source: git/Singular/LIB/schreyer.lib @ d79a74

///////////////////////////////////////////////////////////////////////////
version="version schreyer.lib 4.0.0.0 Jun_2013 "; // $Id$
category="General purpose";
info="
LIBRARY: schreyer.lib     Schreyer resolution computations and helpers for @code{derham.lib}
AUTHOR:  Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.uni-kl.de}
KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy
OVERVIEW:
@* The library contains several procedures for computing a/part of Schreyer resoltion (cf. [SFO]),
   and some helpers for @code{derham.lib} (which requires resolutions over the homogenized Weyl algebra) for that purpose.
@* The input for any resolution computation is a set of vectors @code{M} in form of a module over some basering @code{R}.
   The helpers works both in the commutative and non-commutative setting (cf. [MO]), that is the ring @code{R} may be non-commutative, 
   in which case the ring ordering over it must be global. They produce/work with partial Schreyer resolutions of @code{(R^rank(M))/M} 
   in form of a specially constructed ring (endowed with a special ring ordering that will be extended in the 
   course of a resolution computation) containing a list of modules @code{RES} and a module @code{MRES}:
@* @code{RES}: the list of modules contains the images of maps (also called syzygy modules) substituting the
     computed beginning of a Schreyer resolution, that is, each syzygy module is given by a Groebner basis 
     with respect to the corresponding Schreyer ordering. 
@* @code{RES}: the list of modules which starts with a zero map given by @code{rank(M)} zero generators indicating that the image of 
     the first differential map is zero. The second map @code{RES[2]} is given by @code{M}, which indicates that 
     the resolution of @code{(R^rank(M))/M} is being computed.
@* @code{MRES}: the module is a direct sum of modules from @code{RES} and thus comprises all computed differentials.
@* Syzygies are shifted so that @code{gen(i)} is mapped to @code{MRES[i]} under the differential map.
NOTE:
@* Here, we call a free resolution a Schreyer resolution if each syzygy module is given by a Groebner basis
     with respect to the corresponding Schreyer ordering. 
@* A Schreyer resolution can be much bigger than a minimal resolution of the same module, but may be easier to construct.
@* The Schreyer ordering succesively extends the starting module ordering on @code{M} (defined in Singular by the basering @code{R}) 
     and is extended to higher syzygies using the following definition:
@*        a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ), 
@* where @code{d(a)} is the image of an under the differential (given by @code{MRES}),
     and @code{comp(a)} is the module component, for any module terms @code{a} and @code{b} from the same higher syzygy module.
NOTE: 
@* most comutations require the dynamic or built-in module @code{syzextra}, which will be auto-leaded on demand.
PROCEDURES:
  Sres(M,len)     helper for computing Schreyer resolution of module M of maximal length len
  Ssyz(M)         helper for computing Schreyer resolution of module M of length 1
  Scontinue(len)  helper for extending currently active resolution by (at most) len syszygies
  s_res(M, len)   compute Schreyer resolution of module M of maximal length len via LiftTree method from [BMSS]
REFERENCES:
@*
[BMSS] Burcin, E., Motsak, O., Schreyer, F.-O., Steenpass, A.: NEW ALGORITHMS TO COMPUTE SYZYGIES, 2014. 
@* 
[SFO]  Schreyer, F.O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrassschen Divisionssatz,
       Master's thesis, Univ. Hamburg, 1980. 
@*
[MO]   Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related 
       structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010. 
";


static proc prepareSyz( module I, list # )
{
  int i;
  int k = 0;
  int r = nrows(I);
  int c = ncols(I);


  if( size(#) > 0 )
  {
    if( typeof(#[1]) == "int" || typeof(#[1]) == "bigint" )
    {
      k = #[1];
    }
  }

  if( k < r )
  {
    "// *** Wrong k: ", k, " < nrows: ", r, " => setting k = r = ", r;
    k = r;
  }

//   "k: ", k;  "c: ", c;   "I: ", I;

  for( i = c; i > 0; i-- )
  {
    I[i] = I[i] + gen(k + i);
  }

//  DetailedPrint(I);

  return(I);
}

static proc separateSyzGB( module J, int c )
{
  module II, G; vector v; int i;

  J = simplify(J, 2);

  for( i = ncols(J); i > 0; i-- )
  {
    v = J[i];
    if( leadcomp(v) > c )
    {
      II[i] = v;
    } else
    {
      G[i] = v; // leave only gen(i): i <= c
    }
  }

  II = simplify(II, 2);
  G = simplify(G, 2);

  return (list(G, II));
}

static proc splitSyzGB( module J, int c )
{
  module JJ; vector v, vv; int i;

  for( i = ncols(J); i > 0; i-- )
  {
    v = J[i];

    vv = 0;
    
    while( leadcomp(v) <= c )
    {
      vv = vv + lead(v);
      v  = v  - lead(v);
    }

    J[i] = vv;
    JJ[i] = v;
  }

  J = simplify(J, 2);
  JJ = simplify(JJ, 2);

  return (list(J, JJ));
}


static proc Sinit(module M)
{
  def @save = basering;
  
  int @DEBUG = 0; // !system("with", "ndebug");
  if( @DEBUG )
  {
    "Sinit::Input";
    type(M);
//    DetailedPrint(M);
    attrib(M);
  }

  int @RANK = nrows(M); int @SIZE = ncols(M);

  int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?!

  if( !@IS_A_SB ) 
  {
    M = std(M); // this should be faster than computing std in S (later on)
  }

  def S = MakeInducedSchreyerOrdering(1); // 1 puts history terms to the back
  // TODO: NOTE: +1 causes trouble to Singular interpreter!!!???
  setring S; // a new ring with a Schreyer ordering

  if( @DEBUG )
  {
    "Sinit::StartingISRing";
    basering; 
//    DetailedPrint(basering);
  }

  // Setup the leading syzygy^{-1} module to zero:
  module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0));  

  module MRES = Z;
  
  list RES; RES[1] = Z;

  module F = freemodule(@RANK);
  intvec @V = deg(F[1..@RANK]);
  
  module M = imap(@save, M);
  
  attrib(M, "isHomog", @V);
  attrib(M, "isSB", 1);

  
  if( @DEBUG )
  {
    "Sinit::SB_Input: ";
    type(M);
    attrib(M);
    attrib(M, "isHomog");
//    DetailedPrint(M);
  }

  if( @DEBUG )
  {
    // 0^th syz. property
    if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 )
    {
      transpose( transpose(M) * transpose(MRES) );
      "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!";
      m2_end(666); 
    }
  }

  RES[size(RES)+1] = M; // list of all syzygy modules
  MRES = MRES, M;

  attrib(MRES, "isHomog", @V);  

  attrib(S, "InducionLeads", lead(M));
  attrib(S, "InducionStart", @RANK);  
  
  if( @DEBUG )
  {
    "Sinit::MRES";
    DetailedPrint(MRES);
    attrib(MRES, "isHomog");
    attrib(S);
  }

  export RES;
  export MRES;
  return (S);
}

static proc Sstep()
{
  int @DEBUG = 0; // !system("with", "ndebug");

  if( @DEBUG )
  {
    "Sstep::NextInducedRing";
    DetailedPrint(basering);

    attrib(basering, "InducionLeads");
    attrib(basering, "InducionStart");

    GetInducedData();
  }

  // syzygy step:

/*
  // is initial weights are all zeroes!
  def L =  lead(M);
  intvec @V = deg(M[1..ncols(M)]);  @W;  @V;  @W = @V;  attrib(L, "isHomog", @W);  
  SetInducedReferrence(L, @RANK, 0);
*/

//  def L =  lead(MRES);
//  @W = @W, @V;
//  attrib(L, "isHomog", @W);  


  // General setting:
//  SetInducedReferrence(MRES, 0, 0); // limit: 0!
  int @l = size(RES);

  module M = RES[@l];

  module L = attrib(basering, "InducionLeads");
  int limit = attrib(basering, "InducionStart");

//  L;  limit;
  
  int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?!

