzu-6728y2zu+31/121xz2u+73/106yz2u-91/5z3u-12928x2u2+707xyu2-55/48y2u2-96/25xzu2+15869yzu2-20/107z2u2-10030xu3-13786yu3-122/9zu3+19/59u4-7/52x2yv+101/74xy2v+83/6y3v-91/55x2zv-5266xyzv+85/61y2zv+126/95xz2v+56/51yz2v+13073z3v-50/21x2uv-13553xyuv-116/53y2uv+68/71xzuv-111/98yzuv-11037z2uv+68/121xu2v-124/53yu2v+54/55zu2v+5862u3v+12318x2v2-119/29xyv2+101/17y2v2-51/40xzv2-82/33yzv2-30/41z2v2-29/52xuv2+7817yuv2+8121zuv2-28/99u2v2+1125xv3-73/55yv3-14141zv3+8742uv3-1203v4,x2y2+11357xy3+295y4+144x2yz-31/54xy2z+89/119y3z+1/46x2z2+29/26xyz2+1384y2z2+1461xz3+113/91yz3+9494z4-7/32x2yu+12850xy2u-3626y3u-33/106x2zu-7/60xyzu-5935y2zu-8597xz2u+5527yz2u+1708z3u+6182x2u2-15780xyu2+4669y2u2-38/69xzu2+8412yzu2+9265z2u2-5679xu3-67/18yu3-34/67zu3-7178u4+113/56x2yv-3669xy2v+17/113y3v-87/35x2zv-4871xyzv-111/11y2zv-1131xz2v-72/13yz2v+838z3v-115/4x2uv+3395xyuv-43/68y2uv-82/13xzuv+7042yzuv-88/119z2uv+100/19xu2v+24/11yu2v+89/3zu2v+7395u3v-119/109x2v2+1/104xyv2+18/25y2v2+700xzv2-59/9yzv2-92/87z2v2+2486xuv2-67/103yuv2+1469zuv2-101/91u2v2-79/33xv3+10838yv3+81/4zv3-11843uv3+7204v4,19/125x3-15698x2y-22/117xy2-95/107y3+2027x2z-7750xyz+85/104y2z-15326xz2+31/101yz2+67/81z3-7879x2u-112/115xyu+124/81y2u+99/61xzu-7458yzu+40/33z2u-1502xu2+6591yu2-7/73zu2-42/95u3+93/83x2v-15/112xyv-84/95y2v+35/36xzv+5/24yzv-12768z2v+13232xuv-76/103yuv-79/52zuv-7217u2v+75/92xv2-49/64yv2+17/14zv2-6109uv2+1695v3;
    1697   TestSSresAttribs(I, Name);
    1698   kill R, Name, @p;
    1699 
    1700 
    1701   if( @treeout)
    1702   {
    1703     "] }";
    1704     monitor("");
    1705   }
    1706 
    1707 }
    1708 
    1709 static proc testAGR(list #)
    1710 {
    1711   def DEBUG = 0;
    1712   if(size(#) > 0) { DEBUG = #[1]; }
    1713 
    1714   system("--min-time", "0.01");
    1715   system("--ticks-per-sec", 100);
    1716 
    1717   attrib(SSinit, "DEBUG", 0);
    1718   attrib(SSinit, "SYZCHECK", (DEBUG > 0));
    1719   attrib(SSinit, "KERCHECK", 0);
    1720   attrib(SSinit, "TREEOUTPUT", 0);
    1721   attrib(SSinit, "PROFILE", 0);
    1722   attrib(SSinit, "IGNORETAILS", 0); // not only frame
    1723 
    1724   option(prot);
    1725 
    1726   ring AGR = (101), (a, b, c, d), dp; AGR;
    1727   // lengthy: AGR@101n3d008s058%3, kernel only!
    1728   ideal M = 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    1729   TestSSresAttribs2tr(M, "AGR@101n3d008s058%3");
    1730 
    1731   // AGR@101n3d010s010%3, a bit slower...
    1732   M = 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3*d^3+19*c^2*d^6-50*a*d^7-33*b*d^7+16*c*d^7-45*d^8,a*b*c^3*d^3-6*c^2*d^6-38*a*d^7+35*b*d^7+32*c*d^7-12*d^8,a^2*c^3*d^3+44*c^2*d^6+35*a*d^7+42*b*d^7-10*c*d^7-48*d^8,b^3*c^2*d^3+33*c^2*d^6-7*a*d^7-41*b*d^7-3*c*d^7-33*d^8,a*b^2*c^2*d^3-21*c^2*d^6-22*a*d^7-23*b*d^7+24*c*d^7+47*d^8,a^2*b*c^2*d^3+c^2*d^6-32*a*d^7-34*b*d^7-42*c*d^7+7*d^8,a^3*c^2*d^3+6*c^2*d^6-31*a*d^7-26*b*d^7+19*c*d^7-49*d^8,b^4*c*d^3+6*c^2*d^6-24*a*d^7+10*b*d^7-18*c*d^7-4*d^8,a*b^3*c*d^3+46*c^2*d^6+41*a*d^7+7*b*d^7+8*c*d^7-28*d^8,a^2*b^2*c*d^3+33*c^2*d^6-15*a*d^7-11*b*d^7+38*c*d^7+14*d^8,a^3*b*c*d^3-29*c^2*d^6-4*a*d^7-32*b*d^7+13*c*d^7-3*d^8,a^4*c*d^3-34*c^2*d^6+5*a*d^7+29*b*d^7-15*c*d^7-48*d^8,b^5*d^3-42*c^2*d^6+33*a*d^7-49*b*d^7+33*c*d^7-43*d^8,a*b^4*d^3+25*c^2*d^6-11*a*d^7-16*b*d^7+32*c*d^7-2*d^8,a^2*b^3*d^3-36*c^2*d^6-47*a*d^7-16*b*d^7+19*c*d^7+9*d^8,a^3*b^2*d^3-30*c^2*d^6-21*a*d^7-6*b*d^7+16*c*d^7-14*d^8,a^4*b*d^3+47*c^2*d^6-16*a*d^7-13*b*d^7+21*c*d^7+30*d^8,a^5*d^3-2*c^2*d^6+40*a*d^7+34*b*d^7+14*c*d^7-50*d^8,c^6*d^2-4*c^2*d^6-41*a*d^7+46*b*d^7+17*c*d^7+19*d^8,b*c^5*d^2-49*c^2*d^6+5*a*d^7-31*b*d^7+30*c*d^7+28*d^8,a*c^5*d^2-12*c^2*d^6-23*a*d^7-39*b*d^7+6*c*d^7-27*d^8,b^2*c^4*d^2-12*c^2*d^6-30*a*d^7+13*b*d^7-42*c*d^7+38*d^8,a*b*c^4*d^2-31*c^2*d^6+5*a*d^7-41*b*d^7-24*c*d^7,a^2*c^4*d^2-c^2*d^6+4*a*d^7+21*b*d^7+19*c*d^7-34*d^8,b^3*c^3*d^2-50*c^2*d^6-11*a*d^7+24*b*d^7+24*c*d^7-44*d^8,a*b^2*c^3*d^2+2*c^2*d^6-42*a*d^7-17*b*d^7-33*c*d^7-10*d^8,a^2*b*c^3*d^2+20*c^2*d^6+29*a*d^7+35*b*d^7-31*c*d^7-35*d^8,a^3*c^3*d^2+35*c^2*d^6-13*a*d^7+20*b*d^7-15*c*d^7-45*d^8,b^4*c^2*d^2+c^2*d^6+36*a*d^7-42*b*d^7+32*c*d^7+16*d^8,a*b^3*c^2*d^2-9*c^2*d^6-43*a*d^7-5*b*d^7-17*c*d^7+50*d^8,a^2*b^2*c^2*d^2-36*c^2*d^6+31*a*d^7+4*b*d^7-26*c*d^7-11*d^8,a^3*b*c^2*d^2+15*c^2*d^6+40*a*d^7-18*b*d^7-31*c*d^7+43*d^8,a^4*c^2*d^2+41*c^2*d^6-49*a*d^7+37*b*d^7+47*c*d^7-48*d^8,b^5*c*d^2-49*c^2*d^6+15*a*d^7+48*b*d^7+22*c*d^7+38*d^8,a*b^4*c*d^2+12*c^2*d^6+16*a*d^7-22*b*d^7-c*d^7+29*d^8,a^2*b^3*c*d^2+31*c^2*d^6+19*a*d^7+45*b*d^7-6*c*d^7+42*d^8,a^3*b^2*c*d^2+29*c^2*d^6-39*a*d^7+25*b*d^7-48*c*d^7-d^8,a^4*b*c*d^2-31*c^2*d^6+24*a*d^7-2*b*d^7+36*c*d^7+37*d^8,a^5*c*d^2+33*c^2*d^6-46*a*d^7-41*b*d^7-29*c*d^7-12*d^8,b^6*d^2-39*c^2*d^6+35*a*d^7-8*b*d^7+35*c*d^7+47*d^8,a*b^5*d^2-38*c^2*d^6-11*a*d^7-37*b*d^7-7*c*d^7-5*d^8,a^2*b^4*d^2+29*c^2*d^6+36*a*d^7-29*b*d^7+20*c*d^7+39*d^8,a^3*b^3*d^2-44*c^2*d^6+43*a*d^7-50*b*d^7-24*c*d^7-16*d^8,a^4*b^2*d^2+20*c^2*d^6+33*a*d^7+6*b*d^7+47*c*d^7+40*d^8,a^5*b*d^2-10*c^2*d^6+25*a*d^7-8*b*d^7-14*c*d^7+16*d^8,a^6*d^2+48*c^2*d^6+14*a*d^7+32*b*d^7+17*c*d^7+13*d^8,c^7*d+38*c^2*d^6-39*a*d^7+22*b*d^7+15*c*d^7-d^8,b*c^6*d+9*c^2*d^6+37*a*d^7+12*b*d^7+27*c*d^7+3*d^8,a*c^6*d-5*c^2*d^6+34*a*d^7+15*b*d^7+2*c*d^7-21*d^8,b^2*c^5*d+35*c^2*d^6+27*a*d^7+13*b*d^7-39*c*d^7+8*d^8,a*b*c^5*d-34*c^2*d^6-18*a*d^7-21*b*d^7-31*c*d^7+46*d^8,a^2*c^5*d-16*c^2*d^6-6*a*d^7-18*b*d^7+3*c*d^7+47*d^8,b^3*c^4*d-46*c^2*d^6+4*a*d^7-38*b*d^7-29*c*d^7-4*d^8,a*b^2*c^4*d-35*c^2*d^6-14*a*d^7-32*b*d^7-40*c*d^7-35*d^8,a^2*b*c^4*d+23*c^2*d^6-44*a*d^7-3*b*d^7+4*c*d^7-4*d^8,a^3*c^4*d+24*c^2*d^6-7*a*d^7-44*b*d^7-16*c*d^7+10*d^8,b^4*c^3*d+43*c^2*d^6+12*a*d^7+43*b*d^7-49*c*d^7-23*d^8,a*b^3*c^3*d+22*c^2*d^6+6*a*d^7+2*b*d^7-9*c*d^7,a^2*b^2*c^3*d+4*c^2*d^6+21*a*d^7-24*b*d^7-26*c*d^7+33*d^8,a^3*b*c^3*d+13*c^2*d^6-18*a*d^7+31*b*d^7-28*c*d^7+2*d^8,a^4*c^3*d+10*c^2*d^6-14*a*d^7+30*b*d^7-40*c*d^7+33*d^8,b^5*c^2*d-35*c^2*d^6-33*a*d^7+7*b*d^7+13*c*d^7+26*d^8,a*b^4*c^2*d-49*c^2*d^6+9*a*d^7+20*b*d^7+11*c*d^7-32*d^8,a^2*b^3*c^2*d+33*c^2*d^6-43*a*d^7-27*b*d^7-31*c*d^7-41*d^8,a^3*b^2*c^2*d-6*c^2*d^6+23*a*d^7+20*b*d^7-8*c*d^7-6*d^8,a^4*b*c^2*d+10*c^2*d^6-24*a*d^7+30*b*d^7+42*c*d^7-23*d^8,a^5*c^2*d+12*c^2*d^6+20*a*d^7+24*b*d^7-9*c*d^7-9*d^8,b^6*c*d-12*c^2*d^6+36*a*d^7+4*b*d^7-12*c*d^7+26*d^8,a*b^5*c*d-19*c^2*d^6-39*a*d^7-26*b*d^7-4*c*d^7+10*d^8,a^2*b^4*c*d+38*c^2*d^6-6*a*d^7+6*b*d^7+41*c*d^7+49*d^8,a^3*b^3*c*d-34*c^2*d^6-42*a*d^7+22*b*d^7-26*c*d^7-13*d^8,a^4*b^2*c*d+14*c^2*d^6+40*a*d^7+39*b*d^7-34*d^8,a^5*b*c*d-8*c^2*d^6+45*a*d^7-35*b*d^7+48*c*d^7+47*d^8,a^6*c*d-6*c^2*d^6-24*a*d^7-2*b*d^7-9*c*d^7+7*d^8,b^7*d+34*c^2*d^6-14*a*d^7+46*b*d^7-50*c*d^7+26*d^8,a*b^6*d+6*c^2*d^6+23*a*d^7-27*b*d^7-25*c*d^7-2*d^8,c^8+43*c^2*d^6+11*b*d^7-39*c*d^7-30*d^8,b*c^7-44*c^2*d^6-4*a*d^7-10*b*d^7+31*c*d^7+42*d^8,a*c^7-6*a*d^7+31*b*d^7+37*c*d^7-41*d^8,b^2*c^6-11*c^2*d^6-35*a*d^7+32*b*d^7-25*c*d^7-21*d^8,a*b*c^6+2*c^2*d^6+43*a*d^7-48*b*d^7-49*c*d^7-19*d^8,a^2*c^6-20*c^2*d^6-11*a*d^7-35*b*d^7-33*c*d^7+28*d^8,b^3*c^5+4*c^2*d^6-7*a*d^7-21*b*d^7-14*c*d^7+48*d^8,a*b^2*c^5+17*c^2*d^6+45*a*d^7-32*b*d^7+29*c*d^7+38*d^8,a^2*b*c^5-13*c^2*d^6+46*a*d^7+4*b*d^7-18*c*d^7+19*d^8,a^3*c^5-23*c^2*d^6-a*d^7-3*b*d^7-15*c*d^7+19*d^8,b^4*c^4-50*c^2*d^6+39*a*d^7+49*b*d^7+47*c*d^7+7*d^8,a*b^3*c^4-33*c^2*d^6+10*a*d^7+32*b*d^7+21*c*d^7-39*d^8,a^2*b^2*c^4+23*c^2*d^6+27*a*d^7-17*b*d^7+29*c*d^7+9*d^8,a^3*b*c^4-47*c^2*d^6-43*a*d^7-47*b*d^7-34*c*d^7-23*d^8,a^4*c^4-6*c^2*d^6+7*a*d^7+38*b*d^7-27*c*d^7-9*d^8,b^5*c^3-47*c^2*d^6+18*a*d^7-44*b*d^7-4*c*d^7-18*d^8,a*b^4*c^3+30*c^2*d^6+36*a*d^7+25*b*d^7+42*c*d^7+d^8,a^2*b^3*c^3+10*c^2*d^6+31*a*d^7+45*b*d^7-44*c*d^7+37*d^8,a^3*b^2*c^3-41*c^2*d^6-15*a*d^7-34*b*d^7-22*c*d^7+28*d^8,a^4*b*c^3+19*c^2*d^6-23*a*d^7+18*b*d^7-13*c*d^7-48*d^8,a^5*c^3+16*c^2*d^6+22*a*d^7-31*b*d^7+33*c*d^7+15*d^8,b^6*c^2-42*c^2*d^6-10*a*d^7-16*b*d^7-46*c*d^7+42*d^8,a*b^5*c^2-23*c^2*d^6+34*a*d^7-37*b*d^7+2*c*d^7+10*d^8,a^2*b^4*c^2-45*c^2*d^6-5*a*d^7+43*b*d^7-18*c*d^7+7*d^8,a^3*b^3*c^2+36*c^2*d^6+19*a*d^7+21*b*d^7+46*c*d^7-24*d^8,a^4*b^2*c^2-17*c^2*d^6+30*a*d^7-39*b*d^7-39*c*d^7-24*d^8,a^5*b*c^2+10*c^2*d^6-24*a*d^7-36*b*d^7-14*c*d^7+26*d^8,a^6*c^2+47*c^2*d^6-41*a*d^7+32*b*d^7+6*c*d^7+42*d^8,b^7*c+44*c^2*d^6-6*a*d^7+5*b*d^7+20*c*d^7+50*d^8,a*b^6*c+29*c^2*d^6-16*a*d^7+45*b*d^7-3*c*d^7+14*d^8,b^8+48*c^2*d^6-40*a*d^7-44*b*d^7-10*c*d^7-23*d^8,a*b^7-32*c^2*d^6-41*a*d^7-11*b*d^7+50*c*d^7+13*d^8,d^9,c*d^8,b*d^8,a*d^8,c^2*d^7;
    1733   TestSSresAttribs2tr(M, "AGR@101n3d010s010%3");
    1734   kill AGR;
    1735 
    1736   ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR;
    1737   // AGR@101n7d005s010%2, medium: <= 2
    1738   ideal M =
    1739 f*h-g*h,e*h-g*h,d*h-g*h,c*h-g*h,b*h-g*h,a*h-g*h,e*g+48*f*g-49*g*h,d*g+5*f*g-6*g*h,c*g+49*f*g-50*g*h,b*g-7*f*g+6*g*h,a*g-50*f*g+49*g*h,e*f-20*f*g+19*g*h,d*f+40*f*g-41*g*h,c*f-12*f*g+11*g*h,b*f+45*f*g-46*g*h,a*f+4*f*g-5*g*h,d*e-f*g,c*e-30*f*g+29*g*h,b*e-39*f*g+38*g*h,a*e+10*f*g-11*g*h,c*d-41*f*g+40*g*h,b*d-23*f*g+22*g*h,a*d-20*f*g+19*g*h,b*c+17*f*g-18*g*h,a*c+6*f*g-7*g*h,a*b+28*f*g-29*g*h,g^2*h-g*h^2,f^2*g-8*f*g^2+7*g*h^2,g*h^4+50*h^5,g^5+41*h^5,f*g^4-18*h^5,f^5+29*h^5,e^5+6*h^5,d^5-23*h^5,c^5-32*h^5,
    1740 b^5+17*h^5,a^5+17*h^5,h^6;
    1741   TestSSresAttribs2tr(M, "AGR@101n7d005s010%2");
    1742   kill AGR;
    1743 
    1744 // from Andreas...tooo long!?
