Changeset e98c64 in git


Ignore:
Timestamp:
Aug 9, 2012, 9:27:42 PM (10 years ago)
Author:
Oleksandr Motsak <motsak@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '96ce329119711a2b80858c8365abd29f8460bbfa')
Children:
c814238a3c69aaf59662652396c4843d8c8c52fa
Parents:
5cecde90d96d1acc0cbd216cf0037bd2db293c31
git-author:
Oleksandr Motsak <motsak@mathematik.uni-kl.de>2012-08-09 21:27:42+02:00
git-committer:
Oleksandr Motsak <motsak@mathematik.uni-kl.de>2014-05-07 04:41:46+02:00
Message:
adding IGNORETAILS option for computing pure Schreyer Frames (test with 'testAGRFrame')
Files:
3 edited

Legend:

Unmodified
Added
Removed
  • Singular/LIB/schreyer.lib

    r5cecde re98c64  
    585585  }
    586586
     587  int @IGNORETAILS = 0;
     588
     589  if( typeof( attrib(SSinit, "IGNORETAILS") ) == "int" )
     590  {
     591    @IGNORETAILS = attrib(SSinit, "IGNORETAILS");
     592  }
     593
     594 
    587595  if( @DEBUG )
    588596  {
     
    592600    attrib(M);
    593601  }
    594 
    595   int @RANK = nrows(M); int @SIZE = ncols(M);
    596602
    597603  int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?!
     
    606612  } else
    607613  {
    608     M = simplify(M, 2 + 4 + 32);
    609   }
     614    M = simplify(M, 2 + 4 + 32); // interreduce?
     615  }
     616
     617  if( @IGNORETAILS )
     618  {
     619    M = lead(M);
     620   
     621    if( @DEBUG )
     622    {
     623      "SSinit::Ignorring tails: M: ";
     624      type(M);
     625    }
     626  }
     627
     628 
    610629
    611630  def @N = MySort(M); // TODO: replace with inplace sorting!!!
     
    651670 
    652671  def TAIL = Tail(M);
     672
     673  int @RANK = nrows(M); int @SIZE = ncols(M);
    653674 
    654675  intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements
     
    760781  attrib(S, "SYZCHECK", @SYZCHECK);
    761782  attrib(S, "KERCHECK", @KERCHECK);
     783  attrib(S, "IGNORETAILS", @IGNORETAILS);
    762784 
    763785  if( @DEBUG )
     
    15651587    int @KERCHECK = @DEBUG;
    15661588  }
    1567  
     1589
    15681590  if( @DEBUG )
    15691591  {
     
    16101632    }
    16111633
     1634    if( typeof( attrib(basering, "IGNORETAILS") ) == "int" )
     1635    {
     1636      int @IGNORETAILS = attrib(basering, "IGNORETAILS");
     1637    } else
     1638    {
     1639      int @IGNORETAILS = 0;
     1640    }
     1641   
    16121642    module LL;
    16131643
     