/*
  if( @RANK !=  nrows(M) )
  {
    type(MRES);
    @RANK;
    type(M);
    pause();
  }
*/
  
  intvec @W = attrib(M, "isHomog");
  intvec @V = deg(M[1..ncols(M)]);
  @V = @W, @V;
   
  if( @DEBUG )
  {
    "Sstep::NextInput: ";
    M;
    deg(M[1..ncols(M)]); // no use of @W :(?
    @RANK;   
    DetailedPrint(MRES);
    attrib(MRES, "isHomog"); @W;
    deg(MRES[1..ncols(MRES)]);
  }

  
      
  SetInducedReferrence(L, limit, 0);
  
  def K = prepareSyz(M, @RANK);
//  K;
  
//   attrib(K, "isHomog", @V);   DetailedPrint(K, 1000);

//  pause();
  
  K = idPrepare(K, @RANK); // std(K); // ?
  K = simplify(K, 2);

//  K;

  module N = separateSyzGB(K, @RANK)[2]; // 1^st syz. module: vectors which start in lower part (comp >= @RANK)

// "N_0: "; N; DetailedPrint(N, 10);

//  basering; print(@V); type(N); 
//  attrib(N, "isHomog", @V);  // TODO: fix "wrong weights"!!!? deg is wrong :(((
  N = std(N);
  attrib(N, "isHomog", @V);

//  N;
  
  if( @DEBUG )
  {
    if( size(N) > 0 )
    {
      // next syz. property
      if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 )
      {
        MRES;

        "N: "; N; DetailedPrint(N, 10);

        "K:"; K; DetailedPrint(K, 10);

        "RANKS: ", @RANK;

        "ERROR: transpose( transpose(N) * transpose(MRES) ) != 0!!!";
        transpose( transpose(N) * transpose(MRES) );

        "transpose(N) * transpose(MRES): ";
        transpose(N) * transpose(MRES);
        DetailedPrint(module(_), 2);
        m2_end(666); 
      }
    }
  }
  
  RES[@l + 1] = N; // list of all syzygy modules
  
  MRES = MRES, N;
  attrib(MRES, "isHomog", @V);


  L = L, lead(N);
  attrib(basering, "InducionLeads", L);

  if( @DEBUG )
  {
    "Sstep::NextSyzOutput: ";
    DetailedPrint(N);
    attrib(N, "isHomog");
  }

}

proc Scontinue(int l)
"USAGE:  Scontinue(int len)
RETURN:  nothing, instead it changes the currently active resolution
PURPOSE: extends the currently active resolution by at most len syzygies 
ASSUME:  must be used within a ring returned by Sres or Ssyz
EXAMPLE: example Scontinue; shows an example
"
{
  def data = GetInducedData();
           
  if( (!defined(RES)) || (!defined(MRES)) || (typeof(data) != "list") || (size(data) != 2) )
  {
    ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz");
  }
  for (;  (l != 0) && (size(RES[size(RES)]) > 0); l-- )
  {
    Sstep(); 
  }
}
example
{ "EXAMPLE:"; echo = 2;
  ring r;
  module M = maxideal(1); M;
  def S = Ssyz(M); setring S; S;
  "Only the first syzygy: ";
  RES; MRES;
  "More syzygies: ";
  Scontinue(10);
  RES; MRES;
}

proc Ssyz(module M)
"USAGE:  Ssyz(module M)
RETURN:  ring, containing a Schreyer resolution
PURPOSE: computes a Schreyer resolution of M of length 1 (see the library overview)
SEE ALSO: Sres
EXAMPLE: example Ssyz; shows an example
"
{
  def S = Sinit(M); setring S;
  
  Sstep(); // NOTE: what if M is zero?

  return (S);
}
example
{ "EXAMPLE:"; echo = 2;
  ring r;
  module M = maxideal(1); M;
  def S = Ssyz(M); setring S; S;
  "Only the first syzygy: ";
  RES;
  MRES; // Note gen(i)
  kill S;
  setring r; kill M;

  module M = 0;
  def S = Ssyz(M); setring S; S;
  "Only the first syzygy: ";
  RES;
  MRES;
}

proc Sres(module M, int l)
"USAGE:  Sres(module M, int len)
RETURN:  ring, containing a Schreyer resolution
PURPOSE: computes a Schreyer resolution of M of length at most len (see the library overview)
NOTE:    If given len is zero then nvars(basering) + 1 is used instead.
SEE ALSO: Ssyz
EXAMPLE: example Sres; shows an example
"
{
  def S = Sinit(M); setring S;

  if (l == 0)
  {
    l = nvars(basering) + 1; // not really an estimate...?!
  }
  
  Sstep(); l = l - 1;
  
  Scontinue(l);
  
  return (S);
}
example
{ "EXAMPLE:"; echo = 2;
  ring r;
  module M = maxideal(1); M;
  def S = Sres(M, 0); setring S; S;
  RES;
  MRES;
  kill S;
  setring r; kill M;

  def A = nc_algebra(-1,0); setring A;
  ideal Q = var(1)^2, var(2)^2, var(3)^2;
  qring SCA = twostd(Q);
  basering;

  module M = maxideal(1);
  def S = Sres(M, 2); setring S; S;
  RES;
  MRES;
}



// ================================================================== //


LIB "general.lib"; // for sort

static proc MySort(def M)
" Sorts the given ideal or module wrt >_{(c, ds)}  (.<.<.<.<) "
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG; 
  }


  if( @DEBUG )
  {
    "MySort:: Input: "; M;
  }

  def @N = M;
  
  if( size(M) > 0 )
  {
    Sort_c_ds(@N);

    if( @KERCHECK )
    {
      def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed?
      def @M = M;
      @M = M[iv];

      // 0^th syz. property
      if( (size(@N) + size(@M)) > 0 )
      {
        if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 )
        {
          "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
          
          "@M:"; @M;
          "@N:"; @N;

          "module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ): ";
          module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) );

          "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
          m2_end(666);
        }
      } 
    }
  }

  if( @DEBUG )
  {
    "MySort:: Ouput: "; @N;
  }
 
  return (@N);
}


static proc SSinit(def M)
{
//  rtimer, "***TIMESNAP0 for SSinit: on level: [",-1,"] :: t: ", timer, ", r: ", rtimer;
  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
  {
    ERROR("Sorry: need an ideal or a module for input");
  }
  def @save = basering;
  
  int @DEBUG = 0; // !system("with", "ndebug");

  if( typeof( attrib(SSinit, "DEBUG") ) == "int" )
  {
    @DEBUG = attrib(SSinit, "DEBUG");
  }

  int @SYZCHECK = 0; // @DEBUG; 

  if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" )
  {
    @SYZCHECK = attrib(SSinit, "SYZCHECK");
  }

  int @KERCHECK = 0; // @DEBUG;

  if( typeof( attrib(SSinit, "KERCHECK") ) == "int" )
  {
    @KERCHECK = attrib(SSinit, "KERCHECK");
  }

  int @IGNORETAILS = 0;

  if( typeof( attrib(SSinit, "IGNORETAILS") ) == "int" )
  {
    @IGNORETAILS = attrib(SSinit, "IGNORETAILS");
  }

  int @TREEOUTPUT = 0;

  if( typeof( attrib(SSinit, "TREEOUTPUT") ) == "int" )
  {
    @TREEOUTPUT = attrib(SSinit, "TREEOUTPUT");
  }

  int @RINGCHANGE = 0;

  if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
  {
    @RINGCHANGE = attrib(SSinit, "@RINGCHANGE");
  }


  if( @DEBUG )
  {
    "SSinit::Input";
    type(M);
    attrib(M);
  }

  int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?!

  if( !@IS_A_SB ) 
  {
    def opts = option(get);
    option(redSB); option(redTail); 
    M = std(M);
    option(set, opts);
    kill opts;
  }

  M = simplify(M, 1 + 2 + 4 + 32);

  if( @IGNORETAILS )
  {
    M = lead(M);
    
    if( @DEBUG )
    {
      "SSinit::Ignorring tails: M: ";
      type(M);
    }
  }
  
  def @N = MySort(M); // TODO: replace with inplace sorting!!!
  def LEAD = lead(@N);

  if( @KERCHECK )
  {
    def @LEAD = lead(M);

    // sort wrt neg.deg.rev.lex!
    intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed!

    M = M[iv_ds]; // sort M wrt ds on current leading terms
    @LEAD = @LEAD[iv_ds];

    if( size(module( matrix(@N) - matrix(M) )) > 0 )
    {
      "M:"; M;
      "@N:"; @N;

      "module( matrix(@N) - matrix(M) ): ";
      module( matrix(@N) - matrix(M) );

      "ERROR: wrong sorting (in SSnit): @N != M!!!";
      m2_end(666);
    }

    if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 )
    {
      "LEAD:"; LEAD;
      "@LEAD:"; @LEAD;

      "module( matrix(@LEAD) - matrix(LEAD) ): ";
      module( matrix(@LEAD) - matrix(LEAD) );

      "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!";
      m2_end(666);
    }
    
  }

  M = @N;
  
  def TAIL = Tail(M);

  int @RANK = nrows(M); int @SIZE = ncols(M);
  
  intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements
  
  // TODO: what about real modules? weighted ones?

  if( @RINGCHANGE )
  {
    list @l = ringlist(@save);
    int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]);
    // NOTE: @wdeg will be ignored anyway :(
    @l[3] = list(list("C", @z), list("lp", @wdeg)); 
    kill @z, @m, @wdeg; // since these vars are ring independent!
    def S = ring(@l); // --MakeInducedSchreyerOrdering(1);
    kill @l;
    setring S; // ring with an easy divisibility test ("C, lex") // or not!???
    if( @DEBUG )
    {
      "SSinit::NewRing(C,lex)?";
      basering; 
      DetailedPrint(basering);
    }
  } else 
  { def S = basering; }