    1745 
    1746   ring AGR = (101), (a,b,c,d,e), dp; AGR;
    1747 
    1748   // AGR101n4d007s021%4
    1749   ideal M = b^3*c*d-44*a*b*c^2*d-23*b^2*c^2*d-17*a*c^3*d+25*b*c^3*d-28*c^4*d+21*a^3*d^2+28*a^2*b*d^2+45*a*b^2*d^2-45*b^3*d^2+39*a^2*c*d^2+50*a*b*c*d^2-31*b^2*c*d^2+25*a*c^2*d^2-42*b*c^2*d^2-6*c^3*d^2+10*a^2*d^3-18*a*b*d^3-21*b^2*d^3-9*a*c*d^3+37*b*c*d^3-18*c^2*d^3+5*a*d^4+b*d^4-18*c*d^4+23*d^5-5*a^4*e+6*a^3*b*e-21*a^2*b^2*e-28*a*b^3*e+11*b^4*e+19*a^3*c*e+29*a^2*b*c*e-25*a*b^2*c*e-8*b^3*c*e+17*a^2*c^2*e+45*a*b*c^2*e-28*b^2*c^2*e+22*a*c^3*e+33*b*c^3*e+27*c^4*e-50*a^3*d*e+11*a^2*b*d*e-45*a*b^2*d*e-5*b^3*d*e-2*a^2*c*d*e-30*a*b*c*d*e-17*b^2*c*d*e-45*a*c^2*d*e+12*b*c^2*d*e-8*c^3*d*e+12*a^2*d^2*e+a*b*d^2*e-13*b^2*d^2*e-20*a*c*d^2*e+47*b*c*d^2*e-10*c^2*d^2*e+8*a*d^3*e+32*b*d^3*e-8*c*d^3*e+47*d^4*e+43*a^3*e^2+23*a^2*b*e^2+12*a*b^2*e^2+25*b^3*e^2-23*a^2*c*e^2-12*a*b*c*e^2+5*b^2*c*e^2-25*a*c^2*e^2-8*b*c^2*e^2-48*c^3*e^2+22*a^2*d*e^2+27*a*b*d*e^2-21*b^2*d*e^2+35*a*c*d*e^2-5*b*c*d*e^2+14*c^2*d*e^2+3*a*d^2*e^2-35*b*d^2*e^2+24*c*d^2*e^2-12*d^3*e^2-30*a^2*e^3+5*a*b*e^3-29*b^2*e^3-17*a*c*e^3-41*b*c*e^3-41*c^2*e^3-a*d*e^3-41*b*d*e^3+6*c*d*e^3+24*d^2*e^3+38*a*e^4+46*b*e^4+5*c*e^4-48*d*e^4-33*e^5,
    1750 a*b^2*c*d-8*a^2*c^2*d+35*a*b*c^2*d-9*b^2*c^2*d+41*a*c^3*d+11*b*c^3*d+36*c^4*d-36*a^3*d^2-11*a^2*b*d^2-45*a*b^2*d^2+20*b^3*d^2-38*a^2*c*d^2-21*a*b*c*d^2-26*b^2*c*d^2+26*a*c^2*d^2+45*b*c^2*d^2+2*c^3*d^2+35*a^2*d^3-15*a*b*d^3-30*b^2*d^3-37*a*c*d^3+3*b*c*d^3+29*c^2*d^3-39*a*d^4-13*b*d^4+42*c*d^4+50*d^5-47*a^4*e+a^3*b*e-10*a^2*b^2*e+10*a*b^3*e-19*b^4*e+47*a^3*c*e+29*a^2*b*c*e+33*a*b^2*c*e-7*b^3*c*e+29*a^2*c^2*e-2*b^2*c^2*e-19*a*c^3*e+16*b*c^3*e+44*c^4*e+47*a^3*d*e-14*a^2*b*d*e+48*a*b^2*d*e-21*b^3*d*e+13*a^2*c*d*e+4*a*b*c*d*e+20*b^2*c*d*e-3*a*c^2*d*e-34*b*c^2*d*e-2*c^3*d*e+10*a^2*d^2*e+38*a*b*d^2*e+18*b^2*d^2*e-a*c*d^2*e+24*b*c*d^2*e-11*c^2*d^2*e+24*a*d^3*e-10*b*d^3*e+15*c*d^3*e-44*d^4*e+6*a^3*e^2-7*a^2*b*e^2+30*a*b^2*e^2+25*b^3*e^2+40*a^2*c*e^2+33*a*b*c*e^2+26*b^2*c*e^2-2*a*c^2*e^2-2*b*c^2*e^2+32*c^3*e^2+31*a^2*d*e^2+50*a*b*d*e^2-5*b^2*d*e^2-43*a*c*d*e^2+37*b*c*d*e^2-16*c^2*d*e^2+39*a*d^2*e^2+15*b*d^2*e^2+35*c*d^2*e^2-47*d^3*e^2+38*a^2*e^3+7*a*b*e^3+16*b^2*e^3+43*a*c*e^3+23*b*c*e^3+9*c^2*e^3+37*a*d*e^3-18*b*d*e^3+32*c*d*e^3-2*d^2*e^3-31*a*e^4+18*b*e^4-35*c*e^4+9*d*e^4-49*e^5,
    1751 a^2*b*c*d+7*a^2*c^2*d-15*a*b*c^2*d+20*b^2*c^2*d+8*a*c^3*d-14*b*c^3*d+34*c^4*d+15*a^3*d^2+37*a^2*b*d^2-11*a*b^2*d^2-8*b^3*d^2-15*a^2*c*d^2-22*a*b*c*d^2-30*b^2*c*d^2+23*a*c^2*d^2+34*b*c^2*d^2+41*c^3*d^2-27*a^2*d^3+24*b^2*d^3-15*a*c*d^3+20*b*c*d^3-16*c^2*d^3-31*a*d^4+18*b*d^4-21*c*d^4+19*d^5+20*a^4*e+38*a^3*b*e-7*a^2*b^2*e+8*a*b^3*e-35*b^4*e+30*a^3*c*e-13*a^2*b*c*e+39*a*b^2*c*e-50*b^3*c*e+50*a^2*c^2*e-21*a*b*c^2*e+17*b^2*c^2*e-23*a*c^3*e+32*b*c^3*e-43*c^4*e-39*a^3*d*e+16*a^2*b*d*e+25*a*b^2*d*e-12*b^3*d*e+50*a^2*c*d*e+4*a*b*c*d*e-17*b^2*c*d*e-28*a*c^2*d*e-5*b*c^2*d*e+13*c^3*d*e+23*a^2*d^2*e+17*a*b*d^2*e+14*b^2*d^2*e-2*a*c*d^2*e+3*b*c*d^2*e+20*c^2*d^2*e-14*a*d^3*e+5*b*d^3*e-c*d^3*e+29*d^4*e-42*a^3*e^2-38*a^2*b*e^2-44*a*b^2*e^2-4*b^3*e^2+29*a^2*c*e^2-19*a*b*c*e^2+38*b^2*c*e^2+3*a*c^2*e^2-46*b*c^2*e^2-46*c^3*e^2-44*a^2*d*e^2+16*a*b*d*e^2-38*b^2*d*e^2+12*a*c*d*e^2+45*b*c*d*e^2-48*c^2*d*e^2+34*a*d^2*e^2+32*b*d^2*e^2+37*c*d^2*e^2+34*d^3*e^2+30*a^2*e^3+45*a*b*e^3+8*b^2*e^3+40*a*c*e^3-37*b*c*e^3-16*c^2*e^3-50*a*d*e^3-18*b*d*e^3-9*c*d*e^3-37*a*e^4-22*b*e^4+5*c*e^4+d*e^4+9*e^5,
    1752 a^3*c*d-44*a^2*c^2*d-38*a*b*c^2*d-26*b^2*c^2*d-12*a*c^3*d-21*b*c^3*d+43*c^4*d-22*a^3*d^2-23*a^2*b*d^2+32*a*b^2*d^2+45*b^3*d^2-48*a^2*c*d^2-40*a*b*c*d^2+3*b^2*c*d^2+2*a*c^2*d^2-27*b*c^2*d^2-35*c^3*d^2+33*a^2*d^3-11*a*b*d^3-5*b^2*d^3+8*a*c*d^3-42*b*c*d^3+41*c^2*d^3-41*b*d^4+29*c*d^4+5*d^5+32*a^4*e-46*a^3*b*e-46*a^2*b^2*e+19*a*b^3*e-14*b^4*e-24*a^3*c*e+3*a^2*b*c*e-22*a*b^2*c*e+49*b^3*c*e-47*a^2*c^2*e+27*a*b*c^2*e+48*b^2*c^2*e+20*a*c^3*e-3*b*c^3*e-11*c^4*e-21*a^3*d*e+a^2*b*d*e-13*a*b^2*d*e-33*b^3*d*e+13*a^2*c*d*e-3*a*b*c*d*e+15*b^2*c*d*e+35*a*c^2*d*e-20*b*c^2*d*e+45*c^3*d*e-14*a^2*d^2*e+11*a*b*d^2*e-38*b^2*d^2*e+40*a*c*d^2*e-30*b*c*d^2*e+14*c^2*d^2*e-26*a*d^3*e-43*b*d^3*e+38*c*d^3*e-24*d^4*e-10*a^3*e^2-31*a^2*b*e^2+a*b^2*e^2-34*b^3*e^2+5*a^2*c*e^2-12*a*b*c*e^2-6*b^2*c*e^2-30*a*c^2*e^2-b*c^2*e^2+31*c^3*e^2+22*a^2*d*e^2-26*a*b*d*e^2+9*b^2*d*e^2+32*a*c*d*e^2+24*b*c*d*e^2-36*c^2*d*e^2-a*d^2*e^2-14*b*d^2*e^2-24*c*d^2*e^2+7*d^3*e^2+38*a^2*e^3+35*a*b*e^3+16*b^2*e^3+25*a*c*e^3-30*b*c*e^3+30*c^2*e^3-25*a*d*e^3+3*b*d*e^3+40*c*d*e^3+16*d^2*e^3+45*a*e^4+15*b*e^4-12*c*e^4+42*d*e^4+7*e^5,
    1753 b^4*d+14*a^2*c^2*d+2*a*b*c^2*d+34*b^2*c^2*d-12*a*c^3*d+20*b*c^3*d-20*c^4*d+4*a^3*d^2-47*a^2*b*d^2-34*a*b^2*d^2-22*b^3*d^2+23*a^2*c*d^2-22*a*b*c*d^2-31*b^2*c*d^2-24*a*c^2*d^2+39*b*c^2*d^2-37*c^3*d^2-39*a^2*d^3-49*a*b*d^3-41*b^2*d^3-44*a*c*d^3+33*b*c*d^3-14*c^2*d^3-49*a*d^4+20*b*d^4+37*c*d^4+34*d^5+50*a^4*e-31*a^3*b*e-18*a^2*b^2*e-16*a*b^3*e+45*b^4*e+32*a^3*c*e+43*a^2*b*c*e-27*a*b^2*c*e+5*b^3*c*e+39*a^2*c^2*e+33*a*b*c^2*e-16*b^2*c^2*e-6*a*c^3*e-35*b*c^3*e-4*c^4*e-19*a^3*d*e+25*a^2*b*d*e-20*a*b^2*d*e+6*b^3*d*e-46*a^2*c*d*e-8*a*b*c*d*e+5*b^2*c*d*e+2*a*c^2*d*e-39*b*c^2*d*e-30*c^3*d*e+50*a^2*d^2*e-3*a*b*d^2*e-22*b^2*d^2*e+42*a*c*d^2*e-9*b*c*d^2*e+17*c^2*d^2*e+33*a*d^3*e+29*b*d^3*e-10*c*d^3*e+5*d^4*e+15*a^3*e^2+12*a^2*b*e^2-12*a*b^2*e^2+17*b^3*e^2+26*a^2*c*e^2+23*a*b*c*e^2+4*b^2*c*e^2-8*a*c^2*e^2+49*b*c^2*e^2-25*c^3*e^2-24*a^2*d*e^2-19*a*b*d*e^2+26*b^2*d*e^2+38*a*c*d*e^2+48*b*c*d*e^2-28*c^2*d*e^2-15*a*d^2*e^2+31*b*d^2*e^2-47*c*d^2*e^2-5*d^3*e^2-28*a^2*e^3+46*a*b*e^3-25*b^2*e^3-25*a*c*e^3-42*b*c*e^3-39*c^2*e^3-22*a*d*e^3+7*b*d*e^3+4*c*d*e^3-9*d^2*e^3+50*a*e^4-39*b*e^4+44*c*e^4+28*d*e^4+36*e^5,
    1754 a*b^3*d-32*a^2*c^2*d-43*a*b*c^2*d-38*b^2*c^2*d-33*a*c^3*d-34*b*c^3*d+15*c^4*d-10*a^3*d^2+20*a^2*b*d^2+23*a*b^2*d^2-6*b^3*d^2-46*a^2*c*d^2-29*a*b*c*d^2-20*b^2*c*d^2+17*a*c^2*d^2-42*b*c^2*d^2+27*c^3*d^2-15*a^2*d^3-27*a*b*d^3+43*b^2*d^3-a*c*d^3+45*b*c*d^3+7*c^2*d^3+4*a*d^4-5*b*d^4-13*c*d^4-26*d^5-24*a^4*e-5*a^2*b^2*e-27*a*b^3*e-23*b^4*e+9*a^3*c*e+33*a^2*b*c*e+25*a*b^2*c*e+39*b^3*c*e-30*a^2*c^2*e-33*a*b*c^2*e-37*b^2*c^2*e-13*a*c^3*e+49*b*c^3*e-30*c^4*e+8*a^3*d*e+20*a^2*b*d*e+18*a*b^2*d*e-34*b^3*d*e-19*a^2*c*d*e+39*a*b*c*d*e+21*b^2*c*d*e+12*a*c^2*d*e-15*b*c^2*d*e+39*c^3*d*e+34*a^2*d^2*e+49*a*b*d^2*e-10*b^2*d^2*e-46*a*c*d^2*e+18*b*c*d^2*e-6*c^2*d^2*e+9*a*d^3*e+30*b*d^3*e+20*c*d^3*e+3*d^4*e-15*a^3*e^2-18*a^2*b*e^2+5*a*b^2*e^2+14*b^3*e^2+19*a^2*c*e^2+30*a*b*c*e^2-b^2*c*e^2+33*a*c^2*e^2+41*b*c^2*e^2-7*c^3*e^2+12*a^2*d*e^2-13*a*b*d*e^2-3*b^2*d*e^2-49*a*c*d*e^2-17*b*c*d*e^2+29*c^2*d*e^2-19*a*d^2*e^2-38*b*d^2*e^2-10*c*d^2*e^2+50*d^3*e^2-17*a^2*e^3+47*a*b*e^3-7*b^2*e^3-25*a*c*e^3+29*b*c*e^3-41*c^2*e^3-35*a*d*e^3+b*d*e^3+32*c*d*e^3-15*d^2*e^3+9*a*e^4+22*c*e^4+12*d*e^4+36*e^5,
    1755 a^2*b^2*d-a^2*c^2*d-5*a*b*c^2*d+40*b^2*c^2*d+4*a*c^3*d+35*b*c^3*d+42*c^4*d-23*a^3*d^2-34*a^2*b*d^2+4*a*b^2*d^2+27*b^3*d^2+38*a^2*c*d^2-47*a*b*c*d^2+50*b^2*c*d^2+17*a*c^2*d^2+8*c^3*d^2+26*a^2*d^3-32*a*b*d^3+3*b^2*d^3+16*a*c*d^3-47*b*c*d^3-41*c^2*d^3-22*a*d^4-47*b*d^4-17*c*d^4-43*d^5-49*a^4*e+6*a^3*b*e-46*a^2*b^2*e+30*a*b^3*e-21*b^4*e+30*a^3*c*e+17*a^2*b*c*e+39*a*b^2*c*e+37*b^3*c*e+36*a^2*c^2*e+21*a*b*c^2*e-36*b^2*c^2*e-2*a*c^3*e+18*b*c^3*e-49*c^4*e-47*a^3*d*e+35*a^2*b*d*e+10*a*b^2*d*e+22*b^3*d*e-10*a^2*c*d*e-24*a*b*c*d*e-43*b^2*c*d*e-11*a*c^2*d*e+39*b*c^2*d*e+14*c^3*d*e-15*a^2*d^2*e+36*a*b*d^2*e+42*b^2*d^2*e+32*a*c*d^2*e+7*b*c*d^2*e-4*c^2*d^2*e-13*a*d^3*e+39*b*d^3*e+20*c*d^3*e+7*d^4*e+49*a^3*e^2+39*a^2*b*e^2-12*a*b^2*e^2+36*b^3*e^2+12*a^2*c*e^2-45*a*b*c*e^2+47*b^2*c*e^2+16*a*c^2*e^2+21*b*c^2*e^2+2*c^3*e^2+43*a^2*d*e^2+16*a*b*d*e^2+15*b^2*d*e^2+44*a*c*d*e^2+47*b*c*d*e^2+6*c^2*d*e^2+29*a*d^2*e^2-10*b*d^2*e^2-14*c*d^2*e^2+40*d^3*e^2+10*a^2*e^3-2*a*b*e^3-12*b^2*e^3-11*a*c*e^3+4*b*c*e^3+c^2*e^3-41*a*d*e^3-33*b*d*e^3+13*c*d*e^3+32*d^2*e^3-43*a*e^4+42*b*e^4-4*c*e^4-36*d*e^4,
    1756 a^3*b*d-15*a^2*c^2*d-32*a*b*c^2*d+24*b^2*c^2*d+48*a*c^3*d+6*b*c^3*d-40*a^3*d^2+34*a^2*b*d^2+29*a*b^2*d^2+18*b^3*d^2-17*a^2*c*d^2+34*a*b*c*d^2+5*b^2*c*d^2-31*a*c^2*d^2-29*b*c^2*d^2-12*c^3*d^2+11*a^2*d^3+8*a*b*d^3+3*b^2*d^3-33*a*c*d^3-34*b*c*d^3-12*c^2*d^3-48*a*d^4+18*b*d^4+41*c*d^4-45*d^5-22*a^4*e+a^3*b*e-25*a^2*b^2*e+3*a*b^3*e+49*b^4*e-27*a^3*c*e-42*a^2*b*c*e+2*a*b^2*c*e+3*b^3*c*e-40*a^2*c^2*e-30*a*b*c^2*e+2*b^2*c^2*e-14*a*c^3*e-6*b*c^3*e+22*c^4*e-16*a^3*d*e+32*a^2*b*d*e-2*a*b^2*d*e-27*b^3*d*e+16*a^2*c*d*e+42*a*b*c*d*e-6*b^2*c*d*e-46*a*c^2*d*e-9*b*c^2*d*e+31*c^3*d*e-23*a^2*d^2*e-a*b*d^2*e+22*b^2*d^2*e+29*a*c*d^2*e+22*b*c*d^2*e-28*c^2*d^2*e-32*a*d^3*e-10*b*d^3*e-10*c*d^3*e+19*d^4*e-41*a^3*e^2+27*a^2*b*e^2+44*a*b^2*e^2-32*b^3*e^2-24*a^2*c*e^2-6*a*b*c*e^2-25*b^2*c*e^2+29*a*c^2*e^2+19*b*c^2*e^2-47*c^3*e^2+20*a^2*d*e^2-3*a*b*d*e^2+43*b^2*d*e^2-14*a*c*d*e^2+2*b*c*d*e^2-37*c^2*d*e^2-24*a*d^2*e^2-19*b*d^2*e^2+30*c*d^2*e^2+29*d^3*e^2-a^2*e^3-6*a*b*e^3-18*b^2*e^3-48*a*c*e^3+13*b*c*e^3+40*c^2*e^3-48*a*d*e^3-45*b*d*e^3-23*c*d*e^3-6*d^2*e^3+4*a*e^4+12*b*e^4+36*c*e^4+32*d*e^4-20*e^5,