    16351665      }
    16361666
    1637       vector @tail;
     1667      vector @tail = 0;
    16381668
    16391669      for(int k = ncols(LL); k > 0; k-- )
    16401670      {
    16411671        // leading syz. term:
    1642         a = LL[k]; c = leadcomp(a); r = int(c); aa = leadmonomial(a);
    1643 
    1644         // NF reduction:
    1645         if( !@HYBRIDNF ) // Traverse approach:
    1646         {       
    1647           @tail = SSTraverseTail(aa, T[r], L, T, LS);
    1648 
    1649           // get the 2nd syzygy term...
    1650           if( @LEAD2SYZ ) // with the 2nd syz. term:
    1651           {     
    1652             a2 = LL2[k]; c = leadcomp(a2); r = int(c); aa = leadmonomial(a2);
    1653 
    1654             @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS);
    1655           } else
     1672        a = LL[k];
     1673
     1674        if( !@IGNORETAILS )
     1675        {
     1676          c = leadcomp(a); r = int(c); aa = leadmonomial(a);
     1677         
     1678          // NF reduction:
     1679          if( !@HYBRIDNF ) // Traverse approach:
     1680          {       
     1681            @tail = SSTraverseTail(aa, T[r], L, T, LS);
     1682
     1683            // get the 2nd syzygy term...
     1684            if( @LEAD2SYZ ) // with the 2nd syz. term:
     1685            {     
     1686              a2 = LL2[k]; c = leadcomp(a2); r = int(c); aa = leadmonomial(a2);
     1687
     1688              @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS);
     1689            } else
     1690            {
     1691              @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS);
     1692            }
     1693
     1694          } else // Hybrid approach:
    16561695          {
    1657             @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS);
     1696
     1697            // get the 2nd syzygy term...
     1698            if( @LEAD2SYZ )
     1699            {
     1700              a2 = LL2[k];
     1701            } else
     1702            {
     1703              a2 = SSFindReducer( aa * L[r], a, L, LS);
     1704            }
     1705
     1706            if ( (@SYZCHECK || @DEBUG) )
     1707            {
     1708              if( size(a2) == 0 ) // if syzterm == 0!!!!
     1709              {
     1710                "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!";
     1711                $
     1712              }
     1713            }
     1714
     1715            @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS);
    16581716          }
    1659 
    1660         } else // Hybrid approach:
    1661         {
    1662 
    1663           // get the 2nd syzygy term...
    1664           if( @LEAD2SYZ )
    1665           {
    1666             a2 = LL2[k];
    1667           } else
    1668           {
    1669             a2 = SSFindReducer( aa * L[r], a, L, LS);
    1670           }
    1671 
    1672           if ( (@SYZCHECK || @DEBUG) )
    1673           {
    1674             if( size(a2) == 0 ) // if syzterm == 0!!!!
    1675             {
    1676               "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!";
    1677               $
    1678             }
    1679           }
    1680 
    1681           @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS);
    1682         }
     1717        } // else @tail remains zero!
    16831718
    16841719        TT[k] = @tail;
     
    25662601}
    25672602
     2603
     2604
     2605
     2606
     2607proc testAGRFrame()
     2608{
     2609  system("--min-time", "1.0");
     2610  system("--ticks-per-sec", 1);
     2611
     2612  attrib(SSinit, "DEBUG", 0);
     2613  attrib(SSinit, "SYZCHECK", 0); // no such tests anymore with IGNORETAILS == 1!
     2614  attrib(SSinit, "KERCHECK", 1);
     2615  attrib(SSinit, "IGNORETAILS", 1);
     2616
     2617  ring AGR = (101), (a, b, c, d), dp; AGR;
     2618  // lengthy: AGR@101n3d008s058%3, kernel only!
     2619  ideal M = 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     2620  M;
     2621  TestSSresAttribs(M); 
     2622
     2623  // AGR@101n3d010s010%3, a bit slower...
     2624  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;
     2625  M;
     2626  TestSSresAttribs(M); 
     2627  kill AGR;
     2628
     2629  ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR;
     2630  // AGR@101n7d005s010%2) medium: <= 2
     2631  ideal M =
     2632f*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,
     2633b^5+17*h^5,a^5+17*h^5,h^6;
     2634  M;
     2635  TestSSresAttribs(M); 
     2636/*
     2637with tails:
     2638options:  1 1 0 :  Time:  3/10
     2639options:  1 1 1 :  Time:  2/6
     2640*/
     2641  kill AGR;
     2642
     2643// from Andreas...tooo long!?
     2644
     2645  ring AGR = (101), (a,b,c,d,e), dp; AGR;
     2646
     2647  // AGR101n4d007s021%4
     2648  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,
     2649a*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,
     2650a^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,
     2651a^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,
     2652b^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,
     2653a*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,
     2654a^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,
     2655a^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,
     2656a^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,
     2657c^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,
     2658b*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,
     2659a*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,
     2660b^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,
     2661a*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,
     2662a^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,
     2663b^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,
     2664a*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,
     2665a^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,
     2666a^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,
     2667b^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,
     2668a*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,
     2669a^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,
     2670a^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,
     2671a^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,
     2672b^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,
     2673a*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,
     2674a^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,
     2675a^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,
     2676a^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,
     2677a^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,
     2678e^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,
     2679b*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,
     2680a*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,
     2681c^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,
     2682a*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,
     2683c^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,
     2684c^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,
     2685b^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,
     2686b^2*c^2*e^2, a*b*c^2*e^2;
     2687  M;
     2688  TestSSresAttribs(M); 
     2689/*
     2690with tails:
     2691options:  1 1 0 :  Time:  5/9/10 (35 without LCM)
     2692options:  1 1 1 :  Time:  6/8/25
     2693*/
     2694
     2695  kill M;
     2696
     2697
     2698
     2699  // too big?
     2700  // AGR101n4d008s020%1
     2701  ideal M =
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     2748a^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,
     2749a^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,
     2750a^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,
     2751e^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,
     2752b*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,
     2753a*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,
     2754c^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,
     2755a*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,
     2756c^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,
     2757c^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,
     2758b^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,
     2759b^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,
     2760a^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,
     2761c*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,
     2762b^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,
     2763a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2;
     2764  M;
     2765  TestSSresAttribs(M); 
     2766/*
     2767with tails
     2768options:  1 1 0 :  Time:  34/73/92 (316 without LCM)
     2769options:  1 1 1 :  Time:  35/43/202
     2770*/
     2771  kill M;
     2772
     2773}
     2774
    25682775// TODO: betti!!!
  • dyn_modules/syzextra/syzextra.cc