  // Setup the leading syzygy^{-1} module to zero:
  module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0));  

  if( !@RINGCHANGE )
  {
    if( defined(RES) )  { if( @DEBUG ){ "WARN: killing existing object: RES!"; }; kill RES; }
    if( defined(MRES) ) { if( @DEBUG ){ "WARN: killing existing object: MRES!"; }; kill MRES; }
    if( defined(LRES) ) { if( @DEBUG ){ "WARN: killing existing object: LRES!"; }; kill LRES; }
    if( defined(TRES) ) { if( @DEBUG ){ "WARN: killing existing object: TRES!"; }; kill TRES; }
  }

  module MRES = Z;
  
  list RES;  RES[1] = Z;
  list LRES; LRES[1] = Z;
  list TRES; TRES[1] = Z;
 
  if( !defined(M) )
  {
    def M = imap(@save, M);
  }

  module F = freemodule(@RANK); intvec @V = deg(F[1..@RANK]); kill F;
  
  attrib(M, "isHomog", @V);
  attrib(M, "isSB", 1);
  attrib(M, "degrees", @DEGS);  
  
  if( !defined(LEAD) )
  {
    def LEAD = imap(@save, LEAD);
  }  
  
  attrib(LEAD, "isHomog", @V);
  attrib(LEAD, "isSB", 1);  
  
  if( !defined(TAIL) )
  {
    def TAIL = imap(@save, TAIL);
  }  

  if( @DEBUG )
  {
    "SSinit::(sorted) SB_Input: ";
    type(M);
    attrib(M);
    attrib(M, "isHomog");
  }

  if( @SYZCHECK )
  {
    // 0^th syz. property
    if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 )
    {
      transpose( transpose(M) * transpose(MRES) );
      "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!";
      m2_end(666);
    }
  }

  RES [size(RES)+1] = M; // list of all syzygy modules
  LRES[size(LRES)+1] = LEAD; // list of all syzygy modules
  TRES[size(TRES)+1] = TAIL; // list of all syzygy modules
  
  MRES = MRES, M; //?

  attrib(MRES, "isHomog", @V);
  
//  attrib(S, "InducionStart", @RANK);


  if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" )
  {
    attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") );
  } else
  { 
    attrib(S, "LEAD2SYZ", 0);
  }

  if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" )
  {
    attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") );
  } else
  { 
    attrib(S, "TAILREDSYZ", 1);
  }

  if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" )
  {
    attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") );
  } else
  { 
    attrib(S, "HYBRIDNF", 0);
  }

  // maybe resetting existing ring attributes!
  attrib(S, "DEBUG", @DEBUG);
  attrib(S, "SYZCHECK", @SYZCHECK);
  attrib(S, "KERCHECK", @KERCHECK);
  attrib(S, "IGNORETAILS", @IGNORETAILS);
  attrib(S, "TREEOUTPUT", @TREEOUTPUT);
  attrib(S, "SYZNUMBER", 0);
  
  if( @DEBUG )
  {
    "SSinit::MRES";
    MRES;
//    DetailedPrint(MRES);
    attrib(MRES, "isHomog");
    attrib(S);
  }

  export RES;
  export MRES;
  export LRES;
  export TRES;

//  rtimer, "***TIMESNAP1 for SSinit: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
  
  return (S);
}
example
{ "EXAMPLE:"; echo = 2;
  ring R = 0, (w, x, y, z), dp;

  def M = maxideal(1);
  def S = SSinit(M); setring S; S;
  
  "Only the first initialization: ";
  RES; LRES; TRES;
  MRES; 

  kill S; setring R; kill M;
  
  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
  def S = SSinit(M); setring S; S;

  "Only the first initialization: ";
  RES; LRES; TRES;
  MRES; 

  kill S; setring R; kill M;
}


LIB "poly.lib"; // for lcm



/// Compute L(Syz(L))
static proc SSComputeLeadingSyzygyTerms(def L)
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
  {
    int @SYZCHECK = attrib(basering, "SYZCHECK");
  } else
  {
    int @SYZCHECK = @DEBUG;
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }

  if( @DEBUG )
  {
    "SSComputeLeadingSyzygyTerms::Input: ";
    L;
  }

  module SS = ComputeLeadingSyzygyTerms(L);

  if( @KERCHECK )
  {  
    int i, j, r; 
    int N = ncols(L);
    def a, b;
    poly aa, bb;

    bigint c;

    ideal M;

    module S = 0;

    for(i = 1; i <= N; i++)
    {
      a = L[i];
      c = leadcomp(a);
      r = int(c);

      aa = leadmonomial(a);

      M = 0;

      for(j = i-1; j > 0; j--)
      {
        b = L[j];

        if( leadcomp(b) == c )
        {
          bb = leadmonomial(b);

          M[j] = (lcm(aa, bb) / aa);
        }
      }

      // TODO: add quotient relations here...

      M = simplify(M, 1 + 2 + 32);

      M = MySort(M);

      S = S, M * gen(i);
    }

    S = MySort(simplify(S, 2));

    if( (size(S) + size(SS)) > 0 )
    {
      if( size(module(matrix(S) - matrix(SS))) > 0 )
      {
        "ERROR: SSComputeLeadingSyzygyTerms: S != SS ";

        "basering: "; basering;
//        DetailedPrint(basering);

        "S: ";  S;
//        DetailedPrint(_, 1);
        "SS: "; SS;
//        DetailedPrint(_, 1);

        "DIFF: ";
        module(matrix(S) - matrix(SS));
//        DetailedPrint(_, 2);      
        print(matrix(S) - matrix(SS));
        m2_end(666);
      }
    }
  }

  
  if( @DEBUG )
  {
    "SSComputeLeadingSyzygyTerms::Output: ";
    "SS: "; SS;
  }
  
  if( size(SS) > 0 )
  {
    attrib(SS, "isSB", 1); 
  }
  
  return (SS);
}

/// Compute Syz(L), where L is a monomial (leading) module
static proc SSCompute2LeadingSyzygyTerms(def L)
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
  {
    int @SYZCHECK = attrib(basering, "SYZCHECK");
  } else
  {
    int @SYZCHECK = @DEBUG;
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }

  if( @DEBUG )
  {
    "SSCompute2LeadingSyzygyTerms::Input: ";
    L;
  }

  module SS = Compute2LeadingSyzygyTerms(L);

  if( @DEBUG )
  {
    "SSCompute2LeadingSyzygyTerms::Syz(SS): "; SS;
  }
  
  if( @SYZCHECK )
  {
    if( size(SS) > 0 and size(L) > 0 )
    {
      if( size(module(transpose( transpose(SS) * transpose(L) ))) > 0 )
      {
        transpose( transpose(SS) * transpose(L) );
        "ERROR: transpose( transpose(SS) * transpose(L) ) != 0!!!";
        m2_end(666);
      }
    }
  }
    
  if( @KERCHECK )
  {
    int @TAILREDSYZ = 1;
    if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" )
    {
      @TAILREDSYZ = attrib(basering, "TAILREDSYZ");
    }

    int i, j, r; 
    int N = ncols(L);
    def a, b;

    poly aa, bb, @lcm;

    bigint c;

    module M;

    module S = 0;

    for(i = 1; i <= N; i++)
    {
      a = L[i];
  //    "a: ", a;
      c = leadcomp(a);
      r = int(c);

      aa = leadmonomial(a);

      M = 0;

      for(j = i-1; j > 0; j--)
      {
        b = L[j];
  //      "b: ", b;

        if( leadcomp(b) == c )
        {
          bb = leadmonomial(b);
          @lcm = lcm(aa, bb);

          M[j] = (@lcm / aa)* gen(i) - (@lcm / bb)* gen(j);
        }
      }

      M = simplify(M, 2);

      // TODO: add quotient relations here...
      S = S, M;
    }

    if( @TAILREDSYZ )
    {
      // Make sure that 2nd syzygy terms are not reducible by 1st
      def opts = option(get);
      option(redSB); option(redTail); 
      S = std(S); // binomial module
      option(set, opts);
      //  kill opts;
    } else
    {
      S = simplify(S, 2 + 32);
    }

    S = MySort(S);

    if( @DEBUG )
    {
      "SSCompute2LeadingSyzygyTerms::Syz(S): "; S;
    }

    if( @SYZCHECK )
    {
      if( size(S) > 0 and size(L) > 0 )
      {
        if( size(module(transpose( transpose(S) * transpose(L) ))) > 0 )
        {
          transpose( transpose(S) * transpose(L) );
          "ERROR: transpose( transpose(S) * transpose(L) ) != 0!!!";
          m2_end(666);
        }
      }
    }

    if(size(S) != size(SS))
    {
      "ERROR: SSCompute2LeadingSyzygyTerms: size(S) != size(SS)";

      "basering: "; basering; //      DetailedPrint(basering);

      "S: ";  S;
//      DetailedPrint(S, 2);
      "SS: "; SS;
//      DetailedPrint(SS, 2);
      m2_end(666);
    }    

    if(size(S) > 0 && size(SS) > 0)
    {
      if( size(module(matrix(lead(S)) - matrix(lead(SS)))) > 0 )
      {
        "ERROR: SSCompute2LeadingSyzygyTerms: lead(S) != lead(SS) ";

        "basering: ";  basering;
//        DetailedPrint(basering);

        "lead(S ): "; lead(S );
//        DetailedPrint(_, 2);
        "lead(SS): "; lead(SS);
//        DetailedPrint(_, 2);