    1757 a^4*d+17*a^2*c^2*d-6*a*b*c^2*d-16*b^2*c^2*d-8*a*c^3*d+12*b*c^3*d+31*c^4*d-2*a^3*d^2+45*a^2*b*d^2+29*a*b^2*d^2-47*b^3*d^2+17*a^2*c*d^2-28*a*b*c*d^2-12*b^2*c*d^2-49*a*c^2*d^2-34*b*c^2*d^2-49*c^3*d^2-13*a^2*d^3+12*a*b*d^3-50*b^2*d^3-27*a*c*d^3+17*b*c*d^3+26*c^2*d^3-40*a*d^4+37*b*d^4+31*c*d^4+42*d^5-3*a^4*e+40*a^3*b*e+39*a^2*b^2*e-35*a*b^3*e+2*b^4*e-47*a^3*c*e-45*a^2*b*c*e-24*a*b^2*c*e-20*b^3*c*e+a^2*c^2*e-3*a*b*c^2*e+8*b^2*c^2*e-42*a*c^3*e-49*b*c^3*e-49*c^4*e+42*a^3*d*e+25*a^2*b*d*e+45*a*b^2*d*e+35*b^3*d*e+43*a^2*c*d*e-18*a*b*c*d*e+24*b^2*c*d*e-2*a*c^2*d*e-43*b*c^2*d*e+16*c^3*d*e-44*a^2*d^2*e+31*a*b*d^2*e+17*b^2*d^2*e-36*a*c*d^2*e+25*b*c*d^2*e-20*c^2*d^2*e+17*a*d^3*e-39*b*d^3*e-37*c*d^3*e+10*d^4*e-30*a^3*e^2+34*a^2*b*e^2-43*a*b^2*e^2-2*b^3*e^2-48*a^2*c*e^2+32*a*b*c*e^2+47*b^2*c*e^2+34*a*c^2*e^2-32*b*c^2*e^2+4*c^3*e^2-26*a^2*d*e^2+22*a*b*d*e^2+23*b^2*d*e^2-37*a*c*d*e^2+26*b*c*d*e^2-33*c^2*d*e^2-5*a*d^2*e^2+15*b*d^2*e^2+19*c*d^2*e^2-31*d^3*e^2+42*a^2*e^3+27*a*b*e^3+30*b^2*e^3+22*a*c*e^3-49*b*c*e^3-19*c^2*e^3+42*a*d*e^3+5*b*d*e^3+32*c*d*e^3+9*d^2*e^3-17*a*e^4-46*b*e^4+23*c*e^4-32*d*e^4-2*e^5,
    1758 c^5+40*a^2*c^2*d+34*a*b*c^2*d-16*b^2*c^2*d+9*a*c^3*d-13*b*c^3*d+30*c^4*d+18*a^3*d^2+27*a^2*b*d^2+37*a*b^2*d^2-30*b^3*d^2-38*a^2*c*d^2-40*a*b*c*d^2-10*b^2*c*d^2-28*a*c^2*d^2-26*b*c^2*d^2+15*c^3*d^2-7*a^2*d^3+2*a*b*d^3+28*b^2*d^3+27*a*c*d^3+11*b*c*d^3-9*c^2*d^3-18*a*d^4+39*b*d^4+8*c*d^4+20*d^5+34*a^4*e+27*a^3*b*e+10*a^2*b^2*e-10*a*b^3*e+15*b^4*e+a^3*c*e+16*a^2*b*c*e+47*a*b^2*c*e-50*b^3*c*e-45*a^2*c^2*e-47*a*b*c^2*e-38*b^2*c^2*e+49*a*c^3*e+11*b*c^3*e-8*c^4*e-24*a^3*d*e+41*a^2*b*d*e+31*a*b^2*d*e-31*b^3*d*e-44*a^2*c*d*e-a*b*c*d*e-15*b^2*c*d*e-27*a*c^2*d*e-50*b*c^2*d*e+29*c^3*d*e+30*a^2*d^2*e+41*a*b*d^2*e-31*b^2*d^2*e-40*a*c*d^2*e+14*b*c*d^2*e-18*c^2*d^2*e+4*a*d^3*e-27*b*d^3*e-36*c*d^3*e-26*d^4*e-2*a^3*e^2+39*a^2*b*e^2-17*a*b^2*e^2-b^3*e^2+24*a^2*c*e^2-6*a*b*c*e^2-12*b^2*c*e^2+38*a*c^2*e^2+6*b*c^2*e^2+38*c^3*e^2+15*a^2*d*e^2-2*a*b*d*e^2-22*b^2*d*e^2+30*a*c*d*e^2+50*b*c*d*e^2-37*c^2*d*e^2+2*a*d^2*e^2+27*b*d^2*e^2+2*c*d^2*e^2+19*d^3*e^2+48*a^2*e^3+24*a*b*e^3+49*b^2*e^3-35*a*c*e^3+49*b*c*e^3+2*c^2*e^3+20*a*d*e^3+34*b*d*e^3-50*c*d*e^3-41*d^2*e^3+48*a*e^4-24*b*e^4-14*c*e^4+32*d*e^4-11*e^5,
    1759 b*c^4+9*a^2*c^2*d-47*a*b*c^2*d-29*b^2*c^2*d+24*a*c^3*d-19*b*c^3*d-25*c^4*d+50*a^3*d^2-6*a^2*b*d^2-32*a*b^2*d^2-43*b^3*d^2+42*a^2*c*d^2-16*a*b*c*d^2-40*b^2*c*d^2+3*a*c^2*d^2+9*b*c^2*d^2+34*c^3*d^2-48*a^2*d^3-8*a*b*d^3-22*b^2*d^3+42*a*c*d^3+25*b*c*d^3-31*c^2*d^3-12*a*d^4+25*b*d^4+c*d^4+13*d^5-26*a^4*e+2*a^3*b*e-37*a^2*b^2*e+23*a*b^3*e+25*b^4*e+43*a^3*c*e-10*a^2*b*c*e+16*a*b^2*c*e-24*b^3*c*e+43*a^2*c^2*e-25*a*b*c^2*e+39*b^2*c^2*e+31*a*c^3*e-21*b*c^3*e+16*c^4*e+17*a^3*d*e-33*a^2*b*d*e+34*a*b^2*d*e-16*b^3*d*e+49*a^2*c*d*e+10*a*b*c*d*e-14*b^2*c*d*e+6*a*c^2*d*e+32*b*c^2*d*e-25*c^3*d*e-16*a^2*d^2*e-26*a*b*d^2*e+36*b^2*d^2*e+41*a*c*d^2*e-43*b*c*d^2*e-44*c^2*d^2*e+24*a*d^3*e+12*b*d^3*e-40*c*d^3*e+46*d^4*e-18*a^3*e^2+36*a^2*b*e^2-49*a*b^2*e^2+47*b^3*e^2-30*a^2*c*e^2+11*a*b*c*e^2-17*b^2*c*e^2-19*a*c^2*e^2-33*b*c^2*e^2+4*c^3*e^2-14*a^2*d*e^2-13*a*b*d*e^2-4*b^2*d*e^2-a*c*d*e^2+22*b*c*d*e^2-41*c^2*d*e^2+50*a*d^2*e^2+24*b*d^2*e^2-29*c*d^2*e^2-9*d^3*e^2+10*a^2*e^3+44*a*b*e^3+11*b^2*e^3+25*a*c*e^3+31*b*c*e^3+22*c^2*e^3+a*d*e^3-6*c*d*e^3+26*d^2*e^3-40*a*e^4+31*b*e^4-50*c*e^4+9*d*e^4+39*e^5,
    1760 a*c^4-47*a^2*c^2*d+40*a*b*c^2*d-8*b^2*c^2*d+3*a*c^3*d-3*b*c^3*d+38*c^4*d-13*a^3*d^2+3*a^2*b*d^2+19*a*b^2*d^2+24*b^3*d^2-27*a^2*c*d^2-12*a*b*c*d^2-45*b^2*c*d^2+28*a*c^2*d^2+35*b*c^2*d^2-28*c^3*d^2+7*a^2*d^3+3*a*b*d^3-34*b^2*d^3+15*a*c*d^3+36*b*c*d^3-18*c^2*d^3-49*a*d^4+44*b*d^4+c*d^4-10*d^5+31*a^4*e-18*a^3*b*e+7*a^2*b^2*e+38*a*b^3*e+37*b^4*e+18*a^3*c*e-50*a^2*b*c*e+12*a*b^2*c*e+43*b^3*c*e+33*a^2*c^2*e+13*a*b*c^2*e+13*b^2*c^2*e-4*a*c^3*e+13*b*c^3*e+20*c^4*e-32*a^3*d*e-36*a^2*b*d*e+47*a*b^2*d*e+43*b^3*d*e-13*a^2*c*d*e-27*a*b*c*d*e+7*b^2*c*d*e-40*a*c^2*d*e-30*b*c^2*d*e+21*c^3*d*e-18*a^2*d^2*e-32*a*b*d^2*e-20*b^2*d^2*e-47*a*c*d^2*e+34*b*c*d^2*e-3*c^2*d^2*e-22*a*d^3*e-29*b*d^3*e-47*c*d^3*e-33*d^4*e-3*a^3*e^2+46*a^2*b*e^2-42*a*b^2*e^2+6*b^3*e^2+16*a^2*c*e^2-9*a*b*c*e^2-35*b^2*c*e^2-24*b*c^2*e^2-5*c^3*e^2+18*a^2*d*e^2+43*a*b*d*e^2-43*b^2*d*e^2+6*a*c*d*e^2+8*b*c*d*e^2-33*c^2*d*e^2-26*a*d^2*e^2+31*b*d^2*e^2-29*c*d^2*e^2+d^3*e^2+45*a^2*e^3+45*a*b*e^3-31*b^2*e^3-26*a*c*e^3+35*b*c*e^3+30*c^2*e^3-33*a*d*e^3-4*b*d*e^3+34*c*d*e^3+21*d^2*e^3+41*a*e^4-14*b*e^4-32*c*e^4-19*d*e^4+29*e^5,
    1761 b^2*c^3+10*a^2*c^2*d+20*a*b*c^2*d+36*b^2*c^2*d-7*a*c^3*d+13*b*c^3*d+42*c^4*d-6*a^3*d^2+13*a^2*b*d^2+31*a*b^2*d^2-29*b^3*d^2+44*a^2*c*d^2-20*a*b*c*d^2+27*b^2*c*d^2+17*a*c^2*d^2-7*b*c^2*d^2-18*c^3*d^2-44*a^2*d^3-35*a*b*d^3-11*b^2*d^3-28*a*c*d^3+b*c*d^3+22*c^2*d^3-13*a*d^4-32*b*d^4-33*c*d^4-48*d^5-16*a^4*e+7*a^3*b*e-40*a^2*b^2*e-47*a*b^3*e+20*b^4*e-41*a^3*c*e+50*a^2*b*c*e-35*a*b^2*c*e+44*b^3*c*e-43*a^2*c^2*e+15*a*b*c^2*e-33*b^2*c^2*e-38*a*c^3*e-16*b*c^3*e+11*c^4*e+46*a^3*d*e+32*a^2*b*d*e+3*a*b^2*d*e+39*b^3*d*e-32*a^2*c*d*e-19*a*b*c*d*e+23*b^2*c*d*e-2*a*c^2*d*e-44*b*c^2*d*e-44*c^3*d*e+18*a^2*d^2*e+31*a*b*d^2*e+16*b^2*d^2*e+a*c*d^2*e+45*b*c*d^2*e-18*c^2*d^2*e+22*a*d^3*e+16*b*d^3*e+2*c*d^3*e+48*d^4*e-32*a^3*e^2+49*a^2*b*e^2-3*a*b^2*e^2+30*b^3*e^2+31*a^2*c*e^2+28*a*b*c*e^2-4*b^2*c*e^2+7*a*c^2*e^2+48*b*c^2*e^2+40*c^3*e^2-a^2*d*e^2+19*a*b*d*e^2+40*b^2*d*e^2-3*a*c*d*e^2+9*b*c*d*e^2+21*c^2*d*e^2+28*a*d^2*e^2+49*b*d^2*e^2+19*c*d^2*e^2+41*d^3*e^2-30*a^2*e^3-30*a*b*e^3+5*b^2*e^3-2*a*c*e^3+17*b*c*e^3-16*c^2*e^3+42*b*d*e^3-22*c*d*e^3+34*d^2*e^3+20*a*e^4+42*b*e^4+8*c*e^4+36*d*e^4-25*e^5,
    1762 a*b*c^3-48*a^2*c^2*d-19*a*b*c^2*d+46*b^2*c^2*d-49*a*c^3*d-43*b*c^3*d+c^4*d-12*a^3*d^2+28*a^2*b*d^2+11*a*b^2*d^2+13*b^3*d^2+36*a^2*c*d^2+20*a*b*c*d^2+8*b^2*c*d^2-5*a*c^2*d^2+44*b*c^2*d^2-50*c^3*d^2+34*a^2*d^3+a*b*d^3-25*b^2*d^3+5*a*c*d^3-47*b*c*d^3-4*c^2*d^3-33*a*d^4-29*b*d^4+34*c*d^4+d^5-15*a^4*e+50*a^3*b*e+14*a^2*b^2*e+15*a*b^3*e+34*b^4*e+9*a^3*c*e+38*a^2*b*c*e+12*a*b^2*c*e+21*b^3*c*e+18*a^2*c^2*e+37*a*b*c^2*e-16*b^2*c^2*e+13*a*c^3*e+47*b*c^3*e-41*c^4*e-29*a^3*d*e-45*a^2*b*d*e+3*a*b^2*d*e+44*b^3*d*e-31*a^2*c*d*e-8*a*b*c*d*e-5*b^2*c*d*e-22*a*c^2*d*e-6*b*c^2*d*e+3*c^3*d*e-43*a^2*d^2*e-45*a*b*d^2*e-24*b^2*d^2*e+15*a*c*d^2*e+15*b*c*d^2*e+7*c^2*d^2*e-17*a*d^3*e-8*b*d^3*e-31*c*d^3*e+19*d^4*e-41*a^3*e^2-25*a^2*b*e^2-11*a*b^2*e^2-4*b^3*e^2-25*a^2*c*e^2-32*a*b*c*e^2-42*b^2*c*e^2-46*a*c^2*e^2-41*b*c^2*e^2-36*c^3*e^2+40*a^2*d*e^2-43*a*b*d*e^2+35*b^2*d*e^2+2*a*c*d*e^2-28*b*c*d*e^2-43*c^2*d*e^2+21*a*d^2*e^2+8*b*d^2*e^2-42*c*d^2*e^2+50*d^3*e^2+48*a^2*e^3-25*a*b*e^3+22*b^2*e^3-3*a*c*e^3-42*b*c*e^3+22*c^2*e^3-5*a*d*e^3-35*b*d*e^3+36*c*d*e^3-34*d^2*e^3+14*a*e^4+34*b*e^4+23*c*e^4-35*d*e^4+46*e^5,
    1763 a^2*c^3-17*a^2*c^2*d-7*a*b*c^2*d+15*b^2*c^2*d+35*a*c^3*d-36*b*c^3*d-19*c^4*d+20*a^3*d^2-39*a^2*b*d^2-3*a*b^2*d^2-2*b^3*d^2+8*a^2*c*d^2+13*a*b*c*d^2-20*b^2*c*d^2+6*a*c^2*d^2-48*b*c^2*d^2-21*c^3*d^2+46*a^2*d^3+39*a*b*d^3+32*b^2*d^3-2*a*c*d^3+47*b*c*d^3+16*c^2*d^3+20*a*d^4-36*b*d^4-12*c*d^4+28*d^5+24*a^4*e+17*a^3*b*e-21*a^2*b^2*e+31*a*b^3*e+24*b^4*e-45*a^3*c*e+34*a^2*b*c*e+3*a*b^2*c*e+34*b^3*c*e+39*a^2*c^2*e+12*a*b*c^2*e+18*b^2*c^2*e+19*a*c^3*e-13*b*c^3*e+7*c^4*e+16*a^3*d*e-4*a^2*b*d*e+35*a*b^2*d*e+20*b^3*d*e+38*a^2*c*d*e-41*a*b*c*d*e+49*b^2*c*d*e+7*a*c^2*d*e+39*b*c^2*d*e+15*c^3*d*e+32*a^2*d^2*e+35*a*b*d^2*e-36*b^2*d^2*e+11*a*c*d^2*e+11*b*c*d^2*e-26*c^2*d^2*e+2*a*d^3*e-30*b*d^3*e-2*c*d^3*e+5*d^4*e-2*a^3*e^2-45*a^2*b*e^2-10*a*b^2*e^2-42*b^3*e^2+13*a^2*c*e^2+38*a*b*c*e^2+22*b^2*c*e^2+42*a*c^2*e^2+16*b*c^2*e^2+40*c^3*e^2-19*a^2*d*e^2-35*a*b*d*e^2-24*b^2*d*e^2+33*a*c*d*e^2-48*b*c*d*e^2-6*a*d^2*e^2+2*b*d^2*e^2-31*c*d^2*e^2-5*d^3*e^2+45*a^2*e^3+17*a*b*e^3+50*b^2*e^3-18*a*c*e^3+3*b*c*e^3+32*c^2*e^3+34*a*d*e^3-39*b*d*e^3-35*c*d*e^3+22*d^2*e^3-40*a*e^4+43*b*e^4+48*c*e^4-42*d*e^4+8*e^5,