    r5cecde re98c64  
    516516  assume( m_syzLeads != NULL );
    517517
    518   if( __TAILREDSYZ__ )
    519     assume( m_checker.IsNonempty() );
    520 
    521518  ideal& LL = m_syzLeads;
    522519
     
    534531    const poly a = LL->m[k]; assume( a != NULL );
    535532
    536     const int r = p_GetComp(a, R) - 1;
    537 
    538     assume( r >= 0 && r < IDELEMS(T) );
    539     assume( r >= 0 && r < IDELEMS(L) );
    540 
    541     poly aa = leadmonom(a, R); assume( aa != NULL); // :(   
    542 
    543533    poly a2 = pNext(a);   
    544534
    545535    // Splitting 2-terms Leading syzygy module
    546536    if( a2 != NULL )
     537      pNext(a) = NULL;
     538
     539    if( __IGNORETAILS__ )
    547540    {
    548       TT->m[k] = a2; pNext(a) = NULL;
     541      TT->m[k] = NULL;
     542
     543      if( a2 != NULL )
     544        p_Delete(&a2, R);
     545
     546      continue;
    549547    }
     548   
     549    TT->m[k] = a2;
     550
     551    const int r = p_GetComp(a, R) - 1;
     552
     553    assume( r >= 0 && r < IDELEMS(T) );
     554    assume( r >= 0 && r < IDELEMS(L) );         
     555
     556    poly aa = leadmonom(a, R); assume( aa != NULL); // :(
    550557
    551558    if( ! __HYBRIDNF__ )
     
    579586      p_Delete(&a2, R);
    580587    }
     588
    581589    p_Delete(&aa, R);   
    582590  }
     
    591599//  const BOOLEAN __LEAD2SYZ__   = attributes.__LEAD2SYZ__;
    592600//  const BOOLEAN __TAILREDSYZ__ = attributes.__TAILREDSYZ__;
     601
     602  assume( m_syzLeads == NULL );
    593603
    594604  if( bComputeSecondTerms )
     
    609619  assume( m_syzLeads!= NULL );
    610620
    611   if (__TAILREDSYZ__ && (IDELEMS(m_syzLeads) > 0))
     621  if (__TAILREDSYZ__ && (IDELEMS(m_syzLeads) > 0) && !__IGNORETAILS__)
    612622  {
    613623    m_LS = m_syzLeads;
    614624    m_checker.Initialize(m_syzLeads);
    615   }
    616 
    617   (void)( __LEAD2SYZ__ );
     625    assume( m_checker.IsNonempty() ); // TODO: this always fails... BUG????
     626  }
    618627}
    619628
     
    627636// {
    628637
     638  assume( !__IGNORETAILS__ );
     639
    629640  const ideal& L = m_idLeads;
    630641  const ideal& T = m_idTails;
     
    691702poly SchreyerSyzygyComputation::TraverseTail(poly multiplier, poly tail) const
    692703{
     704  assume( !__IGNORETAILS__ );
     705
    693706  const ideal& L = m_idLeads;
    694707  const ideal& T = m_idTails;
     