        "DIFF: ";
        print( matrix(lead(S)) - matrix(lead(SS))  );
        module(matrix(lead(S)) - matrix(lead(SS)));
//        DetailedPrint(_ , 4);
        m2_end(666);
      }


      if( @TAILREDSYZ )
      {
      if( size(module(matrix(Tail(S)) - matrix(Tail(SS)))) > 0 )
      {
        "ERROR: SSCompute2LeadingSyzygyTerms: Tail(S) != Tail(SS) ";

        "basering: ";  basering;
//        DetailedPrint(basering);

        "Tail(S ): "; Tail(S );
//        DetailedPrint(_, 2);
        "Tail(SS): "; Tail(SS);
//        DetailedPrint(_, 2);

        "DIFF: ";
        module( matrix(Tail(S)) - matrix(Tail(SS)) );
//        DetailedPrint(_, 4);
        print( matrix(Tail(S)) - matrix(Tail(SS)) );
        m2_end(666);
      }
      }
    }
  }
  
  module S2 = Tail(SS);
  SS = lead(SS); // (C,lp) on base ring!

  if( @SYZCHECK )
  {
    if( ncols(SS) != ncols(S2) ) // || size(SS) != ncols(SS) || size(S2) != ncols(S2) 
    {
      "ERROR: SSCompute2LeadingSyzygyTerms: inappropriate S2 / SS: ";      
      type(SS);
      type(S2);
      L;
      m2_end(666);
    }
  }  
              
  if( @DEBUG )
  {
    "SSCompute2LeadingSyzygyTerms::Output: "; SS; S2;
  }  
  
  attrib(SS, "isSB", 1); 

  return (SS, S2);
}

// -------------------------------------------------------- //

/// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz?
static proc SSFindReducer(def product, def syzterm, def L, list #)
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
  {
    int @SYZCHECK = attrib(basering, "SYZCHECK");
  } else
  {
    int @SYZCHECK = @DEBUG;
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }


  if( @DEBUG )
  {
    "SSFindReducer::Input: ";

    "syzterm: ", syzterm;
    "product: ", product;
//    "L: ", L;
//    "T: ", T;
    if( size(#) > 0 )
    {
//      "LSyz: ", #;
    }
  }


  if( @DEBUG && (syzterm != 0) )
  {
    def @@c = leadcomp(syzterm); int @@r = int(@@c);
    def @@product = leadmonomial(syzterm) * L[@@r];

    if( @@product != product)
    {
      "product: ", product, ", @@product: ", @@product;
      "ERROR: 'syzterm' results in wrong product !!!???";
      m2_end(666);
    }
  }

  if( typeof(#[1]) == "module" )
  {
    vector my = FindReducer(product, syzterm, L/*, T*/, #[1]);
  } else
  {
    vector my = FindReducer(product, syzterm, L/*, T*/);
  }
  

  if( @KERCHECK )
  {
    bigint c = leadcomp(product); int r = int(c);

    def a, b, bb;

    vector nf = [0];

    // looking for an appropriate diviser
    for( int k = ncols(L); k > 0; k-- )
    {
      a = L[k];
      // with the same mod. component
      if( leadcomp(a) == c )
      {
        b = - (leadmonomial(product) / leadmonomial(L[k]));

        // which divides the product: looking for the 1st appropriate one!
        if( b != 0 )
        {
          bb = b * gen(k);

          if (size(bb + syzterm) == 0) // cannot allow something like: a*gen(i) - a*gen(i)
          {
            nf = [0];
          } else
          {
            nf = bb;
          }

          // new syz. term should not be in <LS = #>
          if( size(#) > 0 )
          {
            if( typeof(#[1]) == "module" )
            {
              nf = NF(bb, #[1]);
            }
          }

          // while the complement (the fraction) is not reducible by leading syzygies 
          if( nf != 0 ) // nf must be == bb!!!
          {
            /// TODO: save shortcut LM(m) * T[i] -> ?

            // choose ANY such reduction... (with the biggest index?)
            break;
          }
        }
      }
    }

    if( my != nf )
    {
      "ERROR in FindReducer => ", my, " != nf: ", nf;
      m2_end(666);
    }
  }

  if( @DEBUG )
  {
    "SSFindReducer::Output: ", my;
  }
 
  return (my);
}

/// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ?
static proc SSReduceTerm(poly m, def t, def syzterm, def L, def T, list #)
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }


  if( @DEBUG )
  {
    "SSReduce::Input: ";

    "syzterm: ", syzterm;
    "mult: ", m;
    "term: ", t;
//    "L: ", L;
//    "T: ", T;
    if( size(#) > 0 )
    {
//      "LSyz: ", #;
    }
//    "attrib(LS, 'isSB')", attrib(LS, "isSB");
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }
  
  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
  {
    int @SYZCHECK = attrib(basering, "SYZCHECK");
  } else
  {
    int @SYZCHECK = @DEBUG;
  }

  if( @SYZCHECK && (syzterm != 0) )
  {
    def @@c = leadcomp(syzterm); int @@r = int(@@c);
    poly @@m = leadmonomial(syzterm); def @@t = L[@@r];

    if( (@@m != m) || (@@t != t))
    {
      "m: ", m, ", t: ", t;
      "@@m: ", @@m, ", @@t: ", @@t;
      "ERROR: 'syzterm' results in wrong m * t !!!";
      m2_end(666);
    }
  }

  if( typeof(#[1]) == "module" )
  {
    vector ss = ReduceTerm(m, t, syzterm, L, T, #[1]);
  } else
  {
    vector ss = ReduceTerm(m, t, syzterm, L, T);
  }

  if( @KERCHECK )
  {
    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");
  
    vector s = 0;

    if( size(t) > 0 )
    {
      def product = m * t;

      s = SSFindReducer(product, syzterm, L, #);

      if( size(s) != 0 )
      {
        poly @b = leadmonomial(s);

        def @c = leadcomp(s); int k = int(@c);

        if( @TREEOUTPUT ){ "\CHILD{", (s), "}{", ( @b*L[k]), "}"; }

        s = s + SSTraverseTail(@b, T[k], L, T, #); // !!!   
      }
    }
    
    if( s != ss )
    {
      "ERROR in ReduceTerm => old: ", s, " != ker: ", ss;
      "m: ", m;
      "t: ", t;
      "syzterm: ", syzterm;
       L; T; #;
      m2_end(666);
    }  
  }

  if( @DEBUG )
  {
    "SSReduceTerm::Output: ", ss;
  }
  
  return (ss);
}


// TODO: store m * @tail -.-^-.-^-.--> ?
static proc SSTraverseTail(poly m, def @tail, def L, def T, list #)
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }
  

  if( @DEBUG )
  {
    "SSTraverse::Input: ";

    "mult: ", m;
    "tail: ", @tail; // T[i];

    if( size(#) > 0 )
    {
//      "LSyz: "; #[1];
    }
  }

  if( typeof(#[1]) == "module" )
  {
    vector ss = TraverseTail(m, @tail, L, T, #[1]);
  } else
  {
    vector ss = TraverseTail(m, @tail, L, T);
  }

  if( @KERCHECK )
  {
    vector s = 0;

    def @l, @p;
    @p = @tail;

  // iterate tail-terms in ANY order!
    while( size(@p) > 0 )
    {
      @l = lead(@p);
      s = s + SSReduceTerm(m, @l, [0], L, T, #); // :(
      @p = @p - @l;
    }
    
    if( s != ss )
    {
      "ERROR in TraverseTail => old: ", s, " != ker: ", ss;
      "m: ", m;
      "@tail: ", @tail;
      L; T; #;
      m2_end(666);
    }  
  }

  if( @DEBUG )
  {
    "SSTraverseTail::Output: ", ss;
  }
  
  return (ss);
}

// -------------------------------------------------------- //

static proc SSSchreyerSyzygyNF(vector syz_lead, vector syz_2, def L, def T, list #)
"  Hybrid Syzygy computation: 'reduce' spoly by eliminating _any_ terms while discurding terms of lower order!
   Return the tail syzygy (without: syz_lead, starting with: syz_2)"
{
  if( typeof( attrib(basering, "DEBUG") ) == "int" )
  {
    int @DEBUG = attrib(basering, "DEBUG");
  } else
  {
    int @DEBUG = 0; // !system("with", "ndebug");
  }

  if( @DEBUG )
  {
    "SSSchreyerSyzygyNF::Input: ";

    "syzygy_lead: ", syz_lead;
    "syzygy 2nd : ", syz_2;
//    L; T; 
    if( size(#) > 0 )
    {
//      "LSyz: "; #[1];
    }
  }

  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
  {
    int @KERCHECK = attrib(basering, "KERCHECK");
  } else
  {
    int @KERCHECK = @DEBUG;
  }

  if( typeof(#[1]) == "module" )
  {
    def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T, #[1]);
  } else
  {
    def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T);
  }

  if( @KERCHECK )
  {
    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");
    
    def spoly = leadmonomial(syz_lead) * T[int(leadcomp(syz_lead))] 
              + leadmonomial(syz_2)    * T[int(leadcomp(syz_2))];

    vector @tail = syz_2;
    
    poly @b; int k; 

    while (size(spoly) > 0)
    {
      syz_2 = SSFindReducer(lead(spoly), 0, L, #); spoly = Tail(spoly);

      if( size(syz_2) != 0)
      {          
        @b = leadmonomial(syz_2);
        k =  int(leadcomp(syz_2));
        
        if( @TREEOUTPUT ){ "\CHILD{", (syz_2), "}{", ( lead(spoly)), "}"; }
        
        spoly = spoly + @b * T[k];
        @tail = @tail + syz_2;
        