    1764 b^3*c^2+2*a^2*c^2*d-42*a*b*c^2*d-42*b^2*c^2*d+22*a*c^3*d-28*b*c^3*d-24*c^4*d-24*a^3*d^2+40*a^2*b*d^2-7*a*b^2*d^2+31*b^3*d^2+13*a^2*c*d^2+33*a*b*c*d^2+6*b^2*c*d^2+40*a*c^2*d^2+37*b*c^2*d^2+40*c^3*d^2-12*a^2*d^3+26*a*b*d^3+23*b^2*d^3+44*a*c*d^3+13*b*c*d^3-24*c^2*d^3+31*a*d^4+44*b*d^4+32*c*d^4+48*d^5+42*a^4*e+2*a^3*b*e-25*a^2*b^2*e-27*a*b^3*e-21*b^4*e+44*a^3*c*e+50*a^2*b*c*e+42*a*b^2*c*e+28*b^3*c*e+28*a^2*c^2*e+20*a*b*c^2*e+11*b^2*c^2*e-25*a*c^3*e+35*b*c^3*e+11*c^4*e+13*a^3*d*e+13*a^2*b*d*e-33*a*b^2*d*e+26*b^3*d*e+10*a^2*c*d*e-47*a*b*c*d*e+44*b^2*c*d*e-50*a*c^2*d*e+6*b*c^2*d*e+38*c^3*d*e-43*a^2*d^2*e-43*a*b*d^2*e+50*b^2*d^2*e-36*a*c*d^2*e+39*b*c*d^2*e+4*c^2*d^2*e+26*a*d^3*e+6*b*d^3*e-30*c*d^3*e-21*d^4*e+16*a^3*e^2-19*a^2*b*e^2+43*a*b^2*e^2-b^3*e^2-9*a^2*c*e^2-3*a*b*c*e^2-44*b^2*c*e^2-34*a*c^2*e^2-24*b*c^2*e^2+15*c^3*e^2+47*a^2*d*e^2-45*a*b*d*e^2-22*b^2*d*e^2-21*a*c*d*e^2+36*b*c*d*e^2+c^2*d*e^2-13*a*d^2*e^2+47*b*d^2*e^2-12*c*d^2*e^2+16*d^3*e^2-30*a^2*e^3-49*a*b*e^3+40*b^2*e^3+46*a*c*e^3-25*b*c*e^3-38*c^2*e^3-30*a*d*e^3-27*b*d*e^3+47*c*d*e^3+37*d^2*e^3+49*a*e^4+6*b*e^4-6*c*e^4+43*d*e^4+5*e^5,
    1765 a*b^2*c^2-9*a^2*c^2*d+49*a*b*c^2*d+17*b^2*c^2*d-45*a*c^3*d+27*b*c^3*d-8*c^4*d-25*a^3*d^2-23*a^2*b*d^2+47*a*b^2*d^2+8*b^3*d^2+20*a^2*c*d^2+37*a*b*c*d^2+28*b^2*c*d^2+8*a*c^2*d^2+36*b*c^2*d^2+34*c^3*d^2+37*a^2*d^3+23*a*b*d^3+11*b^2*d^3-46*a*c*d^3+45*b*c*d^3-16*c^2*d^3-27*a*d^4-39*b*d^4+31*c*d^4-24*d^5+42*a^4*e-30*a^3*b*e+12*a^2*b^2*e-18*a*b^3*e+8*b^4*e-33*a^3*c*e+21*a^2*b*c*e-9*a*b^2*c*e+10*b^3*c*e+11*a^2*c^2*e-33*a*b*c^2*e-27*b^2*c^2*e+47*a*c^3*e-35*b*c^3*e+15*c^4*e-19*a^3*d*e+20*a^2*b*d*e+41*a*b^2*d*e+39*b^3*d*e+24*a^2*c*d*e-12*a*b*c*d*e-16*b^2*c*d*e+38*a*c^2*d*e-43*b*c^2*d*e+39*c^3*d*e-14*a^2*d^2*e+39*a*b*d^2*e+24*b^2*d^2*e-35*a*c*d^2*e-8*b*c*d^2*e-26*c^2*d^2*e-5*a*d^3*e+34*b*d^3*e+16*c*d^3*e+35*d^4*e-a^3*e^2+44*a^2*b*e^2+33*a*b^2*e^2+41*b^3*e^2+26*a^2*c*e^2-6*a*b*c*e^2-15*b^2*c*e^2-46*a*c^2*e^2-37*b*c^2*e^2-49*c^3*e^2-6*a^2*d*e^2+20*a*b*d*e^2-7*b^2*d*e^2+16*a*c*d*e^2+49*b*c*d*e^2-23*c^2*d*e^2+37*a*d^2*e^2+31*b*d^2*e^2+17*c*d^2*e^2-39*d^3*e^2-46*a^2*e^3-17*a*b*e^3+46*b^2*e^3-31*a*c*e^3+39*b*c*e^3-13*c^2*e^3+40*a*d*e^3+18*b*d*e^3+3*c*d*e^3-6*d^2*e^3-35*a*e^4+22*b*e^4-47*c*e^4-4*d*e^4+35*e^5,
    1766 a^2*b*c^2+25*a^2*c^2*d-27*a*b*c^2*d+43*b^2*c^2*d+3*a*c^3*d+35*b*c^3*d+39*c^4*d+12*a^3*d^2-39*a^2*b*d^2-38*a*b^2*d^2+8*b^3*d^2+14*a^2*c*d^2+42*a*b*c*d^2-16*b^2*c*d^2+32*a*c^2*d^2-26*b*c^2*d^2+31*c^3*d^2-34*a^2*d^3-4*a*b*d^3+40*b^2*d^3+34*a*c*d^3-31*b*c*d^3+11*c^2*d^3+9*a*d^4+27*b*d^4+19*c*d^4-44*d^5-45*a^4*e+43*a^3*b*e-36*a^2*b^2*e+23*a*b^3*e-14*b^4*e-2*a^3*c*e+20*a^2*b*c*e-34*a*b^2*c*e+26*b^3*c*e+2*a^2*c^2*e-32*a*b*c^2*e+35*b^2*c^2*e-44*a*c^3*e-47*b*c^3*e-6*c^4*e+4*a^3*d*e+34*a^2*b*d*e-38*a*b^2*d*e-21*b^3*d*e+45*a^2*c*d*e-25*a*b*c*d*e+30*b^2*c*d*e+43*a*c^2*d*e-2*b*c^2*d*e+17*c^3*d*e+30*a^2*d^2*e+48*a*b*d^2*e+5*b^2*d^2*e+31*a*c*d^2*e+46*b*c*d^2*e+42*c^2*d^2*e-39*a*d^3*e-30*b*d^3*e+34*c*d^3*e+37*d^4*e+45*a^3*e^2-37*a^2*b*e^2+16*a*b^2*e^2-12*b^3*e^2+21*a^2*c*e^2-36*a*b*c*e^2+45*b^2*c*e^2-39*a*c^2*e^2+8*c^3*e^2-47*a^2*d*e^2+38*a*b*d*e^2+48*b^2*d*e^2-30*a*c*d*e^2-40*b*c*d*e^2+34*c^2*d*e^2+42*a*d^2*e^2-38*b*d^2*e^2+24*c*d^2*e^2+37*d^3*e^2-26*a^2*e^3-50*a*b*e^3+10*b^2*e^3-29*a*c*e^3-48*b*c*e^3+8*c^2*e^3+26*a*d*e^3-26*b*d*e^3-44*c*d*e^3+30*d^2*e^3-31*a*e^4-21*b*e^4-44*c*e^4-17*d*e^4+26*e^5,
    1767 a^3*c^2+32*a^2*c^2*d+18*a*b*c^2*d+26*b^2*c^2*d-34*a*c^3*d+29*b*c^3*d+6*c^4*d-46*a^3*d^2-37*a^2*b*d^2-9*a*b^2*d^2+13*b^3*d^2-46*a^2*c*d^2-25*a*b*c*d^2-19*b^2*c*d^2-36*a*c^2*d^2-28*b*c^2*d^2+c^3*d^2-16*a^2*d^3-32*a*b*d^3-39*b^2*d^3-a*c*d^3-44*b*c*d^3-24*c^2*d^3+44*a*d^4-18*b*d^4-11*c*d^4+31*d^5-37*a^4*e+50*a^3*b*e-3*a^2*b^2*e+40*a*b^3*e-19*b^4*e+31*a^3*c*e+49*a^2*b*c*e+14*a*b^2*c*e+22*b^3*c*e-27*a^2*c^2*e-46*a*b*c^2*e+31*b^2*c^2*e+22*a*c^3*e+27*b*c^3*e+25*c^4*e+10*a^3*d*e-21*a^2*b*d*e-13*a*b^2*d*e-46*b^3*d*e-34*a^2*c*d*e+24*a*b*c*d*e-38*b^2*c*d*e-14*a*c^2*d*e+50*b*c^2*d*e+28*c^3*d*e+44*a^2*d^2*e+23*a*b*d^2*e-38*b^2*d^2*e-4*a*c*d^2*e-34*b*c*d^2*e-21*c^2*d^2*e+9*a*d^3*e-14*b*d^3*e-19*c*d^3*e+14*d^4*e+31*a^3*e^2-33*a^2*b*e^2-39*a*b^2*e^2+9*b^3*e^2+7*a^2*c*e^2+13*a*b*c*e^2-12*b^2*c*e^2+24*a*c^2*e^2+18*b*c^2*e^2+19*c^3*e^2+24*a^2*d*e^2-24*a*b*d*e^2-47*b^2*d*e^2-46*a*c*d*e^2+31*b*c*d*e^2+31*c^2*d*e^2-9*a*d^2*e^2+6*b*d^2*e^2+46*c*d^2*e^2+23*d^3*e^2-37*a^2*e^3+14*a*b*e^3-40*b^2*e^3+14*a*c*e^3-46*b*c*e^3-42*c^2*e^3+32*a*d*e^3+5*b*d*e^3-4*c*d*e^3-16*d^2*e^3-4*a*e^4+36*b*e^4+38*c*e^4+30*d*e^4-18*e^5,
    1768 b^4*c+25*a^2*c^2*d+37*a*b*c^2*d+12*b^2*c^2*d-31*b*c^3*d+40*c^4*d-49*a^3*d^2+8*a^2*b*d^2+36*a*b^2*d^2+48*b^3*d^2-15*a^2*c*d^2+20*a*b*c*d^2-13*b^2*c*d^2-2*a*c^2*d^2+11*b*c^2*d^2+46*c^3*d^2+49*a^2*d^3-3*a*b*d^3-31*b^2*d^3-11*a*c*d^3+4*b*c*d^3+7*c^2*d^3-27*b*d^4+c*d^4+43*d^5+41*a^4*e-28*a^3*b*e+37*a^2*b^2*e-18*a*b^3*e+20*b^4*e-3*a^3*c*e+42*a^2*b*c*e-26*a*b^2*c*e-36*b^3*c*e-32*a^2*c^2*e+33*a*b*c^2*e-18*b^2*c^2*e-45*a*c^3*e+22*b*c^3*e+22*c^4*e+28*a^3*d*e-17*a^2*b*d*e-37*a*b^2*d*e-11*b^3*d*e+44*a^2*c*d*e-21*a*b*c*d*e+27*b^2*c*d*e-16*a*c^2*d*e+45*b*c^2*d*e+37*c^3*d*e+13*a^2*d^2*e-24*a*b*d^2*e+46*b^2*d^2*e-18*a*c*d^2*e-24*b*c*d^2*e+10*c^2*d^2*e-22*a*d^3*e-19*b*d^3*e+26*c*d^3*e+24*d^4*e+50*a^3*e^2-21*a^2*b*e^2-31*a*b^2*e^2+12*b^3*e^2+18*a^2*c*e^2-9*a*b*c*e^2-3*b^2*c*e^2+49*a*c^2*e^2-22*b*c^2*e^2-7*c^3*e^2+34*a^2*d*e^2+14*a*b*d*e^2-10*b^2*d*e^2-21*a*c*d*e^2-49*b*c*d*e^2-32*c^2*d*e^2-31*a*d^2*e^2-37*b*d^2*e^2+17*c*d^2*e^2-2*d^3*e^2+23*a^2*e^3+38*a*b*e^3+16*b^2*e^3+7*a*c*e^3-6*b*c*e^3+7*c^2*e^3-35*a*d*e^3+46*b*d*e^3-2*c*d*e^3-47*d^2*e^3+15*a*e^4-22*b*e^4+25*c*e^4+12*d*e^4+36*e^5,
    1769 a*b^3*c+7*a^2*c^2*d-37*a*b*c^2*d-27*b^2*c^2*d-a*c^3*d-28*b*c^3*d+32*c^4*d-17*a^3*d^2+30*a^2*b*d^2+7*a*b^2*d^2-32*b^3*d^2-10*a^2*c*d^2+38*a*b*c*d^2-15*b^2*c*d^2+a*c^2*d^2-37*b*c^2*d^2-9*c^3*d^2-13*a^2*d^3+27*a*b*d^3-11*b^2*d^3+6*a*c*d^3+b*c*d^3-9*c^2*d^3+44*a*d^4+3*b*d^4-36*c*d^4+41*d^5-3*a^4*e+10*a^3*b*e-8*a*b^3*e-3*b^4*e-3*a^3*c*e+34*a^2*b*c*e+3*a*b^2*c*e+15*b^3*c*e-22*a^2*c^2*e-33*a*b*c^2*e-4*b^2*c^2*e+48*a*c^3*e+7*b*c^3*e-29*c^4*e+38*a^3*d*e+14*a^2*b*d*e-26*a*b^2*d*e+48*b^3*d*e-3*a^2*c*d*e-45*a*b*c*d*e+26*b^2*c*d*e+46*a*c^2*d*e+26*b*c^2*d*e+15*c^3*d*e+29*a^2*d^2*e+42*a*b*d^2*e+11*b^2*d^2*e+26*a*c*d^2*e+44*b*c*d^2*e-18*c^2*d^2*e-19*a*d^3*e+47*b*d^3*e+c*d^3*e+50*d^4*e+8*a^3*e^2-19*a^2*b*e^2+49*a*b^2*e^2+17*b^3*e^2-27*a^2*c*e^2+30*a*b*c*e^2+10*b^2*c*e^2+21*a*c^2*e^2+11*b*c^2*e^2+38*c^3*e^2+36*a^2*d*e^2-28*a*b*d*e^2+22*b^2*d*e^2-45*a*c*d*e^2-45*b*c*d*e^2+43*c^2*d*e^2-21*a*d^2*e^2+5*b*d^2*e^2-41*c*d^2*e^2+36*d^3*e^2-25*a^2*e^3-22*a*b*e^3-6*b^2*e^3+31*a*c*e^3+19*b*c*e^3-35*c^2*e^3+44*a*d*e^3+40*b*d*e^3-14*c*d*e^3+6*d^2*e^3+2*a*e^4-26*b*e^4+43*c*e^4+39*d*e^4+7*e^5,
    1770 a^2*b^2*c-22*a^2*c^2*d+2*a*b*c^2*d-39*b^2*c^2*d-32*a*c^3*d-39*b*c^3*d+32*c^4*d+47*a^3*d^2-9*a^2*b*d^2+36*a*b^2*d^2-22*b^3*d^2+a^2*c*d^2+7*a*b*c*d^2+21*b^2*c*d^2+35*a*c^2*d^2+31*b*c^2*d^2+38*c^3*d^2+4*a^2*d^3+50*a*b*d^3-10*b^2*d^3-7*a*c*d^3-8*b*c*d^3-23*c^2*d^3+18*a*d^4+13*b*d^4+5*c*d^4-6*d^5-41*a^4*e+50*a^3*b*e+3*a^2*b^2*e+20*a*b^3*e-26*b^4*e-22*a^3*c*e+9*a^2*b*c*e+5*a*b^2*c*e+38*b^3*c*e-16*a^2*c^2*e-35*a*b*c^2*e-17*b^2*c^2*e-4*a*c^3*e-32*b*c^3*e-19*c^4*e-21*a^3*d*e+23*a^2*b*d*e+37*a*b^2*d*e+48*b^3*d*e-2*a^2*c*d*e-48*a*b*c*d*e-44*b^2*c*d*e+4*a*c^2*d*e+9*b*c^2*d*e-33*c^3*d*e+30*a^2*d^2*e+25*a*b*d^2*e+34*b^2*d^2*e-39*a*c*d^2*e+27*b*c*d^2*e+25*c^2*d^2*e+3*a*d^3*e-50*b*d^3*e-49*c*d^3*e-9*d^4*e-39*a^3*e^2+10*a^2*b*e^2-33*a*b^2*e^2+36*b^3*e^2+20*a^2*c*e^2+43*a*b*c*e^2+7*b^2*c*e^2+36*a*c^2*e^2-39*b*c^2*e^2-33*c^3*e^2+14*a^2*d*e^2-46*a*b*d*e^2+8*b^2*d*e^2+23*a*c*d*e^2+30*b*c*d*e^2-8*c^2*d*e^2+28*a*d^2*e^2-5*b*d^2*e^2+25*c*d^2*e^2+17*d^3*e^2+28*a^2*e^3-38*a*b*e^3-46*b^2*e^3-27*a*c*e^3-5*b*c*e^3-20*c^2*e^3+2*a*d*e^3-4*b*d*e^3+15*c*d*e^3-36*d^2*e^3+41*a*e^4+6*b*e^4+20*c*e^4+8*d*e^4-2*e^5,
    1771 a^3*b*c+40*a^2*c^2*d-47*a*b*c^2*d-27*b^2*c^2*d+41*a*c^3*d-39*b*c^3*d-32*c^4*d+5*a^3*d^2-5*a^2*b*d^2-34*a*b^2*d^2-35*b^3*d^2+29*a^2*c*d^2+4*a*b*c*d^2-6*b^2*c*d^2+25*a*c^2*d^2+6*b*c^2*d^2-44*c^3*d^2-38*a^2*d^3-31*a*b*d^3+37*b^2*d^3-49*a*c*d^3-17*b*c*d^3+9*c^2*d^3+25*a*d^4+4*b*d^4-25*c*d^4-49*d^5-15*a^4*e-11*a^3*b*e+7*a^2*b^2*e+37*a*b^3*e-21*b^4*e+18*a^3*c*e+46*a^2*b*c*e+6*a*b^2*c*e+43*b^3*c*e-5*a^2*c^2*e+49*a*b*c^2*e+44*b^2*c^2*e-18*a*c^3*e+30*b*c^3*e+30*c^4*e+37*a^3*d*e-47*a^2*b*d*e+23*a*b^2*d*e-26*b^3*d*e-12*a^2*c*d*e+49*a*b*c*d*e+37*b^2*c*d*e+3*a*c^2*d*e-15*b*c^2*d*e+c^3*d*e-13*a^2*d^2*e+32*a*b*d^2*e-29*b^2*d^2*e-11*a*c*d^2*e-28*b*c*d^2*e+21*c^2*d^2*e-10*a*d^3*e-20*b*d^3*e-2*c*d^3*e-25*d^4*e-18*a^3*e^2-10*a^2*b*e^2-26*a*b^2*e^2+15*b^3*e^2-6*a^2*c*e^2+48*a*b*c*e^2-36*b^2*c*e^2-18*a*c^2*e^2+8*b*c^2*e^2+36*c^3*e^2+2*a^2*d*e^2+48*a*b*d*e^2-32*b^2*d*e^2+47*a*c*d*e^2+b*c*d*e^2-35*c^2*d*e^2+16*a*d^2*e^2-26*b*d^2*e^2+40*c*d^2*e^2+50*d^3*e^2+16*a^2*e^3+32*a*b*e^3-22*b^2*e^3-43*a*c*e^3+4*b*c*e^3-26*c^2*e^3-29*a*d*e^3+7*b*d*e^3+20*c*d*e^3+8*d^2*e^3-9*a*e^4-7*b*e^4+3*c*e^4+49*d*e^4-48*e^5,