    730743poly SchreyerSyzygyComputation::ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck) const
    731744{
     745  assume( !__IGNORETAILS__ );
     746
    732747  const ideal& L = m_idLeads;
    733748  const ideal& T = m_idTails;
     
    809824    __TAILREDSYZ__( (BOOLEAN)atGetInt(rootRingHdl, "TAILREDSYZ", 1) ),
    810825    __HYBRIDNF__( (BOOLEAN)atGetInt(rootRingHdl, "HYBRIDNF", 0) ),
     826    __IGNORETAILS__( (BOOLEAN)atGetInt(rootRingHdl, "IGNORETAILS", 0) ),
    811827    m_rBaseRing( rootRingHdl->data.uring )
    812828{   
     
    814830  {
    815831    PrintS("SchreyerSyzygyComputationFlags: \n");
    816     Print("   DEBUG     : \t%d\n", __DEBUG__);
     832    Print("        DEBUG: \t%d\n", __DEBUG__);
    817833//    Print("   SYZCHECK  : \t%d\n", __SYZCHECK__);
    818     Print("   LEAD2SYZ  : \t%d\n", __LEAD2SYZ__);
     834    Print("     LEAD2SYZ: \t%d\n", __LEAD2SYZ__);
    819835    Print("   TAILREDSYZ: \t%d\n", __TAILREDSYZ__);
     836    Print("  IGNORETAILS: \t%d\n", __IGNORETAILS__);
     837   
    820838  }
    821839
     
    9821000  const TReducers& reducers = it->second;
    9831001
    984   const BOOLEAN to_check = __TAILREDSYZ__ && (syz_checker.IsNonempty());
     1002  const BOOLEAN to_check = (syz_checker.IsNonempty()); // __TAILREDSYZ__ &&
    9851003
    9861004  const poly q = p_New(r); pNext(q) = NULL;
  • dyn_modules/syzextra/syzextra.h

    r5cecde re98c64  
    6060
    6161/// Computation attribute storage
    62 struct SchreyerSyzygyComputationFlags
    63 {
    64   SchreyerSyzygyComputationFlags(idhdl rootRingHdl);
    65   SchreyerSyzygyComputationFlags(const SchreyerSyzygyComputationFlags& attr):
    66       __DEBUG__(attr.__DEBUG__),
    67 //      __SYZCHECK__(attr.__SYZCHECK__),
    68       __LEAD2SYZ__(attr.__LEAD2SYZ__),  __TAILREDSYZ__(attr.__TAILREDSYZ__),
    69       __HYBRIDNF__(attr.__HYBRIDNF__),  m_rBaseRing(attr.m_rBaseRing)
    70   {}
    71      
     62class SchreyerSyzygyComputationFlags
     63{
     64  public:
     65    SchreyerSyzygyComputationFlags(idhdl rootRingHdl);
     66
     67    SchreyerSyzygyComputationFlags(const SchreyerSyzygyComputationFlags& attr):
     68        __DEBUG__(attr.__DEBUG__),
     69  //      __SYZCHECK__(attr.__SYZCHECK__),
     70        __LEAD2SYZ__(attr.__LEAD2SYZ__),  __TAILREDSYZ__(attr.__TAILREDSYZ__),
     71        __HYBRIDNF__(attr.__HYBRIDNF__), __IGNORETAILS__(attr.__IGNORETAILS__),
     72        m_rBaseRing(attr.m_rBaseRing)
     73    {}   
    7274
    7375  /// output all the intermediate states
    7476  const bool __DEBUG__; // DebugOutput;
    7577
    76 //  const bool __SYZCHECK__; // CheckSyzygyProperty: never tested here...
     78  //  const bool __SYZCHECK__; // CheckSyzygyProperty: never tested here...
    7779
    7880  /// ?
     
    8587  const bool __HYBRIDNF__; // UseHybridNF
    8688
     89
     90  /// ignore tails and compute the pure Schreyer frame
     91  const bool __IGNORETAILS__; // @IGNORETAILS
     92 
    8793  /// global base ring
    8894  const ring m_rBaseRing;
     
    142148    bool IsDivisible(const poly q) const;
    143149
    144     bool IsNonempty() const { return (m_hash.size() > 0); }
     150    bool IsNonempty() const { return !m_hash.empty(); }
    145151
    146152  private:
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