      }
    }
    
    if( my != @tail )
    {
      "ERROR in SchreyerSyzygyNF => old: ", @tail, " != ker: ", my;
      
      "syzygy_lead: ", syz_lead;
      "syzygy 2nd : ", syz_2;
      
      L; T; #;
      m2_end(666);
    }
  }

  if( @DEBUG )
  {
    "SSSchreyerSyzygyNF::Output: ", my;
  }
  
  return (my);
}



// -------------------------------------------------------- //

// module (N, LL, TT) = SSComputeSyzygy(L, T);
// Compute Syz(L ++ T) = N = LL ++ TT
static proc SSComputeSyzygy(def L, def T)
{
//  rtimer, "***TIMESNAP0 for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
  int @DEBUG    = attrib(basering, "DEBUG");
  int @KERCHECK = attrib(basering, "KERCHECK");
  int @SYZCHECK = attrib(basering, "SYZCHECK");

  if( @DEBUG )
  {
    "SSComputeSyzygy::Input";
    "basering: ", basering; attrib(basering);
//    DetailedPrint(basering);

//    "iCompShift: ", iCompShift;

    "L: "; L;
    "T: "; T;
  } 

//  option(prot); 
//  rtimer, "***TIME for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
  list @res=ComputeSyzygy(L,T);
//  rtimer, "***TIME for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
//  option(noprot); // TODO: restore!


  module @LL = @res[1]; module @TT = @res[2];

  if( @KERCHECK )
  {
    int @SYZCHECK    = attrib(basering, "SYZCHECK");
    int @LEAD2SYZ    = attrib(basering, "LEAD2SYZ");
    int @TAILREDSYZ  = attrib(basering, "TAILREDSYZ");
    int @HYBRIDNF    = attrib(basering, "HYBRIDNF");
    int @IGNORETAILS = attrib(basering, "IGNORETAILS");
    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");

    int @SYZNUMBER   = attrib(basering,"SYZNUMBER");
    
    if( @HYBRIDNF == 2 )
    {
      if( @SYZNUMBER < 3 ){ @HYBRIDNF = 1; } else { @HYBRIDNF = 0; }
    }
    
    module LL;

    /// Get the critical leading syzygy terms
    if( @LEAD2SYZ ) // & 2nd syz. term
    {
      module LL2;
      (LL, LL2) = SSCompute2LeadingSyzygyTerms(L); 
    } else
    {
      LL = SSComputeLeadingSyzygyTerms(L);
    }

    if( ncols(LL) != ncols(@LL) )
    {
      "ERROR in SSComputeSyzygy: wrong leading syzygies!?";
      "";
      L; T;
      "";
      type(LL);
      type(@LL);
      m2_end(666);
    }

    if( size( module( matrix(LL) - matrix(@LL) ) ) != 0 )
    {
      "ERROR in SSComputeSyzygy: wrong leading syzygies!?";
      "";
      L; T;
      "";
      type(LL);
      type(@LL);
      m2_end(666);
    }

    module TT, SYZ;

    vector a, a2; bigint c; int r; poly aa;

    if( size(LL) > 0 )
    {
      list LS;

      if( @TAILREDSYZ)
      {
        LS = list(LL);
      }

      vector @tail = 0;

//      for(int k = 1; k <= ncols(LL); k++ )
      for(int k = ncols(LL); k > 0; k-- )
      {
        // leading syz. term:
        a = LL[k]; 
        
        if( !@IGNORETAILS )
        {
          c = leadcomp(a); r = int(c); aa = leadmonomial(a);
          
          if( @TREEOUTPUT ){ "\ROOT{", (lead(a)), "}"; }
          
          // NF reduction:
          if( @HYBRIDNF == 0 ) // Traverse approach:
          {
            @tail = SSTraverseTail(aa, T[r], L, T, LS);

            // get the 2nd syzygy term...
            if( @LEAD2SYZ ) // with the 2nd syz. term:
            {      
              a2 = LL2[k]; c = leadcomp(a2); r = int(c); aa = leadmonomial(a2);
              
              if( @TREEOUTPUT ){ "\CHILD{", (lead(a2)), "}{", ( aa*L[r]), "}"; }
              
              @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS);
            } else
            {
              @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS);
            }

          } else // Hybrid approach:
          {

            // get the 2nd syzygy term...
            if( @LEAD2SYZ )
            {
              a2 = LL2[k];
            } else
            {
              a2 = SSFindReducer( aa * L[r], a, L, LS);
            }

            if ( (@SYZCHECK || @DEBUG) )
            {
              if( size(a2) == 0 ) // if syzterm == 0!!!!
              {
                "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!";
                m2_end(666);
              }
            }
            
            if( @TREEOUTPUT ){ "\CHILD{", (a2), "}{", ( aa*L[r]), "}"; }

            @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS);
          }
        } // else @tail remains zero!

        TT[k] = @tail;
        SYZ[k] = a + @tail;

        if ( TT[k] != @TT[k] )
        {
          "ERROR in SSComputeSyzygy: wrong tail syzygy!?";
          "INPUT";
          L; T;
          "LEADING SYZYGY TERMS";
          type(LL);
          
          "CURRENT TAILS";
          type(TT);
          type(@TT);
          
          "WRONG TAIL [", k, "]:";
          type(TT[k]);
          type(@TT[k]);

//          "IMAGES:";
//              transpose( transpose(N) * transpose(MRES) );              
          
          m2_end(666);
        }

      } // FOR
    }

    if( ncols(TT) != ncols(@TT) )
    {
      "ERROR in SSComputeSyzygy: wrong tail syzygies!?";
      "";
      L; T;
      "";
      type(LL);
      type(@LL);
      "";
      type(TT);
      type(@TT);
      m2_end(666);
    }

    if( size( module( matrix(TT) - matrix(@TT) ) ) != 0 )
    {
      "ERROR in SSComputeSyzygy: wrong tail syzygies!?";
      "";
      TT; @TT;
      "";
      L; T;
      "";
      type(LL);
      type(@LL);
      m2_end(666);
    }   
    
  }

  module @SYZ;
  
  for(int @k = ncols(@LL); @k > 0; @k-- )
  {
    @SYZ[@k] = @LL[@k] + @TT[@k];
  }
  
  if( @DEBUG )
  {
    "SSComputeSyzygy::Output";

//    "SYZ: "; @SYZ;
    "LL: "; @LL;
    "TT: "; @TT;
  }

//  rtimer, "***TIMESNAP1 for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
  return (@SYZ, @LL, @TT);
}

// resolution/syzygy step:
static proc SSstep()
{
//  rtimer, "***TIMESNAP0 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
  
  int @DEBUG = attrib(basering, "DEBUG");
  int @SYZCHECK = attrib(basering, "SYZCHECK");

  if( @DEBUG )
  {
    "SSstep::NextInducedRing"; 
    "basering: ", basering; attrib(basering);
  }

/*
  // is initial weights are all zeroes!
  def L =  lead(M);
  intvec @V = deg(M[1..ncols(M)]);  @W;  @V;  @W = @V;  attrib(L, "isHomog", @W);  
  SetInducedReferrence(L, @RANK, 0);
*/

//  def L =  lead(MRES);
//  @W = @W, @V;
//  attrib(L, "isHomog", @W);  


  // General setting:
//  SetInducedReferrence(MRES, 0, 0); // limit: 0!
  int @l = size(RES);

  def M =  RES[@l];

  def L = LRES[@l];
  def T = TRES[@l];


  //// TODO: wrong !!!!!
  int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?!