    1772 a^4*c-40*a^2*c^2*d+21*a*b*c^2*d+43*b^2*c^2*d+31*a*c^3*d-4*b*c^3*d+49*c^4*d+24*a^3*d^2-14*a^2*b*d^2+3*a*b^2*d^2-6*b^3*d^2+27*a^2*c*d^2+24*a*b*c*d^2-47*b^2*c*d^2-16*a*c^2*d^2+21*b*c^2*d^2-33*c^3*d^2+39*a^2*d^3-34*a*b*d^3-7*b^2*d^3+3*a*c*d^3+30*b*c*d^3-10*c^2*d^3+17*a*d^4+28*b*d^4+16*c*d^4-19*d^5+16*a^4*e-14*a^3*b*e+19*a^2*b^2*e-12*a*b^3*e-41*b^4*e-28*a^3*c*e+13*a^2*b*c*e+35*a*b^2*c*e-35*b^3*c*e+37*a^2*c^2*e-7*a*b*c^2*e+33*b^2*c^2*e-30*a*c^3*e+36*b*c^3*e-26*c^4*e-27*a^3*d*e+28*a^2*b*d*e+2*a*b^2*d*e+22*b^3*d*e-9*a^2*c*d*e+39*a*b*c*d*e-11*b^2*c*d*e+48*a*c^2*d*e+b*c^2*d*e-25*c^3*d*e-28*a^2*d^2*e-38*a*b*d^2*e-13*b^2*d^2*e-12*a*c*d^2*e-35*b*c*d^2*e-45*c^2*d^2*e-27*a*d^3*e-31*b*d^3*e+20*c*d^3*e+40*d^4*e+11*a^3*e^2-33*a^2*b*e^2-3*a*b^2*e^2+32*b^3*e^2+10*a^2*c*e^2+48*a*b*c*e^2-50*b^2*c*e^2+2*a*c^2*e^2-46*b*c^2*e^2+15*c^3*e^2-15*a^2*d*e^2+29*a*b*d*e^2+4*b^2*d*e^2-16*a*c*d*e^2+34*b*c*d*e^2-21*c^2*d*e^2+44*a*d^2*e^2-35*b*d^2*e^2+4*c*d^2*e^2-16*d^3*e^2-14*a^2*e^3+39*a*b*e^3+44*b^2*e^3-22*a*c*e^3-16*b*c*e^3+38*c^2*e^3-a*d*e^3+14*b*d*e^3-44*c*d*e^3-31*d^2*e^3+4*a*e^4+33*c*e^4-5*d*e^4+46*e^5,
    1773 b^5-5*a^2*c^2*d-23*a*b*c^2*d+3*b^2*c^2*d-30*a*c^3*d-48*b*c^3*d-40*c^4*d-21*a^3*d^2-13*a^2*b*d^2+36*a*b^2*d^2-35*b^3*d^2-9*a^2*c*d^2+32*a*b*c*d^2-19*b^2*c*d^2+3*a*c^2*d^2-2*b*c^2*d^2+22*c^3*d^2-37*a^2*d^3+46*a*b*d^3-38*b^2*d^3-33*a*c*d^3-7*b*c*d^3+3*c^2*d^3-33*a*d^4+b*d^4+22*c*d^4+50*d^5-33*a^4*e+18*a^3*b*e+11*a^2*b^2*e-19*a*b^3*e+49*b^4*e+3*a^3*c*e-10*a^2*b*c*e-29*a*b^2*c*e-17*b^3*c*e-15*a^2*c^2*e+30*a*b*c^2*e+39*b^2*c^2*e+7*a*c^3*e-46*b*c^3*e+29*c^4*e-17*a^3*d*e+26*a^2*b*d*e+27*a*b^2*d*e-27*b^3*d*e-27*a^2*c*d*e-7*a*b*c*d*e-36*b^2*c*d*e+18*a*c^2*d*e-34*b*c^2*d*e+31*c^3*d*e+22*a^2*d^2*e-2*a*b*d^2*e+39*b^2*d^2*e+40*a*c*d^2*e+49*b*c*d^2*e-41*c^2*d^2*e-46*a*d^3*e-33*b*d^3*e-40*c*d^3*e+16*d^4*e-37*a^3*e^2-14*a^2*b*e^2-49*a*b^2*e^2+39*b^3*e^2-20*a^2*c*e^2-39*a*b*c*e^2+20*b^2*c*e^2+10*a*c^2*e^2+29*b*c^2*e^2+20*c^3*e^2-19*a^2*d*e^2+37*a*b*d*e^2+20*b^2*d*e^2+26*a*c*d*e^2-8*b*c*d*e^2+14*c^2*d*e^2+24*a*d^2*e^2-14*b*d^2*e^2-33*c*d^2*e^2-18*d^3*e^2-2*a^2*e^3-32*a*b*e^3-37*b^2*e^3+45*a*c*e^3-33*b*c*e^3+28*c^2*e^3-19*a*d*e^3-43*b*d*e^3-10*c*d*e^3+30*d^2*e^3+44*a*e^4+40*b*e^4-20*c*e^4-40*d*e^4-2*e^5,
    1774 a*b^4-14*a^2*c^2*d+14*b^2*c^2*d+36*a*c^3*d+7*b*c^3*d-14*c^4*d-11*a^3*d^2+40*a^2*b*d^2-29*a*b^2*d^2-45*b^3*d^2+23*a^2*c*d^2+8*a*b*c*d^2+28*b^2*c*d^2+42*a*c^2*d^2+14*b*c^2*d^2+42*c^3*d^2-36*a^2*d^3-4*a*b*d^3+6*a*c*d^3-18*b*c*d^3+40*c^2*d^3-47*a*d^4-19*b*d^4-16*c*d^4+31*d^5-15*a^4*e+46*a^3*b*e+13*a^2*b^2*e-18*a*b^3*e+9*b^4*e+50*a^3*c*e-10*a^2*b*c*e-12*a*b^2*c*e+44*b^3*c*e+7*a^2*c^2*e+39*a*b*c^2*e-36*b^2*c^2*e+29*a*c^3*e-37*b*c^3*e-28*c^4*e-43*a^3*d*e+50*a^2*b*d*e-16*a*b^2*d*e+17*b^3*d*e+23*a^2*c*d*e-14*a*b*c*d*e+10*b^2*c*d*e+18*a*c^2*d*e+40*b*c^2*d*e-30*c^3*d*e+44*a^2*d^2*e+26*a*b*d^2*e+17*b^2*d^2*e+9*a*c*d^2*e+37*b*c*d^2*e-38*c^2*d^2*e+46*a*d^3*e+15*b*d^3*e+33*c*d^3*e+20*d^4*e+4*a^3*e^2-43*a^2*b*e^2-14*a*b^2*e^2-29*b^3*e^2+44*a^2*c*e^2-37*a*b*c*e^2-2*b^2*c*e^2+39*a*c^2*e^2-36*b*c^2*e^2+45*c^3*e^2-34*a^2*d*e^2-48*a*b*d*e^2-25*b^2*d*e^2+48*a*c*d*e^2+5*b*c*d*e^2-16*c^2*d*e^2+20*a*d^2*e^2+8*b*d^2*e^2-48*c*d^2*e^2+27*d^3*e^2-39*a^2*e^3-23*a*b*e^3-45*b^2*e^3-34*a*c*e^3-50*b*c*e^3-42*c^2*e^3+50*a*d*e^3+26*b*d*e^3+48*c*d*e^3-37*d^2*e^3-20*a*e^4-19*b*e^4+23*c*e^4+23*d*e^4+12*e^5,
    1775 a^2*b^3-25*a^2*c^2*d+26*a*b*c^2*d+32*b^2*c^2*d-48*a*c^3*d-7*b*c^3*d-44*c^4*d+14*a^3*d^2+19*a^2*b*d^2-7*a*b^2*d^2-15*b^3*d^2+50*a^2*c*d^2-11*a*b*c*d^2-13*b^2*c*d^2-33*a*c^2*d^2-46*b*c^2*d^2+12*c^3*d^2-26*a^2*d^3-11*a*b*d^3+22*b^2*d^3+24*a*c*d^3-12*b*c*d^3-22*c^2*d^3+40*a*d^4-23*b*d^4-48*c*d^4-20*d^5+17*a^4*e-41*a^3*b*e-a^2*b^2*e-12*a*b^3*e-9*b^4*e-30*a^3*c*e+50*a^2*b*c*e+31*a*b^2*c*e+5*b^3*c*e+33*a^2*c^2*e+15*a*b*c^2*e-50*b^2*c^2*e+24*a*c^3*e-b*c^3*e-6*c^4*e-31*a^3*d*e-26*a^2*b*d*e+49*a*b^2*d*e-13*b^3*d*e+43*a^2*c*d*e-10*a*b*c*d*e+35*b^2*c*d*e+36*a*c^2*d*e-22*b*c^2*d*e+40*c^3*d*e-7*a^2*d^2*e+28*a*b*d^2*e-b^2*d^2*e+17*a*c*d^2*e+13*b*c*d^2*e+26*c^2*d^2*e+32*a*d^3*e+3*b*d^3*e+12*c*d^3*e+40*d^4*e-40*a^3*e^2+12*a^2*b*e^2+27*a*b^2*e^2-24*b^3*e^2+13*a^2*c*e^2-19*a*b*c*e^2-27*b^2*c*e^2-28*a*c^2*e^2+50*b*c^2*e^2-48*c^3*e^2-14*a^2*d*e^2+26*a*b*d*e^2+35*b^2*d*e^2-43*a*c*d*e^2+42*b*c*d*e^2+9*c^2*d*e^2-10*a*d^2*e^2+21*c*d^2*e^2-5*d^3*e^2-30*a^2*e^3+38*a*b*e^3-25*b^2*e^3-28*a*c*e^3+23*b*c*e^3+38*c^2*e^3-30*a*d*e^3-16*b*d*e^3-35*c*d*e^3+2*d^2*e^3+33*a*e^4+12*b*e^4-25*c*e^4+26*d*e^4-40*e^5,
    1776 a^3*b^2-40*a^2*c^2*d+50*a*b*c^2*d+25*b^2*c^2*d+46*a*c^3*d-45*b*c^3*d-6*c^4*d-24*a^3*d^2-9*a^2*b*d^2-15*a*b^2*d^2+5*b^3*d^2+36*a^2*c*d^2-19*a*b*c*d^2+19*b^2*c*d^2+17*a*c^2*d^2+12*b*c^2*d^2-25*c^3*d^2-33*a^2*d^3-27*a*b*d^3+42*b^2*d^3-4*a*c*d^3+33*b*c*d^3+32*c^2*d^3+10*a*d^4+47*c*d^4-3*d^5-23*a^4*e-45*a^3*b*e+41*a^2*b^2*e+47*a*b^3*e+15*b^4*e-2*a^3*c*e+12*a^2*b*c*e+13*a*b^2*c*e-45*b^3*c*e-28*a^2*c^2*e-3*a*b*c^2*e-37*b^2*c^2*e+39*a*c^3*e+37*c^4*e-12*a^3*d*e-48*a^2*b*d*e-5*a*b^2*d*e+47*b^3*d*e-41*a^2*c*d*e-36*a*b*c*d*e-37*b^2*c*d*e-a*c^2*d*e-38*b*c^2*d*e+17*c^3*d*e-29*a^2*d^2*e-3*a*b*d^2*e-23*b^2*d^2*e-19*a*c*d^2*e+43*b*c*d^2*e-48*c^2*d^2*e-46*a*d^3*e+48*b*d^3*e+40*c*d^3*e-15*d^4*e-23*a^3*e^2-22*a^2*b*e^2-50*a*b^2*e^2-33*b^3*e^2+27*a^2*c*e^2-46*a*b*c*e^2+29*b^2*c*e^2-14*a*c^2*e^2+9*b*c^2*e^2-43*c^3*e^2-19*a^2*d*e^2-38*a*b*d*e^2+12*b^2*d*e^2+18*a*c*d*e^2+20*b*c*d*e^2+3*c^2*d*e^2-9*a*d^2*e^2-27*b*d^2*e^2-6*c*d^2*e^2+38*d^3*e^2+43*a^2*e^3+43*a*b*e^3+3*b^2*e^3+10*a*c*e^3+8*b*c*e^3+13*c^2*e^3+37*a*d*e^3+b*d*e^3-21*c*d*e^3+27*d^2*e^3+26*a*e^4-29*b*e^4-39*c*e^4+29*d*e^4+21*e^5,
    1777 a^4*b-45*a^2*c^2*d-6*a*b*c^2*d-42*b^2*c^2*d-4*a*c^3*d-49*b*c^3*d+14*c^4*d+35*a^3*d^2-3*a^2*b*d^2+23*a*b^2*d^2+21*b^3*d^2-24*a^2*c*d^2-14*a*b*c*d^2+20*b^2*c*d^2-20*a*c^2*d^2+41*b*c^2*d^2-34*c^3*d^2-13*a^2*d^3-48*a*b*d^3-13*b^2*d^3+38*a*c*d^3+21*b*c*d^3+40*c^2*d^3-28*a*d^4-34*b*d^4+38*c*d^4-24*d^5-48*a^4*e-2*a^3*b*e-35*a^2*b^2*e+2*a*b^3*e-25*b^4*e+47*a^3*c*e-14*a^2*b*c*e+25*a*b^2*c*e-12*b^3*c*e-11*a^2*c^2*e+22*a*b*c^2*e+15*b^2*c^2*e+17*a*c^3*e+47*b*c^3*e-43*c^4*e+28*a^3*d*e+9*a^2*b*d*e+6*a*b^2*d*e+30*a^2*c*d*e+31*a*b*c*d*e-2*b^2*c*d*e-6*a*c^2*d*e-45*b*c^2*d*e-24*c^3*d*e-39*a^2*d^2*e-7*a*b*d^2*e-11*b^2*d^2*e+8*a*c*d^2*e-47*b*c*d^2*e+c^2*d^2*e+30*a*d^3*e-30*b*d^3*e-38*c*d^3*e-14*d^4*e-25*a^3*e^2-14*a^2*b*e^2+24*a*b^2*e^2-37*b^3*e^2-14*a^2*c*e^2+40*a*b*c*e^2+27*b^2*c*e^2+22*a*c^2*e^2-38*b*c^2*e^2+43*c^3*e^2-44*a^2*d*e^2+28*a*b*d*e^2-4*b^2*d*e^2-26*a*c*d*e^2+18*b*c*d*e^2+24*c^2*d*e^2-35*a*d^2*e^2+6*b*d^2*e^2+5*c*d^2*e^2-38*d^3*e^2-37*a^2*e^3+34*a*b*e^3-27*b^2*e^3-4*a*c*e^3-3*b*c*e^3-16*c^2*e^3+22*a*d*e^3-4*b*d*e^3-41*c*d*e^3+25*d^2*e^3-38*a*e^4+49*b*e^4+c*e^4+14*d*e^4+47*e^5,
    1778 a^5-45*a^2*c^2*d-14*a*b*c^2*d-47*b^2*c^2*d-8*a*c^3*d+13*b*c^3*d+50*c^4*d-34*a^3*d^2-5*a^2*b*d^2+36*a*b^2*d^2+11*b^3*d^2+41*a^2*c*d^2-32*a*b*c*d^2+41*b^2*c*d^2-40*a*c^2*d^2+14*b*c^2*d^2+5*c^3*d^2+25*a^2*d^3+10*a*b*d^3-24*b^2*d^3-33*b*c*d^3-21*c^2*d^3+a*d^4+44*b*d^4-46*c*d^4-23*d^5-13*a^4*e+13*a^3*b*e-49*a*b^3*e+18*b^4*e+2*a^3*c*e+15*a^2*b*c*e-14*a*b^2*c*e-38*b^3*c*e+34*a^2*c^2*e+42*a*b*c^2*e-42*b^2*c^2*e-36*a*c^3*e+35*b*c^3*e-11*c^4*e+20*a^3*d*e+41*a*b^2*d*e+40*b^3*d*e-39*a^2*c*d*e-35*a*b*c*d*e-7*b^2*c*d*e-34*a*c^2*d*e-35*b*c^2*d*e+45*c^3*d*e+17*a^2*d^2*e+39*a*b*d^2*e+5*b^2*d^2*e-35*a*c*d^2*e-26*b*c*d^2*e-47*c^2*d^2*e+5*a*d^3*e-2*b*d^3*e+44*c*d^3*e+9*d^4*e-12*a^3*e^2+49*a^2*b*e^2-2*a*b^2*e^2-11*b^3*e^2-49*a^2*c*e^2-16*a*b*c*e^2-34*b^2*c*e^2+19*a*c^2*e^2-24*b*c^2*e^2-33*c^3*e^2-39*a^2*d*e^2+2*a*b*d*e^2+46*b^2*d*e^2-17*a*c*d*e^2+47*b*c*d*e^2+39*c^2*d*e^2+13*a*d^2*e^2+50*b*d^2*e^2-11*c*d^2*e^2+3*d^3*e^2+22*a^2*e^3-50*a*b*e^3+30*b^2*e^3-22*a*c*e^3-29*b*c*e^3-40*c^2*e^3+34*a*d*e^3+15*b*d*e^3-17*c*d*e^3+43*d^2*e^3+46*a*e^4-19*b*e^4-46*c*e^4-39*d*e^4-e^5,
    1779 e^6, d*e^5, c*e^5, b*e^5, a*e^5, d^2*e^4, c*d*e^4, b*d*e^4, a*d*e^4, c^2*e^4,
    1780 b*c*e^4, a*c*e^4, b^2*e^4, a*b*e^4, a^2*e^4, d^3*e^3, c*d^2*e^3, b*d^2*e^3,
    1781 a*d^2*e^3, c^2*d*e^3, b*c*d*e^3, a*c*d*e^3, b^2*d*e^3, a*b*d*e^3, a^2*d*e^3,
    1782 c^3*e^3, b*c^2*e^3, a*c^2*e^3, b^2*c*e^3, a*b*c*e^3, a^2*c*e^3, b^3*e^3,
    1783 a*b^2*e^3, a^2*b*e^3, a^3*e^3, d^4*e^2, c*d^3*e^2, b*d^3*e^2, a*d^3*e^2,
    1784 c^2*d^2*e^2, b*c*d^2*e^2, a*c*d^2*e^2, b^2*d^2*e^2, a*b*d^2*e^2, a^2*d^2*e^2,
    1785 c^3*d*e^2, b*c^2*d*e^2, a*c^2*d*e^2, b^2*c*d*e^2, a*b*c*d*e^2, a^2*c*d*e^2,
    1786 b^3*d*e^2, a*b^2*d*e^2, a^2*b*d*e^2, a^3*d*e^2, c^4*e^2, b*c^3*e^2, a*c^3*e^2,
    1787 b^2*c^2*e^2, a*b*c^2*e^2;
    1788   TestSSresAttribs2tr(M, "AGR101n4d007s021%4");
    1789 /*
    1790 options:  1 1 0 :  Time:  5/9/10 (35 without LCM)
    1791 options:  1 1 1 :  Time:  6/8/25
    1792 lres  Time:  5
    1793 nres  Time:  5
    1794 sres  Time:  693
    1795 */
    1796 
    1797   kill M;
    1798 
    1799 
    1800 
    1801   // AGR101n4d008s020%1, too big?