  

/*
  if( @RANK !=  nrows(M) )
  {
    type(MRES);
    @RANK;
    type(M);
    pause();
  }
*/
  
  intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V;
   
  if( @DEBUG )
  {
    "Sstep::NextInput: ";
    M;
    L;
    @V;
    @RANK;
//    DetailedPrint(MRES);
    attrib(MRES, "isHomog");
  }

      
  // TODO: N  = SYZ( M )!!!
  module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/);

  // shift syz.comp by @RANK:
  module Z;
  Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL);   LL = transpose(Z);
  Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT);   TT = transpose(Z);
  Z = 0; Z[@RANK] = 0; Z = Z, transpose(N);     N = transpose(Z);


  if( @SYZCHECK )
  {
    if( size(N) > 0 )
    {
      // next syz. property
      if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 )
      {
        "MRES", MRES;

        "N: "; N; // DetailedPrint(N, 2);

        "LL:"; LL; // DetailedPrint(LL, 1);
        "TT:"; TT; // DetailedPrint(TT, 10);

        "RANKS: ", @RANK;

        "transpose( transpose(N) * transpose(MRES) ) != 0!!!";
        transpose( transpose(N) * transpose(MRES) );

        "transpose(N) * transpose(MRES): ";
        transpose(N) * transpose(MRES);
        // DetailedPrint(module(_), 2);
        m2_end(666);
      }
    }
  }

  attrib(N, "isHomog", @V);

  // TODO: correct the following: 
  intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :(

  
  attrib(N, "degrees", @DEGS);
  
   RES[@l + 1] = N; // list of all syzygy modules
  LRES[@l + 1] = LL; // list of all syzygy modules
  TRES[@l + 1] = TT; // list of all syzygy modules

  MRES = MRES, N;
  
  attrib(MRES, "isHomog", @V);

//  L = L, lead(N);  attrib(basering, "InducionLeads", L);

  if( @DEBUG )
  {
    "SSstep::NextSyzOutput: ";
    N;
//    DetailedPrint(N);
    attrib(N);
  }

  int ss = attrib(basering, "SYZNUMBER");
  attrib(basering, "SYZNUMBER", ss + 1 );

//  rtimer, "***TIMESNAP1 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
}

static proc SScontinue(int l)
"USAGE:  SScontinue(l)
RETURN:  nothing, instead it changes RES and MRES variables in the current ring
PURPOSE: computes further (at most l) syzygies 
NOTE:    must be used within a ring returned by Sres or Ssyz. RES and MRES are
         explained in Sres
EXAMPLE: example Scontinue; shows an example
"
{
//  rtimer, "***TIMESNAP0 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;

  /// TODO!
//  def data = GetInducedData();

  if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */
  {
    ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz");
  }
  for (;  (l != 0) && (size(RES[size(RES)]) > 0); l-- )
  {
    SSstep(); 
  }
  
//  rtimer, "***TIMESNAP1 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;

}
example
{ "EXAMPLE:"; echo = 2;
  ring r;
  module M = maxideal(1); M;
  def S = SSsyz(M); setring S; S;
  "Only the first syzygy: ";
  RES; MRES;
  "More syzygies: ";
  SScontinue(10);
  RES; MRES;
}

static proc SSsyz(def M)
"USAGE:  SSsyz(M)
RETURN:  ring, containing a list of modules RES and a module MRES
PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)?
NOTE:    The output is explained in Sres
EXAMPLE: example Ssyz; shows an example
"
{
  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
  {
    ERROR("Sorry: need an ideal or a module for input");
  }

  def SS = SSinit(M); setring SS;
  
  SSstep(); // NOTE: what if M is zero?

  return (SS);
}
example
{ "EXAMPLE:"; echo = 2;
  ring r;

/*  ideal M = 0;
  def S = SSsyz(M); setring S; S;
  "Only the first syzygy: ";
  RES; LRES; TRES;
  MRES;
  
  kill S; setring r; kill M;
*/  

  ideal M = maxideal(1); M;

  def S = SSres(M, 0); setring S; S;
  MRES;
  print(_);
  RES;

  kill S; setring r; kill M;

  kill r;
  
  ring R = 0, (w, x, y, z), dp;
  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
  
  def S = SSres(M, 0); setring S; S;
  "";
  LRES;
  "";
  TRES; 
  "";
  MRES;
  print(_);
  RES;
}

static proc SSres(def M, int l)
"USAGE:  SSres(I, l)
RETURN:  ring, containing a list of modules RES and a module MRES
PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer
         induced ordering with gen(i) > gen(j) if i > j, provided both gens
         are from the same syzygy level.???
NOTE:    RES contains the images of maps subsituting the beginning of the
         Schreyer free resolution of baseRing^r/M, while MRES is a sum of
         these images in a big free sum, containing all the syzygy modules.
         The syzygy modules are shifted so that gen(i) correspons to MRES[i].
         The leading zero module RES[0] indicates the fact that coker of the
         first map is zero. The number of zeroes inducates the rank of input.
NOTE:    If l == 0 then l is set to be nvars(basering) + 1
EXAMPLE: example SSres; shows an example
"
{
  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
  {
    ERROR("Sorry: need an ideal or a module for input");
  }
/*
  "KERCHECK: ", attrib(SSinit, "KERCHECK");
  "SYZCHECK: ", attrib(SSinit, "SYZCHECK");
  "DEBUG: ", attrib(SSinit, "DEBUG");
  "HYBRIDNF: ", attrib(SSinit, "HYBRIDNF");
  "TAILREDSYZ: ", attrib(SSinit, "TAILREDSYZ");
  "LEAD2SYZ: ", attrib(SSinit, "LEAD2SYZ");
*/
  
  def SS = SSinit(M); setring SS;
/*  
  "KERCHECK: ", attrib(SS, "KERCHECK");
  "SYZCHECK: ", attrib(SS, "SYZCHECK");
  "DEBUG: ", attrib(SS, "DEBUG");
  "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
  "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
  "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
  "";
  "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
  "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
*/
  if (l == 0)
  {
    l = nvars(basering) + 2; // not really an estimate...?!
  }

  SSstep(); l = l - 1;

  SScontinue(l);
/*
  "KERCHECK: ", attrib(SS, "KERCHECK");
  "SYZCHECK: ", attrib(SS, "SYZCHECK");
  "DEBUG: ", attrib(SS, "DEBUG");
  "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
  "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
  "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
  "";
  "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
  "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
*/  
  return (SS);
}
example
{ "EXAMPLE:"; echo = 2;
  ring r;
  module M = maxideal(1); M;
  def S = SSres(M, 0); setring S; S;
  RES;
  MRES;
}

static proc SRES_betti2(SRES SR, def a)
{
  def R = SR.r; setring R;
  return ( betti(SR.rsltn, a) );
}

static proc SRES_betti1(SRES SR)
{
  def R = SR.r; setring R;
  return ( betti(SR.rsltn) );  
}

static proc SRES_print(SRES SR)
{
  def R = SR.r; setring R;
  "Schreyer resolution: ";
  SR.rsltn; //  print ();
  "over the ring: "; R;
}

static proc SRES_minres(SRES SR)
{
  def save = basering;
  SRES S;
  def R = SR.r; S.r = R;
  setring R;
  S.rsltn = minres(SR.rsltn); // in target ring :(
  return (S);
}


// cannot be automatically used via overloading :(
proc SRES_list(def SR)
"USAGE:  SRES_list(resolution)
RETURN:  list
PURPOSE: convert given resolution to a list
NOTE:    result is over basering
SEE ALSO: s_res, resolution
EXAMPLE: example s_res; shows an example
"
{
  if( typeof(SR) != "SRES" )
  {
    list L = SR;
    return (L);
  }
  
  def save = basering;  
  def R = SR.r;

//    if( 0 )  // ( save == R ) // TODO: not implemented :(((
//    {      list L = SR.rsltn;      return (L);    }
    
  setring R;
  list L = SR.rsltn;
  setring save;  
  return (imap( R, L ));    
}

static proc loadme()
{
  int @DEBUG = 0; // !system("with", "ndebug"); //    "om_ndebug?: ", system("with", "om_ndebug");

  if( @DEBUG )  {    listvar(Syzextra);    listvar(Schreyer);    listvar(Top);  }

  if( !defined(Schreyer::ComputeResolution) )
  {
    load("syzextra.so");
      
      if( @DEBUG ){        listvar(Syzextra);      }
      
//      exportto(Top, Syzextra::ClearContent); //      exportto(Top, Syzextra::ClearDenominators);     exportto(Schreyer, Syzextra::noop);
//      exportto(Schreyer, Syzextra::leadrawexp); //      exportto(Schreyer, Syzextra::ISUpdateComponents);
//      exportto(Schreyer, Syzextra::GetAMData);//      exportto(Schreyer, Syzextra::SetSyzComp);
//      exportto(Schreyer, Syzextra::MakeSyzCompOrdering); //      exportto(Schreyer, Syzextra::reduce_syz);//      exportto(Schreyer, Syzextra::p_Content);
    exportto(Schreyer, Syzextra::DetailedPrint);
    exportto(Schreyer, Syzextra::m2_end);
    exportto(Schreyer, Syzextra::leadmonomial);
    exportto(Schreyer, Syzextra::leadcomp);
    exportto(Schreyer, Syzextra::SetInducedReferrence);
    exportto(Schreyer, Syzextra::GetInducedData);
    exportto(Schreyer, Syzextra::MakeInducedSchreyerOrdering);
    exportto(Schreyer, Syzextra::idPrepare);
    
    exportto(Schreyer, Syzextra::ProfilerStart);   exportto(Schreyer, Syzextra::ProfilerStop);
    exportto(Schreyer, Syzextra::NumberStatsInit); exportto(Schreyer, Syzextra::NumberStatsPrint);
    
    exportto(Schreyer, Syzextra::Tail);
    exportto(Schreyer, Syzextra::ComputeLeadingSyzygyTerms);
    exportto(Schreyer, Syzextra::Compute2LeadingSyzygyTerms);
    exportto(Schreyer, Syzextra::Sort_c_ds);
    
    exportto(Schreyer, Syzextra::FindReducer);

    exportto(Schreyer, Syzextra::ReduceTerm);
    exportto(Schreyer, Syzextra::TraverseTail);
    
    exportto(Schreyer, Syzextra::SchreyerSyzygyNF);
    exportto(Schreyer, Syzextra::ComputeSyzygy);
    exportto(Schreyer, Syzextra::ComputeResolution);
    