    1802   ideal M =
    1803 c^5*d-49*a^4*d^2-36*a^3*b*d^2-a^2*b^2*d^2-26*a*b^3*d^2+2*b^4*d^2+8*a^3*c*d^2-46*a^2*b*c*d^2-43*a*b^2*c*d^2-46*b^3*c*d^2-3*a^2*c^2*d^2-43*a*b*c^2*d^2+49*b^2*c^2*d^2-10*a*c^3*d^2+35*b*c^3*d^2+20*c^4*d^2-42*a^3*d^3+45*a^2*b*d^3+32*a*b^2*d^3-45*b^3*d^3-27*a^2*c*d^3+13*a*b*c*d^3+25*b^2*c*d^3+8*a*c^2*d^3+9*b*c^2*d^3+9*c^3*d^3+45*a^2*d^4+30*a*b*d^4+39*b^2*d^4-23*a*c*d^4+2*b*c*d^4-16*c^2*d^4+32*a*d^5-34*b*d^5+39*c*d^5+12*d^6-29*a^5*e-23*a^4*b*e-29*a^3*b^2*e-a^2*b^3*e-20*a*b^4*e+42*b^5*e+20*a^4*c*e-27*a^3*b*c*e-5*a^2*b^2*c*e-14*b^4*c*e-27*a^3*c^2*e-7*a^2*b*c^2*e-25*a*b^2*c^2*e+14*b^3*c^2*e+19*a^2*c^3*e+43*a*b*c^3*e-31*b^2*c^3*e+37*a*c^4*e-34*b*c^4*e+44*c^5*e+21*a^4*d*e+22*a^3*b*d*e+14*a^2*b^2*d*e-35*a*b^3*d*e-29*b^4*d*e-9*a^3*c*d*e-41*a^2*b*c*d*e+28*a*b^2*c*d*e+35*b^3*c*d*e+48*a^2*c^2*d*e+26*a*b*c^2*d*e-47*b^2*c^2*d*e+18*a*c^3*d*e+8*b*c^3*d*e-46*c^4*d*e+50*a^3*d^2*e-46*a^2*b*d^2*e-41*a*b^2*d^2*e-44*b^3*d^2*e+7*a^2*c*d^2*e-a*b*c*d^2*e+38*b^2*c*d^2*e+33*a*c^2*d^2*e-24*b*c^2*d^2*e-7*c^3*d^2*e+27*a^2*d^3*e+19*a*b*d^3*e-14*b^2*d^3*e+9*a*c*d^3*e+3*b*c*d^3*e+34*c^2*d^3*e-49*a*d^4*e-2*b*d^4*e+9*c*d^4*e+17*d^5*e+12*a^4*e^2-17*a^3*b*e^2+16*a^2*b^2*e^2+2*a*b^3*e^2+25*b^4*e^2+49*a^3*c*e^2+10*a^2*b*c*e^2-43*a*b^2*c*e^2+5*b^3*c*e^2+4*a^2*c^2*e^2-44*a*b*c^2*e^2-25*b^2*c^2*e^2+15*a*c^3*e^2-44*b*c^3*e^2-17*c^4*e^2+17*a^3*d*e^2+40*a^2*b*d*e^2+3*a*b^2*d*e^2-25*b^3*d*e^2-47*a^2*c*d*e^2-45*a*b*c*d*e^2+9*b^2*c*d*e^2-41*a*c^2*d*e^2-36*b*c^2*d*e^2-17*c^3*d*e^2-15*a^2*d^2*e^2+49*a*b*d^2*e^2+13*b^2*d^2*e^2-39*a*c*d^2*e^2+36*b*c*d^2*e^2-32*c^2*d^2*e^2+23*a*d^3*e^2+14*b*d^3*e^2+10*c*d^3*e^2-d^4*e^2+24*a^3*e^3+27*a^2*b*e^3+31*a*b^2*e^3-45*b^3*e^3-50*a^2*c*e^3-a*b*c*e^3+43*b^2*c*e^3+46*a*c^2*e^3-25*b*c^2*e^3+2*c^3*e^3+44*a^2*d*e^3+43*a*b*d*e^3-30*b^2*d*e^3-18*a*c*d*e^3+44*b*c*d*e^3-34*c^2*d*e^3-49*a*d^2*e^3-18*b*d^2*e^3-21*c*d^2*e^3-43*d^3*e^3-26*a^2*e^4-18*a*b*e^4+6*b^2*e^4-48*a*c*e^4+6*b*c*e^4-16*c^2*e^4-2*a*d*e^4-21*b*d*e^4+5*c*d*e^4-18*d^2*e^4+33*a*e^5-23*b*e^5-48*c*e^5+37*d*e^5-44*e^6,
    1804 b*c^4*d-26*a^4*d^2-47*a^3*b*d^2+28*a^2*b^2*d^2+5*a*b^3*d^2+37*b^4*d^2-32*a^3*c*d^2+44*a^2*b*c*d^2+13*a*b^2*c*d^2-45*b^3*c*d^2+35*a^2*c^2*d^2-18*a*b*c^2*d^2-3*b^2*c^2*d^2-4*a*c^3*d^2-27*b*c^3*d^2-37*a^3*d^3-44*a^2*b*d^3-36*a*b^2*d^3+49*b^3*d^3-16*a^2*c*d^3+24*a*b*c*d^3+43*b^2*c*d^3-40*a*c^2*d^3-3*b*c^2*d^3-16*c^3*d^3+6*a^2*d^4+46*a*b*d^4+8*b^2*d^4-11*a*c*d^4-4*b*c*d^4-40*c^2*d^4-31*a*d^5-41*b*d^5-35*c*d^5-35*d^6+5*a^5*e-20*a^4*b*e+48*a^3*b^2*e-42*a^2*b^3*e+46*a*b^4*e-28*b^5*e+42*a^4*c*e+22*a^3*b*c*e+23*a^2*b^2*c*e-6*a*b^3*c*e-2*b^4*c*e+26*a^3*c^2*e+28*a^2*b*c^2*e+28*a*b^2*c^2*e-31*b^3*c^2*e-50*a^2*c^3*e+3*a*b*c^3*e+39*b^2*c^3*e-21*b*c^4*e+24*c^5*e-a^4*d*e+12*a^3*b*d*e+43*a^2*b^2*d*e+17*a*b^3*d*e-33*b^4*d*e-31*a^3*c*d*e+11*a^2*b*c*d*e-16*a*b^2*c*d*e-49*b^3*c*d*e+6*a^2*c^2*d*e+49*a*b*c^2*d*e-47*b^2*c^2*d*e-40*a*c^3*d*e-11*b*c^3*d*e-7*a^3*d^2*e+10*a^2*b*d^2*e-37*a*b^2*d^2*e+37*b^3*d^2*e+49*a^2*c*d^2*e+11*b^2*c*d^2*e-43*a*c^2*d^2*e+46*b*c^2*d^2*e-18*c^3*d^2*e+38*a^2*d^3*e+20*a*b*d^3*e-22*b^2*d^3*e-32*a*c*d^3*e+41*b*c*d^3*e+c^2*d^3*e+7*a*d^4*e+18*b*d^4*e-12*c*d^4*e-15*d^5*e+34*a^4*e^2-a^3*b*e^2+47*a^2*b^2*e^2+47*a*b^3*e^2-37*b^4*e^2-36*a^3*c*e^2-21*a^2*b*c*e^2-3*b^3*c*e^2-34*a^2*c^2*e^2-4*a*b*c^2*e^2+33*b^2*c^2*e^2+19*a*c^3*e^2+3*b*c^3*e^2-13*c^4*e^2-45*a^3*d*e^2+28*a^2*b*d*e^2-23*a*b^2*d*e^2+30*b^3*d*e^2+15*a^2*c*d*e^2+a*b*c*d*e^2-50*a*c^2*d*e^2-6*b*c^2*d*e^2+32*c^3*d*e^2+17*a^2*d^2*e^2-15*a*b*d^2*e^2+6*b^2*d^2*e^2+15*a*c*d^2*e^2-b*c*d^2*e^2+41*c^2*d^2*e^2-47*a*d^3*e^2+49*b*d^3*e^2-4*c*d^3*e^2-5*d^4*e^2+35*a^3*e^3+36*a^2*b*e^3+49*a*b^2*e^3+b^3*e^3-11*a^2*c*e^3+a*b*c*e^3+18*b^2*c*e^3+19*a*c^2*e^3+11*b*c^2*e^3-41*c^3*e^3-42*a^2*d*e^3+6*a*b*d*e^3-23*b^2*d*e^3+47*a*c*d*e^3+35*b*c*d*e^3+39*c^2*d*e^3-30*a*d^2*e^3-21*b*d^2*e^3-48*c*d^2*e^3-6*d^3*e^3+38*a^2*e^4-43*a*b*e^4-10*b^2*e^4-a*c*e^4+2*b*c*e^4-29*c^2*e^4+31*a*d*e^4+24*b*d*e^4+18*c*d*e^4+38*d^2*e^4+36*a*e^5-32*b*e^5-17*c*e^5+36*d*e^5+13*e^6,
    1805 a*c^4*d+8*a^4*d^2+41*a^3*b*d^2-36*a^2*b^2*d^2+7*a*b^3*d^2+35*b^4*d^2+19*a^3*c*d^2-31*a^2*b*c*d^2+23*a*b^2*c*d^2-18*b^3*c*d^2+14*a*b*c^2*d^2-8*b^2*c^2*d^2+31*a*c^3*d^2-46*b*c^3*d^2-29*c^4*d^2-42*a^3*d^3+46*a^2*b*d^3-24*a*b^2*d^3+46*b^3*d^3-18*a^2*c*d^3-49*a*b*c*d^3-6*b^2*c*d^3+20*a*c^2*d^3+17*b*c^2*d^3+38*c^3*d^3-36*a^2*d^4+16*a*b*d^4+23*b^2*d^4-34*a*c*d^4-9*b*c*d^4-18*c^2*d^4-18*a*d^5+26*b*d^5-9*c*d^5-3*d^6-17*a^5*e+32*a^4*b*e-23*a^3*b^2*e-4*a^2*b^3*e+42*a*b^4*e-43*b^5*e+28*a^4*c*e+5*a^3*b*c*e-14*a^2*b^2*c*e-43*a*b^3*c*e+41*b^4*c*e+2*a^3*c^2*e-27*a^2*b*c^2*e-35*a*b^2*c^2*e+2*b^3*c^2*e-42*a^2*c^3*e+47*a*b*c^3*e+50*b^2*c^3*e-a*c^4*e+10*b*c^4*e+47*c^5*e-23*a^4*d*e+25*a^3*b*d*e-41*a^2*b^2*d*e+32*a*b^3*d*e-35*b^4*d*e+14*a^3*c*d*e-25*a^2*b*c*d*e+47*a*b^2*c*d*e-32*b^3*c*d*e+50*a^2*c^2*d*e-30*a*b*c^2*d*e+39*b^2*c^2*d*e+30*a*c^3*d*e-33*b*c^3*d*e+37*c^4*d*e-21*a^3*d^2*e+34*a^2*b*d^2*e+7*a*b^2*d^2*e-43*b^3*d^2*e+13*a^2*c*d^2*e+32*a*b*c*d^2*e-35*b^2*c*d^2*e+18*a*c^2*d^2*e-2*b*c^2*d^2*e+9*c^3*d^2*e+13*a^2*d^3*e-32*a*b*d^3*e-9*b^2*d^3*e-35*a*c*d^3*e-14*b*c*d^3*e+9*c^2*d^3*e+19*a*d^4*e-50*b*d^4*e+28*c*d^4*e-40*d^5*e+17*a^4*e^2-44*a^3*b*e^2+30*a^2*b^2*e^2+41*a*b^3*e^2+20*b^4*e^2+21*a^3*c*e^2+48*a^2*b*c*e^2+15*a*b^2*c*e^2-40*b^3*c*e^2-6*a^2*c^2*e^2-29*a*b*c^2*e^2-42*b^2*c^2*e^2-40*a*c^3*e^2-48*b*c^3*e^2+36*c^4*e^2+38*a^3*d*e^2+19*a^2*b*d*e^2+41*a*b^2*d*e^2+34*b^3*d*e^2+20*a^2*c*d*e^2-23*a*b*c*d*e^2-2*b^2*c*d*e^2+36*a*c^2*d*e^2-37*b*c^2*d*e^2+9*c^3*d*e^2-47*a^2*d^2*e^2-35*a*b*d^2*e^2+13*b^2*d^2*e^2-20*a*c*d^2*e^2-45*b*c*d^2*e^2+17*c^2*d^2*e^2-32*a*d^3*e^2+13*b*d^3*e^2-4*c*d^3*e^2-26*d^4*e^2+32*a^3*e^3-25*a^2*b*e^3+30*a*b^2*e^3-12*b^3*e^3+28*a^2*c*e^3+41*a*b*c*e^3-49*b^2*c*e^3+35*a*c^2*e^3+38*b*c^2*e^3+49*c^3*e^3-9*a^2*d*e^3-31*a*b*d*e^3-6*b^2*d*e^3+29*a*c*d*e^3+13*b*c*d*e^3-14*c^2*d*e^3+36*a*d^2*e^3+33*b*d^2*e^3-46*c*d^2*e^3+50*d^3*e^3-47*a^2*e^4+5*a*b*e^4+36*b^2*e^4-5*a*c*e^4+4*b*c*e^4-20*c^2*e^4+29*a*d*e^4+25*b*d*e^4-24*c*d*e^4-10*d^2*e^4-2*a*e^5-29*b*e^5-34*c*e^5-d*e^5+e^6,
    1806 b^2*c^3*d-49*a^4*d^2+36*a^3*b*d^2-3*a^2*b^2*d^2+12*a*b^3*d^2+11*b^4*d^2+10*a^3*c*d^2+9*a^2*b*c*d^2-13*a*b^2*c*d^2+43*b^3*c*d^2-27*a^2*c^2*d^2-20*a*b*c^2*d^2+34*b^2*c^2*d^2-30*a*c^3*d^2-50*b*c^3*d^2+43*c^4*d^2+17*a^3*d^3+5*a^2*b*d^3+16*a*b^2*d^3+27*b^3*d^3-26*a^2*c*d^3+17*a*b*c*d^3-31*b^2*c*d^3-43*a*c^2*d^3-18*b*c^2*d^3-8*c^3*d^3-8*a^2*d^4+8*a*b*d^4+23*b^2*d^4+7*a*c*d^4-48*b*c*d^4+21*c^2*d^4+5*a*d^5+4*b*d^5+40*c*d^5-22*d^6+3*a^5*e-a^4*b*e+26*a^3*b^2*e+16*a^2*b^3*e-29*a*b^4*e-50*b^5*e-6*a^4*c*e+31*a^3*b*c*e+43*a^2*b^2*c*e+12*a*b^3*c*e+31*b^4*c*e-21*a^3*c^2*e+25*a^2*b*c^2*e+20*a*b^2*c^2*e+15*b^3*c^2*e-4*a^2*c^3*e-48*a*b*c^3*e-29*b^2*c^3*e+43*a*c^4*e-41*b*c^4*e-15*c^5*e-13*a^4*d*e-29*a^3*b*d*e+7*a^2*b^2*d*e+4*a*b^3*d*e-50*b^4*d*e+3*a^3*c*d*e+4*a^2*b*c*d*e+7*a*b^2*c*d*e+4*b^3*c*d*e+16*a^2*c^2*d*e-42*a*b*c^2*d*e+36*b^2*c^2*d*e-5*a*c^3*d*e+13*b*c^3*d*e+17*c^4*d*e+18*a^3*d^2*e-16*a^2*b*d^2*e-32*a*b^2*d^2*e-16*b^3*d^2*e-34*a^2*c*d^2*e-22*a*b*c*d^2*e-12*b^2*c*d^2*e+35*a*c^2*d^2*e+33*b*c^2*d^2*e-47*c^3*d^2*e+12*a^2*d^3*e-43*a*b*d^3*e+11*b^2*d^3*e+2*a*c*d^3*e+42*b*c*d^3*e-18*c^2*d^3*e+44*a*d^4*e+25*b*d^4*e+41*c*d^4*e+40*d^5*e+40*a^4*e^2-3*a^3*b*e^2-8*a^2*b^2*e^2+a*b^3*e^2-27*b^4*e^2+15*a^3*c*e^2+49*a^2*b*c*e^2-14*a*b^2*c*e^2+31*b^3*c*e^2+36*a^2*c^2*e^2-14*a*b*c^2*e^2-31*b^2*c^2*e^2+48*a*c^3*e^2-24*b*c^3*e^2-30*c^4*e^2-47*a^3*d*e^2+12*a^2*b*d*e^2+44*a*b^2*d*e^2+47*b^3*d*e^2-5*a^2*c*d*e^2+23*a*b*c*d*e^2+48*b^2*c*d*e^2-25*a*c^2*d*e^2-7*b*c^2*d*e^2+32*a^2*d^2*e^2+35*a*b*d^2*e^2-19*b^2*d^2*e^2+19*a*c*d^2*e^2+26*b*c*d^2*e^2+26*c^2*d^2*e^2+8*a*d^3*e^2-21*b*d^3*e^2-6*c*d^3*e^2-35*d^4*e^2-30*a^3*e^3+36*a^2*b*e^3-27*a*b^2*e^3-33*b^3*e^3-50*a^2*c*e^3+41*a*b*c*e^3+13*b^2*c*e^3+20*a*c^2*e^3+36*b*c^2*e^3+14*c^3*e^3+40*a^2*d*e^3-35*a*b*d*e^3+11*b^2*d*e^3+36*a*c*d*e^3+23*b*c*d*e^3-34*c^2*d*e^3+25*a*d^2*e^3-14*b*d^2*e^3-5*c*d^2*e^3+11*d^3*e^3+42*a^2*e^4-48*a*b*e^4-27*b^2*e^4-17*a*c*e^4+32*b*c*e^4-3*c^2*e^4-3*a*d*e^4-33*b*d*e^4-3*c*d*e^4-14*d^2*e^4+8*a*e^5+14*b*e^5+3*c*e^5-34*d*e^5-46*e^6,
    1807 a*b*c^3*d-20*a^4*d^2+23*a^3*b*d^2-14*a^2*b^2*d^2+29*a*b^3*d^2-36*b^4*d^2-48*a^3*c*d^2+39*a^2*b*c*d^2-34*a*b^2*c*d^2+b^3*c*d^2-25*a^2*c^2*d^2+22*a*b*c^2*d^2-12*b^2*c^2*d^2+48*a*c^3*d^2-41*b*c^3*d^2+13*c^4*d^2-24*a^3*d^3-43*a^2*b*d^3-31*a*b^2*d^3-13*b^3*d^3+10*a^2*c*d^3-16*a*b*c*d^3+48*b^2*c*d^3-18*a*c^2*d^3+7*b*c^2*d^3+8*c^3*d^3-14*a^2*d^4-14*a*b*d^4+49*b^2*d^4+43*a*c*d^4+7*b*c*d^4-50*c^2*d^4-21*a*d^5-33*b*d^5-44*c*d^5-40*d^6-42*a^5*e+39*a^4*b*e-14*a^3*b^2*e+34*a^2*b^3*e+22*a*b^4*e+37*b^5*e+24*a^4*c*e+39*a^3*b*c*e-43*a^2*b^2*c*e-40*a*b^3*c*e-6*b^4*c*e-45*a^3*c^2*e+18*a^2*b*c^2*e-8*a*b^2*c^2*e+22*b^3*c^2*e-36*a^2*c^3*e+31*a*b*c^3*e+15*b^2*c^3*e+7*a*c^4*e-18*b*c^4*e-31*c^5*e-20*a^4*d*e+25*a^3*b*d*e-11*a^2*b^2*d*e-21*a*b^3*d*e-23*b^4*d*e+18*a^3*c*d*e-49*a^2*b*c*d*e+5*a*b^2*c*d*e+21*b^3*c*d*e-2*a^2*c^2*d*e+42*a*b*c^2*d*e-37*b^2*c^2*d*e+28*a*c^3*d*e-8*b*c^3*d*e+c^4*d*e+10*a^3*d^2*e-16*a^2*b*d^2*e-20*a*b^2*d^2*e+42*b^3*d^2*e+23*a^2*c*d^2*e-16*a*b*c*d^2*e+39*b^2*c*d^2*e+3*a*c^2*d^2*e+25*b*c^2*d^2*e-16*c^3*d^2*e-33*a^2*d^3*e-28*a*b*d^3*e+4*b^2*d^3*e-15*a*c*d^3*e-30*b*c*d^3*e-5*c^2*d^3*e-8*b*d^4*e-21*c*d^4*e+6*d^5*e-9*a^4*e^2-23*a^3*b*e^2-45*a^2*b^2*e^2+33*a*b^3*e^2+14*b^4*e^2+8*a^3*c*e^2+5*a^2*b*c*e^2-13*a*b^2*c*e^2-39*b^3*c*e^2-4*a^2*c^2*e^2+30*a*b*c^2*e^2-38*b^2*c^2*e^2+24*a*c^3*e^2-29*b*c^3*e^2-3*c^4*e^2+3*a^3*d*e^2+43*a^2*b*d*e^2-21*a*b^2*d*e^2-45*b^3*d*e^2-3*a^2*c*d*e^2-22*a*b*c*d*e^2+16*b^2*c*d*e^2-42*b*c^2*d*e^2-43*c^3*d*e^2-10*a*b*d^2*e^2+23*b^2*d^2*e^2-36*a*c*d^2*e^2+29*b*c*d^2*e^2-11*c^2*d^2*e^2+18*a*d^3*e^2-46*b*d^3*e^2-34*c*d^3*e^2+21*d^4*e^2+4*a^3*e^3+23*a^2*b*e^3-18*a*b^2*e^3-10*b^3*e^3+3*a^2*c*e^3+a*b*c*e^3-32*b^2*c*e^3-19*a*c^2*e^3-5*b*c^2*e^3+25*c^3*e^3-40*a^2*d*e^3-37*a*b*d*e^3-10*b^2*d*e^3-20*a*c*d*e^3+35*b*c*d*e^3+2*c^2*d*e^3+46*a*d^2*e^3+46*b*d^2*e^3+25*c*d^2*e^3+14*d^3*e^3-28*a^2*e^4+24*a*b*e^4-38*b^2*e^4+11*a*c*e^4+15*b*c*e^4-10*c^2*e^4-32*a*d*e^4+37*b*d*e^4+21*c*d*e^4-25*d^2*e^4-47*a*e^5-32*b*e^5+5*c*e^5+17*d*e^5+44*e^6,
    1808 a^2*c^3*d+25*a^4*d^2-40*a^3*b*d^2-49*a^2*b^2*d^2+30*a*b^3*d^2-36*b^4*d^2+41*a^3*c*d^2+23*a^2*b*c*d^2-16*a*b^2*c*d^2-20*b^3*c*d^2-46*a^2*c^2*d^2-29*a*b*c^2*d^2-14*b^2*c^2*d^2-38*a*c^3*d^2+9*b*c^3*d^2+50*c^4*d^2-20*a^3*d^3-14*a^2*b*d^3+13*a*b^2*d^3+5*b^3*d^3+7*a^2*c*d^3+46*a*b*c*d^3+40*b^2*c*d^3-46*a*c^2*d^3+27*b*c^2*d^3-5*c^3*d^3+43*a^2*d^4+5*a*b*d^4+3*b^2*d^4+29*a*c*d^4-43*b*c*d^4-31*c^2*d^4-24*a*d^5-45*b*d^5-26*c*d^5-6*d^6+18*a^5*e+22*a^4*b*e-12*a^3*b^2*e+40*a^2*b^3*e-8*a*b^4*e+36*b^5*e+5*a^4*c*e+46*a^3*b*c*e+6*a^2*b^2*c*e-39*a*b^3*c*e-29*b^4*c*e+36*a^3*c^2*e+35*a^2*b*c^2*e+11*a*b^2*c^2*e-12*b^3*c^2*e+13*a^2*c^3*e+15*a*b*c^3*e+38*b^2*c^3*e-4*a*c^4*e-46*b*c^4*e+25*c^5*e-31*a^4*d*e+35*a^3*b*d*e+37*a^2*b^2*d*e+27*a*b^3*d*e-30*b^4*d*e-37*a^3*c*d*e-2*a^2*b*c*d*e+10*a*b^2*c*d*e+12*b^3*c*d*e+39*a^2*c^2*d*e+35*a*b*c^2*d*e-17*b^2*c^2*d*e-30*a*c^3*d*e+32*b*c^3*d*e+41*c^4*d*e+49*a^3*d^2*e-42*a^2*b*d^2*e-22*a*b^2*d^2*e-3*b^3*d^2*e+17*a^2*c*d^2*e+31*a*b*c*d^2*e+23*b^2*c*d^2*e+4*a*c^2*d^2*e+50*b*c^2*d^2*e+43*c^3*d^2*e+17*a^2*d^3*e-30*a*b*d^3*e+43*b^2*d^3*e+7*a*c*d^3*e+30*b*c*d^3*e+37*c^2*d^3*e-a*d^4*e+6*b*d^4*e+22*c*d^4*e-34*d^5*e-48*a^4*e^2+14*a^3*b*e^2+17*a^2*b^2*e^2-39*a*b^3*e^2+37*b^4*e^2-27*a^3*c*e^2+14*a^2*b*c*e^2-43*a*b^2*c*e^2+42*b^3*c*e^2-31*a^2*c^2*e^2+43*a*b*c^2*e^2-34*b^2*c^2*e^2-40*a*c^3*e^2-14*b*c^3*e^2+19*c^4*e^2+11*a^3*d*e^2+23*a^2*b*d*e^2+11*a*b^2*d*e^2+22*b^3*d*e^2+41*a^2*c*d*e^2-20*a*b*c*d*e^2+b^2*c*d*e^2-34*a*c^2*d*e^2-39*b*c^2*d*e^2-20*c^3*d*e^2+25*a^2*d^2*e^2+33*a*b*d^2*e^2-38*b^2*d^2*e^2-34*a*c*d^2*e^2-37*b*c*d^2*e^2-15*c^2*d^2*e^2-13*a*d^3*e^2-42*b*d^3*e^2+49*c*d^3*e^2+29*d^4*e^2-48*a^3*e^3+49*a^2*b*e^3-50*a*b^2*e^3-44*b^3*e^3-42*a^2*c*e^3+14*a*b*c*e^3-34*b^2*c*e^3+3*a*c^2*e^3-b*c^2*e^3+28*c^3*e^3+24*a^2*d*e^3+37*a*b*d*e^3+29*b^2*d*e^3-a*c*d*e^3+31*b*c*d*e^3-14*c^2*d*e^3-36*a*d^2*e^3-4*b*d^2*e^3+29*c*d^2*e^3-47*d^3*e^3-36*a^2*e^4-13*a*b*e^4-45*b^2*e^4-23*a*c*e^4-32*b*c*e^4+2*c^2*e^4+11*a*d*e^4-24*b*d*e^4-46*c*d*e^4-40*d^2*e^4-4*a*e^5-29*b*e^5+14*c*e^5-44*d*e^5+32*e^6,
    1809 b^3*c^2*d+13*a^4*d^2+14*a^3*b*d^2-11*a^2*b^2*d^2-12*a*b^3*d^2-8*b^4*d^2-46*a^3*c*d^2-26*a^2*b*c*d^2+28*a*b^2*c*d^2+13*b^3*c*d^2-36*a^2*c^2*d^2+35*a*b*c^2*d^2+49*b^2*c^2*d^2+32*a*c^3*d^2+17*b*c^3*d^2+34*c^4*d^2-8*a^3*d^3-10*a^2*b*d^3+31*a*b^2*d^3-22*b^3*d^3+a^2*c*d^3+32*a*b*c*d^3+33*b^2*c*d^3+34*a*c^2*d^3-36*b*c^2*d^3-11*c^3*d^3-42*a^2*d^4-15*a*b*d^4-3*b^2*d^4-48*a*c*d^4+12*b*c*d^4+35*c^2*d^4-43*a*d^5+9*b*d^5+47*c*d^5+19*d^6-18*a^5*e+9*a^4*b*e+34*a^3*b^2*e+5*a^2*b^3*e+46*a*b^4*e-34*b^5*e-42*a^4*c*e-36*a^3*b*c*e+5*a^2*b^2*c*e+43*a*b^3*c*e-18*b^4*c*e+21*a^3*c^2*e-45*a^2*b*c^2*e-31*a*b^2*c^2*e+2*b^3*c^2*e+a*b*c^3*e-45*b^2*c^3*e+41*a*c^4*e+37*b*c^4*e-32*c^5*e+19*a^4*d*e-30*a^3*b*d*e+5*a^2*b^2*d*e+17*a*b^3*d*e+47*b^4*d*e-23*a^3*c*d*e+4*a^2*b*c*d*e+14*a*b^2*c*d*e-31*b^3*c*d*e+50*a^2*c^2*d*e-18*a*b*c^2*d*e-37*b^2*c^2*d*e-35*a*c^3*d*e+29*b*c^3*d*e-28*c^4*d*e+3*a^3*d^2*e+13*a^2*b*d^2*e-30*a*b^2*d^2*e-9*b^3*d^2*e+20*a^2*c*d^2*e+17*a*b*c*d^2*e-21*b^2*c*d^2*e-41*a*c^2*d^2*e-32*b*c^2*d^2*e+33*c^3*d^2*e-3*a^2*d^3*e-23*a*b*d^3*e-47*b^2*d^3*e-19*c^2*d^3*e+12*a*d^4*e-32*b*d^4*e-37*c*d^4*e+20*d^5*e+21*a^4*e^2+18*a^3*b*e^2-4*a^2*b^2*e^2+25*a*b^3*e^2-13*b^4*e^2+28*a^3*c*e^2-28*a^2*b*c*e^2-37*a*b^2*c*e^2-32*b^3*c*e^2+8*a^2*c^2*e^2+34*a*b*c^2*e^2-21*b^2*c^2*e^2+15*a*c^3*e^2-39*b*c^3*e^2-45*c^4*e^2-26*a^3*d*e^2+34*a^2*b*d*e^2-25*a*b^2*d*e^2+24*b^3*d*e^2+5*a^2*c*d*e^2+36*a*b*c*d*e^2-27*b^2*c*d*e^2+31*a*c^2*d*e^2+31*b*c^2*d*e^2+13*c^3*d*e^2-3*a^2*d^2*e^2-18*a*b*d^2*e^2+47*b^2*d^2*e^2+20*a*c*d^2*e^2+8*b*c*d^2*e^2-37*c^2*d^2*e^2+21*a*d^3*e^2+3*b*d^3*e^2-34*c*d^3*e^2+28*d^4*e^2-19*a^3*e^3+33*a^2*b*e^3-50*a*b^2*e^3-44*b^3*e^3+17*a^2*c*e^3-48*a*b*c*e^3-3*b^2*c*e^3+33*a*c^2*e^3+13*b*c^2*e^3-29*c^3*e^3+38*a^2*d*e^3-44*a*b*d*e^3-36*b^2*d*e^3-17*a*c*d*e^3+38*b*c*d*e^3+47*c^2*d*e^3+4*a*d^2*e^3-11*b*d^2*e^3-14*c*d^2*e^3-46*d^3*e^3-17*a^2*e^4-23*a*b*e^4+26*b^2*e^4+24*a*c*e^4-37*b*c*e^4+34*c^2*e^4+24*a*d*e^4-32*b*d*e^4-19*c*d*e^4+15*d^2*e^4-33*a*e^5+7*b*e^5-29*c*e^5+37*d*e^5-16*e^6,
    1810 a*b^2*c^2*d-26*a^4*d^2-24*a^3*b*d^2-36*a^2*b^2*d^2+26*a*b^3*d^2+26*b^4*d^2+44*a^3*c*d^2-31*a^2*b*c*d^2-49*a*b^2*c*d^2-30*b^3*c*d^2-13*a^2*c^2*d^2+49*a*b*c^2*d^2-50*b^2*c^2*d^2+27*a*c^3*d^2+24*c^4*d^2-47*a^3*d^3+29*a^2*b*d^3+31*a*b^2*d^3-30*b^3*d^3+39*a^2*c*d^3+23*a*b*c*d^3+5*b^2*c*d^3-30*a*c^2*d^3-20*b*c^2*d^3-27*c^3*d^3-40*a^2*d^4+36*a*b*d^4+28*b^2*d^4+29*a*c*d^4+2*b*c*d^4+14*c^2*d^4-41*a*d^5+22*b*d^5+22*c*d^5+9*d^6-22*a^5*e-33*a^4*b*e-19*a^3*b^2*e+30*a^2*b^3*e+4*a*b^4*e+42*b^5*e-13*a^4*c*e+27*a^3*b*c*e-10*a^2*b^2*c*e+21*a*b^3*c*e-46*b^4*c*e-22*a^3*c^2*e-9*a^2*b*c^2*e+11*a*b^2*c^2*e+33*b^3*c^2*e-4*a^2*c^3*e-26*a*b*c^3*e+47*b^2*c^3*e+41*a*c^4*e-23*b*c^4*e-35*c^5*e-28*a^4*d*e+6*a^3*b*d*e+39*a^2*b^2*d*e+12*a*b^3*d*e-46*b^4*d*e+5*a^3*c*d*e-4*a^2*b*c*d*e+45*a*b^2*c*d*e-8*b^3*c*d*e-46*a^2*c^2*d*e-34*a*b*c^2*d*e-47*b^2*c^2*d*e+20*a*c^3*d*e+10*b*c^3*d*e+2*c^4*d*e+22*a^3*d^2*e-5*a^2*b*d^2*e+24*a*b^2*d^2*e+27*b^3*d^2*e+10*a^2*c*d^2*e-27*a*b*c*d^2*e+13*b^2*c*d^2*e+38*a*c^2*d^2*e+20*b*c^2*d^2*e-46*c^3*d^2*e-47*a^2*d^3*e+42*a*b*d^3*e-34*b^2*d^3*e-3*a*c*d^3*e+4*b*c*d^3*e+4*c^2*d^3*e+47*a*d^4*e+46*b*d^4*e+29*c*d^4*e+28*d^5*e+18*a^4*e^2+19*a^3*b*e^2+6*a^2*b^2*e^2-38*a*b^3*e^2-22*b^4*e^2-21*a^3*c*e^2+44*a^2*b*c*e^2-23*a*b^2*c*e^2-20*b^3*c*e^2-35*a^2*c^2*e^2-33*a*b*c^2*e^2+b^2*c^2*e^2+2*a*c^3*e^2+36*b*c^3*e^2+29*c^4*e^2-14*a^2*b*d*e^2-44*a*b^2*d*e^2+7*b^3*d*e^2+17*a^2*c*d*e^2-2*a*b*c*d*e^2+18*b^2*c*d*e^2-41*a*c^2*d*e^2+41*b*c^2*d*e^2+40*c^3*d*e^2+6*a^2*d^2*e^2-15*a*b*d^2*e^2-39*b^2*d^2*e^2-50*a*c*d^2*e^2-43*b*c*d^2*e^2-3*c^2*d^2*e^2+29*a*d^3*e^2-3*b*d^3*e^2+48*c*d^3*e^2+22*d^4*e^2+24*a^3*e^3+5*a^2*b*e^3-3*a*b^2*e^3-36*b^3*e^3-50*a^2*c*e^3+23*a*b*c*e^3+9*b^2*c*e^3+3*a*c^2*e^3+45*b*c^2*e^3-24*c^3*e^3-30*a^2*d*e^3+31*a*b*d*e^3+26*b^2*d*e^3-37*a*c*d*e^3-38*b*c*d*e^3-36*c^2*d*e^3-8*a*d^2*e^3-41*b*d^2*e^3-40*c*d^2*e^3+25*d^3*e^3-25*a^2*e^4+12*a*b*e^4-25*b^2*e^4-39*a*c*e^4-19*b*c*e^4-21*c^2*e^4+34*a*d*e^4-35*b*d*e^4+9*c*d*e^4-32*d^2*e^4+29*a*e^5+32*b*e^5-25*c*e^5-31*d*e^5-34*e^6,
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    1849 a^4*b^2-31*a^4*d^2+30*a^3*b*d^2-42*a^2*b^2*d^2-32*a*b^3*d^2-38*b^4*d^2-49*a^3*c*d^2-4*a^2*b*c*d^2-45*a*b^2*c*d^2+8*b^3*c*d^2+44*a^2*c^2*d^2+21*a*b*c^2*d^2-13*b^2*c^2*d^2-16*a*c^3*d^2+31*b*c^3*d^2-42*c^4*d^2+49*a^3*d^3+44*a^2*b*d^3+a*b^2*d^3+47*b^3*d^3-31*a^2*c*d^3+42*a*b*c*d^3-34*b^2*c*d^3-44*a*c^2*d^3-3*b*c^2*d^3-14*c^3*d^3+24*a^2*d^4+12*a*b*d^4+14*b^2*d^4-32*a*c*d^4+16*b*c*d^4+40*c^2*d^4+8*a*d^5+5*b*d^5+35*c*d^5+2*d^6+7*a^5*e+a^4*b*e-24*a^3*b^2*e-25*a^2*b^3*e-8*a*b^4*e-46*b^5*e+12*a^4*c*e-49*a^3*b*c*e+47*a^2*b^2*c*e-22*a*b^3*c*e-22*b^4*c*e+31*a^3*c^2*e-48*a^2*b*c^2*e-46*a*b^2*c^2*e+28*b^3*c^2*e-5*a^2*c^3*e+42*a*b*c^3*e-9*b^2*c^3*e+13*a*c^4*e+23*b*c^4*e-29*c^5*e+9*a^4*d*e+9*a^3*b*d*e+3*a^2*b^2*d*e+47*a*b^3*d*e+31*b^4*d*e-25*a^3*c*d*e-37*a*b^2*c*d*e-23*b^3*c*d*e+18*a^2*c^2*d*e+8*a*b*c^2*d*e-15*b^2*c^2*d*e-40*a*c^3*d*e+26*b*c^3*d*e-29*c^4*d*e+20*a^3*d^2*e-25*a^2*b*d^2*e+41*a*b^2*d^2*e+10*b^3*d^2*e-12*a^2*c*d^2*e+38*a*b*c*d^2*e-30*b^2*c*d^2*e-49*b*c^2*d^2*e-34*c^3*d^2*e+14*a^2*d^3*e+45*a*b*d^3*e-29*b^2*d^3*e-23*a*c*d^3*e+33*b*c*d^3*e-23*c^2*d^3*e-36*a*d^4*e+29*b*d^4*e+22*c*d^4*e+45*d^5*e-46*a^4*e^2-37*a^3*b*e^2-36*a^2*b^2*e^2-23*a*b^3*e^2-4*b^4*e^2+31*a^3*c*e^2+45*a^2*b*c*e^2-34*a*b^2*c*e^2+6*b^3*c*e^2-38*a^2*c^2*e^2-26*a*b*c^2*e^2-5*b^2*c^2*e^2-24*a*c^3*e^2-28*b*c^3*e^2+20*c^4*e^2+25*a^3*d*e^2+14*a^2*b*d*e^2+a*b^2*d*e^2+18*b^3*d*e^2+12*a^2*c*d*e^2+32*a*b*c*d*e^2+17*b^2*c*d*e^2+50*a*c^2*d*e^2-12*b*c^2*d*e^2-46*c^3*d*e^2+4*a^2*d^2*e^2-29*a*b*d^2*e^2-16*b^2*d^2*e^2+38*a*c*d^2*e^2+3*b*c*d^2*e^2-19*c^2*d^2*e^2+50*a*d^3*e^2+23*b*d^3*e^2+5*c*d^3*e^2+47*d^4*e^2-38*a^3*e^3-31*a^2*b*e^3+14*a*b^2*e^3-43*b^3*e^3+22*a^2*c*e^3+26*a*b*c*e^3-28*b^2*c*e^3-49*a*c^2*e^3+15*c^3*e^3-40*a^2*d*e^3+5*a*b*d*e^3-20*b^2*d*e^3-40*a*c*d*e^3+35*b*c*d*e^3+17*c^2*d*e^3-8*a*d^2*e^3-6*b*d^2*e^3+3*c*d^2*e^3-7*d^3*e^3+45*a^2*e^4-49*a*b*e^4+45*b^2*e^4-25*a*c*e^4+b*c*e^4-33*c^2*e^4-44*a*d*e^4+30*b*d*e^4-26*c*d*e^4+42*d^2*e^4+14*b*e^5-3*c*e^5-47*d*e^5+22*e^6,
    1850 a^5*b-48*a^4*d^2-33*a^3*b*d^2-34*a^2*b^2*d^2-14*a*b^3*d^2-29*b^4*d^2-7*a^3*c*d^2-13*a^2*b*c*d^2+15*a*b^2*c*d^2+27*b^3*c*d^2+49*a^2*c^2*d^2-a*b*c^2*d^2+46*b^2*c^2*d^2+37*a*c^3*d^2+20*b*c^3*d^2-27*c^4*d^2+33*a^3*d^3+30*a^2*b*d^3+32*a*b^2*d^3+b^3*d^3-47*a^2*c*d^3-2*a*b*c*d^3-36*b^2*c*d^3-7*a*c^2*d^3-23*b*c^2*d^3-41*c^3*d^3-43*a^2*d^4-4*a*b*d^4+14*b^2*d^4+38*a*c*d^4+41*b*c*d^4+27*c^2*d^4-33*a*d^5-50*b*d^5+8*c*d^5+42*d^6-21*a^5*e+46*a^4*b*e+6*a^3*b^2*e+22*a^2*b^3*e+2*a*b^4*e-15*b^5*e+50*a^4*c*e-40*a^2*b^2*c*e+49*a*b^3*c*e+5*b^4*c*e+a^3*c^2*e+47*a^2*b*c^2*e-36*a*b^2*c^2*e+25*b^3*c^2*e-36*a^2*c^3*e+46*a*b*c^3*e+24*b^2*c^3*e-9*a*c^4*e+39*b*c^4*e-40*c^5*e+29*a^4*d*e-49*a^3*b*d*e+16*a^2*b^2*d*e+7*a*b^3*d*e-30*b^4*d*e+42*a^3*c*d*e+22*a^2*b*c*d*e-49*a*b^2*c*d*e+19*b^3*c*d*e-23*a^2*c^2*d*e+7*a*b*c^2*d*e+2*b^2*c^2*d*e-2*a*c^3*d*e-2*b*c^3*d*e+5*c^4*d*e+35*a^3*d^2*e-47*a^2*b*d^2*e-28*a*b^2*d^2*e+5*b^3*d^2*e+45*a^2*c*d^2*e+7*a*b*c*d^2*e+3*b^2*c*d^2*e+33*a*c^2*d^2*e-37*b*c^2*d^2*e+26*c^3*d^2*e-18*a*b*d^3*e-42*b^2*d^3*e-22*a*c*d^3*e-46*b*c*d^3*e-25*c^2*d^3*e+6*a*d^4*e-50*b*d^4*e+22*c*d^4*e-4*d^5*e-42*a^4*e^2+43*a^3*b*e^2+39*a^2*b^2*e^2+12*a*b^3*e^2-20*b^4*e^2+2*a^3*c*e^2+27*a^2*b*c*e^2-21*a*b^2*c*e^2+36*b^3*c*e^2+47*a^2*c^2*e^2-41*a*b*c^2*e^2-23*b^2*c^2*e^2+34*a*c^3*e^2-29*b*c^3*e^2-46*c^4*e^2+15*a^3*d*e^2+4*a^2*b*d*e^2-13*a*b^2*d*e^2+43*b^3*d*e^2-7*a^2*c*d*e^2+4*a*b*c*d*e^2-37*a*c^2*d*e^2-34*b*c^2*d*e^2+20*c^3*d*e^2-5*a^2*d^2*e^2-42*a*b*d^2*e^2+14*b^2*d^2*e^2+9*a*c*d^2*e^2-19*b*c*d^2*e^2+15*c^2*d^2*e^2-35*a*d^3*e^2+24*b*d^3*e^2-35*c*d^3*e^2-14*d^4*e^2-27*a^3*e^3-39*a^2*b*e^3-44*a*b^2*e^3-6*b^3*e^3-30*a^2*c*e^3+47*a*b*c*e^3-26*b^2*c*e^3+9*a*c^2*e^3+16*b*c^2*e^3+37*c^3*e^3-49*a^2*d*e^3+19*a*b*d*e^3+44*b^2*d*e^3-9*a*c*d*e^3-41*b*c*d*e^3+29*c^2*d*e^3-43*a*d^2*e^3+33*b*d^2*e^3-2*c*d^2*e^3-15*d^3*e^3-4*a^2*e^4-46*a*b*e^4+15*b^2*e^4+21*a*c*e^4+13*b*c*e^4+38*c^2*e^4-20*a*d*e^4+16*b*d*e^4-9*c*d*e^4-19*d^2*e^4+14*a*e^5-33*b*e^5+34*c*e^5+16*d*e^5-24*e^6,