    // TODO: SSres - return SRESOLUTION?
    newstruct("SRES","ring r,resolution rsltn"); // http://www.singular.uni-kl.de/Manual/latest/sing_179.htm#SEC218
//      system("install","SRES","string",SRES_string, 1);
    system("install","SRES","print",SRES_print, 1);
    system("install","SRES","betti",SRES_betti1, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
    system("install","SRES","betti",SRES_betti2, 2); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
    system("install","SRES","minres",SRES_minres, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_344.htm#SEC383
    system("install","SRES","list", SRES_list, 1); // will never work :(((

//    exportto(Top, DetailedPrint);
//    exportto(Top, s_res); // GetInducedData);

    if( @DEBUG )    {      listvar(Top);      listvar(Schreyer);    }
  }
  
  mod_assure_load();
}



static proc mod_assure_load()
{
  if( !defined(Schreyer::ComputeResolution) )
  {
    "ERROR: Sorry but you seems to be missing the necessary dynamic module (syzextra.so)!";
//    $
    // m2_end(666); // :(
  }
}

static proc mod_init()
{
  loadme();
}


static proc testallSexamples()
{
  example Ssyz;
  example Scontinue;
  example Sres;  
}

static proc testallSSexamples()
{
  example SSsyz;
  example SScontinue;
  example SSres;  
}
example
{ "EXAMPLE:"; echo = 2;
  testallSexamples();
  testallSSexamples();
}

static proc  StartResTesting(list #)
{
  int @treeout = attrib(SSinit, "TREEOUTPUT");
  
  if( defined(@save_res_list) ) 
  { ERROR("Sorry: existing global variable @save_res_list - run StopAddResTesting before another Start!!!"); }
  
  string @save_res_desc = string(#);
  
  if( !@treeout )
  {
    ">>>>>>>>> {{{{{{{{{ STARTING TESTING ('" + @save_res_desc + "') :::::::::::: ";
  } else 
  {
    "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
  }
  
  list @save_res_list = list(); 
  export @save_res_list;
  export @save_res_desc;
}

static proc  StopResTesting()
{
  int @treeout = attrib(SSinit, "TREEOUTPUT");
  
  if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
  { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }

  if( !defined(@save_res_list) || !defined(@save_res_desc) ) 
  { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }

  int i, j; 
  int f = 0;
  def m, mm;

  if( !@treeout )
  {
  for (i = size(@save_res_list); i > 0; i--)
  {
    "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];
  }
  
  }
  
  for (i = size(@save_res_list); i > 1; i--)
  {
    m = @save_res_list[i][4];
    
    for (j = i-1; j > 0; j--)
    {
      mm = @save_res_list[j][4];
      if( (nrows(m) != nrows(mm)) || (ncols(m) != ncols(mm)) )
      {
        "ERROR: SIZE(Betti[j: ", j, "]) != SIZE(Betti[i: ", i, "]):"; 
        "j: ", j;
        print( @save_res_list[j][4], "betti");
        print(@save_res_list[j]);
        
        "i: ", i;
        print( @save_res_list[i][4], "betti");
        print(@save_res_list[i]);

        f = 1;

      } else
      {
        if( m != mm )
        {
          "ERROR: Betti[j: ", j, "] != Betti[i: ", i, "]:"; 
          "j: ", j;
          print( @save_res_list[j][4], "betti");
          print(@save_res_list[j]);

          "i: ", i;
          print( @save_res_list[i][4], "betti");
          print(@save_res_list[i]);

          f = 1;
        };
      };
  
    };
  
  };
  
  if( f ) 
  {
    print(@save_res_list);
    "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
    
    "ERROR: There were some wrong betti numbers... ";
//    m2_end(666);    
  } else
  {
    if( !@treeout )
    {
      "BETTI: "; print( @save_res_list[1][4], "betti");
    }
  }

  kill @save_res_list;
    
  if( !@treeout )
  {
    "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
  } else
  {
//    "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
    "] },";
  }
  kill @save_res_desc;
}

static proc StartAddResTest(string method, string desc)
{
  int @treeout = attrib(SSinit, "TREEOUTPUT");
  
  if( !defined(@save_res_list) ) 
  { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }

  if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
  { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }
  
  
  def @save_opts = option(get); export @save_opts;
  def @save_method = method; export @save_method;
  def @save_desc = desc; export @save_desc;
  
  if( !@treeout )
  {
    "< START RES TEST{{{ ", @save_method, ", with:", @save_desc, " ... ";
  } else
  {
//    Print("{ \"RESOLUTION: HYBRIDNF:%d, TAILREDSYZ: %d, LEAD2SYZ: %d, IGNORETAILS: %d\": [\n", 
//       attributes.__HYBRIDNF__, attributes.__TAILREDSYZ__, attributes.__LEAD2SYZ__, attributes.__IGNORETAILS__);
    " { \"RESOLUTION: " + @save_method + ", with: " + @save_desc + "\": [";
  }
}


static proc StopAddResTest(def RR, intmat S, int @t, int @m)
{
  int @treeout = attrib(SSinit, "TREEOUTPUT");
  
  if( !(defined(@save_opts) && defined(@save_method) && defined(@save_desc)) )
  { ERROR("Sorry: no global variables - run StartAddResTest beforehand!!!"); }

  list @l = list(@save_method, @save_desc, option(get), S, @t, @m); 
  
//  RR,  
//  print(S, "betti");
  
  if( !@treeout )
  {
    "> -STOP RES TEST}}} ", @save_method, ", with:", @save_desc, ", Timer:", @t; option();
  } else
  {
    " ] },";
  }

  
  option(set, @save_opts); kill @save_opts;

  kill @save_method; kill @save_desc;
  
  @save_res_list[1 + size(@save_res_list)] = @l;
}


static proc SCheck(def S)
{
  setring S; // for checking...

  module M = MRES;
  if( ncols(M) < nrows(M) )
  {
    M[nrows(M)] = 0;
  } else
  {
    M = transpose(M);
    if( ncols(M) < nrows(M) )
    {
      M[nrows(M)] = 0;
    }
    M = transpose(M);
  }

  if( nrows(M) != ncols(M) )
  {
    "ERROR: non-square M!!!";
    m2_end(666);
  }

  if( size(module( M*M )) > 0 )
  {
    "ERROR: module( M*M ) != 0!!!";
    module( M*M );

    "MRES': "; M; print(M);

    m2_end(666);
  }
//  "MRES': "; M; print(M);

  if( size(RES[1]) != 0 )
  {
    "ERROR: wrong starting zero module!!!";
    m2_end(666);
  }

//  RES;
/*  
  MRES;
  RES;
  "";
  LRES;
  "";
  TRES;
*/  
}

//// TODO: SSres(0) fails..!!!??
static proc TestSSres(def I)
{
  def save = basering;
  int @t,@m,r,rr,i;
  string name = 
    "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
    ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
    ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));

  int @PROFILE = attrib(SSinit, "PROFILE");
  if(@PROFILE){ string @prof = "SSres_" + @save_res_desc + "_" + name + ".prof"; }

  StartAddResTest(
   "SSres",
   "minres + betti(,1) + mods: {" + name + "}"
  );
  
  option(redSB); option(redTail);
  if(@PROFILE){ProfilerStart(@prof);}
  timer=0;rtimer=0;def R=SSres(I,0);@m=rtimer;
  if(@PROFILE){ProfilerStop();}
  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;
//  DetailedPrint(RR,0);
  SCheck(R);
  StopAddResTest(RR, S, @t,@m); 
  kill S, RR; setring save; kill R;
}

proc s_res(def I, int l)
"USAGE:  s_res(ideal/module M, int len)
RETURN:  resolution object or SRES
PURPOSE: compute a Schreyer resolution of M of length at most len (see [BMSS])
NOTE:    If given len is zero then nvars(basering) + 1 is used instead.
@* This functions is not related to other helpers from this library.
@* One can switch on computation protocol and statistic (depending on the build) by setting the @code{prot} option.
@* Further recognized switches are the following attributes of @code{Schreyer::SSinit} procedure:
LEAD2SYZ, TAILREDSYZ, HYBRIDNF
DEBUG, ...
SEE ALSO: sres
EXAMPLE: example s_res; shows an example
"
{
  int @prot = (find(option(),"prot") != 0) && (defined(NumberStatsInit)) && (defined(NumberStatsPrint));
  def @save = basering;
  
  int @RINGCHANGE = 0;

  if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
  {
    @RINGCHANGE = attrib(SSinit, "@RINGCHANGE");
  }
  
  def R=SSinit(I);
  if( @RINGCHANGE ){ setring R; }
  
  int @l = size(RES);
  if(@prot){ NumberStatsInit(); }
  def rsltn = ComputeResolution(RES[@l], LRES[@l], TRES[@l], l);
  if(@prot){ NumberStatsPrint("Number statistic for s_res with ComputeResolution"); }
  
  if( !@RINGCHANGE )
  {
    return (rsltn); // ret
  }
  
  SRES ret; ret.r = R; ret.rsltn = rsltn;  
  return (ret);
}
example
{ "EXAMPLE:"; echo = 2;
  ring R;
  module M = maxideal(1); M;
  def  rs = s_res(M, 0); 
  print(rs);
  print(betti(rs, 0)); // non-minimal betties
  print(SRES_list(rs));
  print(betti(rs, 1)); //minimal betties
  print(minres(rs));
}

static proc s_syz(def I)
{
  def R=SSinit(I); setring R;
  int @l = size(RES); //   def M =  RES[@l];
  module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(LRES[@l], TRES[@l]);
  SSYZ ret; ret.r = R; ret.szg = N; // Schreyer::ComputeResolution(RES[2], LRES[2], TRES[2], 0);
  return (ret);
}

static proc TestSSSres(def I)
{
  def save = basering;
  int @t,@m,r,rr,i;
  string name = 
    "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
    ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
    ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));

  int @PROFILE = attrib(SSinit, "PROFILE");
  if(@PROFILE){ string @prof = "SSSres_" + @save_res_desc + "_" + name + ".prof"; }

  StartAddResTest(
   "SSSres",
   "minres + betti(,1) + mods: {" + name + "}"
  );
  
  option(redSB); option(redTail);
  if(@PROFILE){ProfilerStart(@prof);}
  timer=0;rtimer=0;def R=SSinit(I);setring R;def RR=ComputeResolution(RES[2], LRES[2], TRES[2], 0);
@m=rtimer;
  if(@PROFILE){ProfilerStop();}
RR=minres(RR); def S=betti(RR,1);@t=rtimer;
//  DetailedPrint(RR,0);  print(RR);  print(S, "betti");
  SCheck(R);
  StopAddResTest(RR, S, @t,@m); 
  kill S, RR; setring save; kill R;
}


static proc TestSres(def I)
{
  def save = basering;
  int @t,r,rr,i,@m;
  StartAddResTest(
  "Sres", 
  "minres + betti(,1)"
  );
  option(redSB); option(redTail);
  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;
  SCheck(R);
  StopAddResTest(RR, S, @t,@m);  
  kill S, RR; setring save; kill R;
}


static proc Testsres(def M)
{
  int @t,@m;
  StartAddResTest("sres", "no minres + betti(,1)");
  option(redSB);option(redTail);
  timer=0;rtimer=0;def RR=sres(groebner(M),0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
  StopAddResTest(RR, S, @t,@m); kill S, RR;
}

static proc Testlres(def M)
{
  int @t,@m; 
  StartAddResTest("lres", "no minres + betti(,1)");
  option(redSB);option(redTail);
  timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
  StopAddResTest(RR, S, @t,@m); kill S, RR;

  StartAddResTest("lres", "minres + betti()");
  option(redSB);option(redTail);
  timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(minres(RR));@t=rtimer;
  StopAddResTest(RR, S, @t,@m);
  kill S, RR;
}


static proc Testnres(def M)
{
  int @t,@m;
  StartAddResTest("nres", "no minres + betti(,1)");
  
  option(redSB); option(redTail); 
  timer=0;rtimer=0;def RR=nres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
  
  StopAddResTest(RR, S, @t,@m); kill S, RR;
}

static proc TestSSresAttribs(def M, list #)
{
  M = groebner(M);
  
  StartResTesting(#);

  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);

 // WRONG???! LEAD2SYZ?
//  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
//  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);

  int @treeout = attrib(SSinit, "TREEOUTPUT");
  if( !@treeout )
  {
   Testlres(M); Testnres(M);
//   Testsres(M); //   TestSres(M); // too long for the last medium test :(
  }
  
  StopResTesting();
}

static proc TestSSresAttribs2tr(def M, list #)
{
  M = groebner(M);
  
  StartResTesting(#);
  
  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
  Testlres(M);  

  StopResTesting();
}

static proc testSimple(list #)
{
  mod_assure_load();

  def DEBUG = 0;
  if(size(#) > 0) { DEBUG = #[1]; }

  system("--min-time", "0.01");
  system("--ticks-per-sec", 100);

//  option(prot);

  // TODO: only for now!!
  attrib(SSinit, "DEBUG", (DEBUG > 0) );
  attrib(SSinit, "SYZCHECK", (DEBUG > 0) );
  attrib(SSinit, "KERCHECK", (DEBUG > 0) ); 

  attrib(SSinit, "TREEOUTPUT", 0); 
  attrib(SSinit, "PROFILE", 0);
  attrib(SSinit, "IGNORETAILS", 0); // not only frame

  int @treeout = attrib(SSinit, "TREEOUTPUT");
  
  if( @treeout)
  {
    monitor("SimpleTests.json", "o");
    "{ \"SimpleTests\": [";
  } else { option(prot); }
 

  ring r; ideal M = maxideal(1); 
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill r;

  ring r = 0, (a, b, c, d), lp; ideal M = maxideal(1); 
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill r;

  ring R = 0, (w, x, y, z), dp; 
  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z; 
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill R;


  ring r = 0, (a, b, c, d, e, f), dp; ideal M = maxideal(1); 
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill r;  


  ring r = 0, (x, y), lp; ideal M = x2, xy, y2;  // Schreyer conterexample???
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill r;

  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?
  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
  kill r;

  
  ring AGR = (101), (a, b, c, d), dp; 
  // simple: AGR@101n3d002s004%1:
  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;
  TestSSresAttribs(M, "simple: AGR@101n3d002s004%1");

  // medium: AGR@101n3d004s009%1;
  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;
  TestSSresAttribs(M, "medium: AGR@101n3d004s009%1");

  if( @treeout)
  {
    "] }";
    monitor("");
  }

}

static proc testAGR(list #)
{
  def DEBUG = 0;
  if(size(#) > 0) { DEBUG = #[1]; }

  system("--min-time", "0.01");
  system("--ticks-per-sec", 100);

  attrib(SSinit, "DEBUG", 0); 
  attrib(SSinit, "SYZCHECK", (DEBUG > 0)); 
  attrib(SSinit, "KERCHECK", 0); 
  attrib(SSinit, "TREEOUTPUT", 0); 
  attrib(SSinit, "PROFILE", 0);
  attrib(SSinit, "IGNORETAILS", 0); // not only frame
 
  option(prot);

  ring AGR = (101), (a, b, c, d), dp; AGR;
  // lengthy: AGR@101n3d008s058%3, kernel only!
  ideal M = 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  TestSSresAttribs2tr(M, "AGR@101n3d008s058%3");

  // AGR@101n3d010s010%3, a bit slower...
  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;
  TestSSresAttribs2tr(M, "AGR@101n3d010s010%3");  
  kill AGR;

  ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR;
  // AGR@101n7d005s010%2, medium: <= 2
  ideal M = 
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,
b^5+17*h^5,a^5+17*h^5,h^6;
  TestSSresAttribs2tr(M, "AGR@101n7d005s010%2");
  kill AGR;

// from Andreas...tooo long!?

  ring AGR = (101), (a,b,c,d,e), dp; AGR;

  // AGR101n4d007s021%4
  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,
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,
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,
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,
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,
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,
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,
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,
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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,
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,
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,
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,
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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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
b^2*c^2*e^2, a*b*c^2*e^2;
  TestSSresAttribs2tr(M, "AGR101n4d007s021%4");
/*
options:  1 1 0 :  Time:  5/9/10 (35 without LCM)
options:  1 1 1 :  Time:  6/8/25
lres  Time:  5
nres  Time:  5
sres  Time:  693
*/

  kill M;



  // AGR101n4d008s020%1, too big? 
  ideal M = 
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,
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,
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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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2;
//  M;
  TestSSresAttribs2tr(M, "AGR101n4d008s020%1_big");
/*
options:  1 1 0 :  Time:  29/32/73/92 (316 without LCM)
options:  1 1 1 :  Time:  32/34/43/202
lres  Time:  24
nres  Time:  19
sres  Time:  71
*/
  kill M;

  kill AGR;

  ring AGR = (101), (a,b,c,d,e,f), dp; AGR;

  // AGR@101n5d005s016%1, new, medium difficulty?
  ideal M = 
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;
  TestSSresAttribs(M, "AGR@101n5d005s016%1");
  kill M;
}

static proc testAGRhard(list #)
{
  def DEBUG = 0;
  if(size(#) > 0) { DEBUG = #[1]; }

  system("--min-time", "0.01");
  system("--ticks-per-sec", 100);

  attrib(SSinit, "DEBUG", 0); 
  attrib(SSinit, "SYZCHECK", (DEBUG > 0)); 
  attrib(SSinit, "KERCHECK", 0); 
  attrib(SSinit, "TREEOUTPUT", 0);
  attrib(SSinit, "PROFILE", 0);
 
  option(prot);
  // AGR@101n5d006s016%1, new, hard
  ring AGR = (101), (a,b,c,d,e,f), dp; AGR;
  ideal M = 
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;
  TestSSresAttribs2tr(M, "AGR@101n5d006s016%1_hard");
 kill M;
}