    1851 a^6-2*a^4*d^2+3*a^3*b*d^2+18*a^2*b^2*d^2-46*a*b^3*d^2-31*b^4*d^2+48*a^3*c*d^2+7*a^2*b*c*d^2+26*a*b^2*c*d^2+17*b^3*c*d^2-30*a^2*c^2*d^2-2*a*b*c^2*d^2+5*b^2*c^2*d^2-43*a*c^3*d^2-33*b*c^3*d^2-28*c^4*d^2-26*a^3*d^3-5*a^2*b*d^3+48*a*b^2*d^3+2*b^3*d^3-15*a^2*c*d^3-18*a*b*c*d^3-16*b^2*c*d^3-12*a*c^2*d^3+21*b*c^2*d^3-31*c^3*d^3+34*a^2*d^4-40*a*b*d^4+41*b^2*d^4+21*a*c*d^4+26*b*c*d^4+50*c^2*d^4-20*a*d^5+8*b*d^5+30*c*d^5+48*d^6-37*a^5*e+28*a^4*b*e+8*a^3*b^2*e+30*a^2*b^3*e-a*b^4*e-49*b^5*e-8*a^4*c*e+26*a^3*b*c*e+20*a^2*b^2*c*e+19*a*b^3*c*e-23*b^4*c*e+11*a^3*c^2*e+37*a^2*b*c^2*e+40*a*b^2*c^2*e-33*b^3*c^2*e-26*a^2*c^3*e+12*a*b*c^3*e+29*b^2*c^3*e-a*c^4*e-15*b*c^4*e-24*c^5*e-41*a^4*d*e-4*a^3*b*d*e+42*a^2*b^2*d*e+9*a*b^3*d*e-49*b^4*d*e-11*a^3*c*d*e+21*a^2*b*c*d*e+22*a*b^2*c*d*e+22*b^3*c*d*e-9*a^2*c^2*d*e+27*a*b*c^2*d*e-36*b^2*c^2*d*e-10*a*c^3*d*e-39*b*c^3*d*e-3*c^4*d*e+16*a^3*d^2*e+9*a^2*b*d^2*e+7*a*b^2*d^2*e+33*b^3*d^2*e+42*a^2*c*d^2*e-38*a*b*c*d^2*e+33*b^2*c*d^2*e+41*a*c^2*d^2*e-36*b*c^2*d^2*e-21*c^3*d^2*e+34*a^2*d^3*e-43*a*b*d^3*e+32*b^2*d^3*e-9*a*c*d^3*e-34*b*c*d^3*e-4*c^2*d^3*e-10*a*d^4*e-29*b*d^4*e+4*c*d^4*e+36*d^5*e+40*a^4*e^2-32*a^3*b*e^2+13*a^2*b^2*e^2+22*a*b^3*e^2-15*b^4*e^2+31*a^3*c*e^2+7*a^2*b*c*e^2-15*a*b^2*c*e^2+43*b^3*c*e^2-45*a^2*c^2*e^2-42*a*b*c^2*e^2+41*b^2*c^2*e^2-46*a*c^3*e^2-6*b*c^3*e^2+26*c^4*e^2+45*a^3*d*e^2+11*a^2*b*d*e^2+10*a*b^2*d*e^2+5*b^3*d*e^2+3*a^2*c*d*e^2-49*a*b*c*d*e^2-10*b^2*c*d*e^2-50*a*c^2*d*e^2+38*b*c^2*d*e^2+21*c^3*d*e^2+37*a^2*d^2*e^2+a*b*d^2*e^2+38*b^2*d^2*e^2+25*a*c*d^2*e^2-7*b*c*d^2*e^2-13*c^2*d^2*e^2+32*a*d^3*e^2+37*b*d^3*e^2-27*c*d^3*e^2-7*d^4*e^2+44*a^3*e^3+48*a^2*b*e^3+21*a*b^2*e^3+11*b^3*e^3+9*a^2*c*e^3+49*a*b*c*e^3-39*b^2*c*e^3+24*a*c^2*e^3+35*b*c^2*e^3-11*c^3*e^3+17*a^2*d*e^3+36*a*b*d*e^3-19*b^2*d*e^3-47*a*c*d*e^3-47*b*c*d*e^3-12*c^2*d*e^3+34*a*d^2*e^3+35*b*d^2*e^3+18*d^3*e^3-31*a^2*e^4+45*a*b*e^4+27*b^2*e^4+43*a*c*e^4-35*b*c*e^4-29*c^2*e^4-21*a*d*e^4+49*b*d*e^4-23*c*d*e^4+34*d^2*e^4-2*a*e^5+47*b*e^5+31*c*e^5-46*d*e^5-13*e^6,
    1852 e^7, d*e^6, c*e^6, b*e^6, a*e^6, d^2*e^5, c*d*e^5, b*d*e^5, a*d*e^5, c^2*e^5,
    1853 b*c*e^5, a*c*e^5, b^2*e^5, a*b*e^5, a^2*e^5, d^3*e^4, c*d^2*e^4, b*d^2*e^4,
    1854 a*d^2*e^4, c^2*d*e^4, b*c*d*e^4, a*c*d*e^4, b^2*d*e^4, a*b*d*e^4, a^2*d*e^4,
    1855 c^3*e^4, b*c^2*e^4, a*c^2*e^4, b^2*c*e^4, a*b*c*e^4, a^2*c*e^4, b^3*e^4,
    1856 a*b^2*e^4, a^2*b*e^4, a^3*e^4, d^4*e^3, c*d^3*e^3, b*d^3*e^3, a*d^3*e^3,
    1857 c^2*d^2*e^3, b*c*d^2*e^3, a*c*d^2*e^3, b^2*d^2*e^3, a*b*d^2*e^3, a^2*d^2*e^3,
    1858 c^3*d*e^3, b*c^2*d*e^3, a*c^2*d*e^3, b^2*c*d*e^3, a*b*c*d*e^3, a^2*c*d*e^3,
    1859 b^3*d*e^3, a*b^2*d*e^3, a^2*b*d*e^3, a^3*d*e^3, c^4*e^3, b*c^3*e^3, a*c^3*e^3,
    1860 b^2*c^2*e^3, a*b*c^2*e^3, a^2*c^2*e^3, b^3*c*e^3, a*b^2*c*e^3, a^2*b*c*e^3,
    1861 a^3*c*e^3, b^4*e^3, a*b^3*e^3, a^2*b^2*e^3, a^3*b*e^3, a^4*e^3, d^5*e^2,
    1862 c*d^4*e^2, b*d^4*e^2, a*d^4*e^2, c^2*d^3*e^2, b*c*d^3*e^2, a*c*d^3*e^2,
    1863 b^2*d^3*e^2, a*b*d^3*e^2, a^2*d^3*e^2, c^3*d^2*e^2, b*c^2*d^2*e^2,
    1864 a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2;
    1865 //  M;
    1866   TestSSresAttribs2tr(M, "AGR101n4d008s020%1_big");
    1867 /*
    1868 options:  1 1 0 :  Time:  29/32/73/92 (316 without LCM)
    1869 options:  1 1 1 :  Time:  32/34/43/202
    1870 lres  Time:  24
    1871 nres  Time:  19
    1872 sres  Time:  71
    1873 */
    1874   kill M;
    1875 
    1876   kill AGR;
    1877 
    1878   ring AGR = (101), (a,b,c,d,e,f), dp; AGR;
    1879 
    1880   // AGR@101n5d005s016%1, new, medium difficulty?
    1881   ideal M =
    1882 b*d-13*c*d+7*a*e-32*b*e+31*c*e+3*d*e+46*a*f-13*b*f+22*c*f-19*d*f-33*e*f, a*d+2*c*d-42*a*e+46*b*e+7*c*e-38*d*e+31*a*f+9*b*f+27*c*f-19*d*f-24*e*f, b*c-35*c*d-34*a*e+4*b*e+33*c*e+23*d*e+4*a*f-43*b*f+43*c*f+17*d*f-13*e*f, a*c+49*c*d-28*a*e+18*b*e-23*c*e+3*d*e-5*a*f-23*b*f+2*c*f+46*d*f-40*e*f, a*b-38*c*d+a*e-49*b*e-20*c*e+32*d*e+13*a*f+25*b*f+37*c*f-27*d*f+25*e*f, f^4, e*f^3, d*f^3, c*f^3, b*f^3, a*f^3, e^2*f^2, d*e*f^2, c*e*f^2, b*e*f^2, a*e*f^2, d^2*f^2, c*d*f^2, c^2*f^2, b^2*f^2, a^2*f^2, e^3*f, d*e^2*f, c*e^2*f, b*e^2*f, a*e^2*f, d^2*e*f, d^3*f, c^3*f, b^3*f, a^3*f, e^4, d^4, c^4, b^4, a^4;
    1883   TestSSresAttribs(M, "AGR@101n5d005s016%1");
    1884   kill M;
    1885 }
    1886 
    1887 static proc testAGRhard(list #)
    1888 {
    1889   def DEBUG = 0;
    1890   if(size(#) > 0) { DEBUG = #[1]; }
    1891 
    1892   system("--min-time", "0.01");
    1893   system("--ticks-per-sec", 100);
    1894 
    1895   attrib(SSinit, "DEBUG", 0);
    1896   attrib(SSinit, "SYZCHECK", (DEBUG > 0));
    1897   attrib(SSinit, "KERCHECK", 0);
    1898   attrib(SSinit, "TREEOUTPUT", 0);
    1899   attrib(SSinit, "PROFILE", 0);
    1900 
    1901   option(prot);
    1902   // AGR@101n5d006s016%1, new, hard
    1903   ring AGR = (101), (a,b,c,d,e,f), dp; AGR;
    1904   ideal M =
    1905 b*d+47*c*d-27*a*e+37*b*e+21*c*e+31*d*e-31*a*f+23*b*f+47*c*f+42*d*f+11*e*f, a*d+7*c*d+19*a*e+28*b*e-33*c*e-28*d*e+15*a*f+28*b*f+47*c*f+3*d*f+14*e*f, b*c+29*c*d-25*a*e+12*b*e+23*c*e-50*d*e-17*a*f+30*b*f-37*c*f+35*d*f-e*f, a*c+46*c*d+12*a*e+27*b*e+39*c*e+23*d*e-45*a*f+39*b*f-35*c*f+4*d*f-10*e*f, a*b+38*c*d-18*a*e-34*b*e-30*c*e+38*d*e+22*a*f+34*b*f+39*c*f+30*d*f-19*e*f, f^5, e*f^4, d*f^4, c*f^4, b*f^4, a*f^4, e^2*f^3, d*e*f^3, c*e*f^3, b*e*f^3, a*e*f^3, d^2*f^3, c*d*f^3, c^2*f^3, b^2*f^3, a^2*f^3, e^3*f^2, d*e^2*f^2, c*e^2*f^2, b*e^2*f^2, a*e^2*f^2, d^2*e*f^2, d^3*f^2, c^3*f^2, b^3*f^2, a^3*f^2, e^4*f, e^5, d^5, c^5, b^5, a^5;
    1906   TestSSresAttribs2tr(M, "AGR@101n5d006s016%1_hard");
    1907  kill M;
    1908 }
     321}

  • Singular/dyn_modules/syzextra/test.sh

    r0277c5 rdcad76  
    44#"$SINGULAR_EXECUTABLE" -teq "$srcdir/ederc.tst" || exit 1
    55#"$SINGULAR_EXECUTABLE" -teq "$srcdir/syzextra.tst" || exit 1
    6 "$SINGULAR_EXECUTABLE" -tec 'LIB "schreyer.lib"; listvar(Top); proc T(){ Schreyer::testSimple(1, 0); /* Schreyer::testAGR(0); Schreyer::testAGRhard(0); */ } T(); $' || exit 1
     6"$SINGULAR_EXECUTABLE" -tec 'LIB "schreyer.lib"; listvar(Top); example Sres; $' || exit 1

  • Singular/iparith.cc

    r0277c5 rdcad76  
    56345634  mp_Monomials((matrix)res->data, rank, pVar((poly)v->Data()),(matrix)w->Data(),currRing);
    56355635  return FALSE;
     5636}
     5637static BOOLEAN jjELIMIN_ALG(leftv res, leftv u, leftv v, leftv w)
     5638{
     5639  ideal I=(ideal)u->Data();
     5640  GbVariant alg=syGetAlgorithm((char*)w->Data(),currRing,I);
     5641  res->data=(char *)idElimination(I,(poly)v->Data(),NULL,alg);
     5642  //setFlag(res,FLAG_STD);
     5643  return v->next!=NULL; //do not allow next like in eliminate(I,a(1..4))
    56365644}
    56375645static BOOLEAN jjELIMIN_HILB(leftv res, leftv u, leftv v, leftv w)

  • Singular/table.h

    r0277c5 rdcad76  
    759759,{D(jjELIMIN_HILB),    ELIMINATION_CMD,IDEAL_CMD, IDEAL_CMD, POLY_CMD, INTVEC_CMD, NO_PLURAL |ALLOW_RING}
    760760,{D(jjELIMIN_HILB),    ELIMINATION_CMD,MODUL_CMD, MODUL_CMD, POLY_CMD, INTVEC_CMD, NO_PLURAL |ALLOW_RING}
     761,{D(jjELIMIN_ALG),     ELIMINATION_CMD,IDEAL_CMD, IDEAL_CMD,  POLY_CMD, STRING_CMD, ALLOW_PLURAL |ALLOW_RING}
     762,{D(jjELIMIN_ALG),     ELIMINATION_CMD,MODUL_CMD, MODUL_CMD,  POLY_CMD, STRING_CMD, ALLOW_PLURAL |ALLOW_RING}
    761763,{D(jjFIND3),          FIND_CMD,   INT_CMD,    STRING_CMD, STRING_CMD, INT_CMD, ALLOW_PLURAL |ALLOW_RING}
    762764,{D(jjFRES3),          FRES_CMD,   RESOLUTION_CMD, IDEAL_CMD, INT_CMD, STRING_CMD, NO_PLURAL |NO_RING}

  • doc/NEWS.texi

    r0277c5 rdcad76  
    2121
    2222@heading News for version @value{VERSION}
     23Changed libraries:
     24@itemize
     25@item schreyer.lib: deprecated
     26@item grobcov.lib: small bug fix (@nref{grobcov_lib})
     27@end itemize
     28
     29@heading News for version 4-1-1
    2330
    2431New syntax:

  • kernel/ideals.cc

    r1cc42d rdcad76  
    540540  {
    541541    tempstd=idInit(1,1);
    542     Werror("wrong algorith %d for SB",(int)alg);
     542    Werror("wrong algorithm %d for SB",(int)alg);
    543543  }
    544544
    … …  
    715715  {
    716716    h3=idInit(1,1);
    717     Werror("wrong algorith %d for SB",(int)alg);
     717    Werror("wrong algorithm %d for SB",(int)alg);
    718718  }
    719719

  • kernel/ideals.h

    r0277c5 rdcad76  
    154154
    155155//ideal   idElimination (ideal h1,poly delVar);
    156 ideal   idElimination (ideal h1,poly delVar, intvec *hilb=NULL);
     156ideal   idElimination (ideal h1,poly delVar, intvec *hilb=NULL, GbVariant a=GbDefault);
    157157
    158158#ifdef WITH_OLD_MINOR
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