source: git/Singular/LIB/schreyer.lib @ 350269

spielwiese
Last change on this file since 350269 was 350269, checked in by Oleksandr Motsak <motsak@…>, 9 years ago
Fix package/namespace/exportto problem in schreyer.lib (mod_init) chg: cleanup for s_res_bm
  • Property mode set to 100644
File size: 228.5 KB
Line 
1///////////////////////////////////////////////////////////////////////////
2version="version schreyer.lib 4.0.0.0 Jun_2013 "; // $Id$
3category="General purpose";
4info="
5LIBRARY: schreyer.lib     Schreyer resolution computations and helpers for @code{derham.lib}
6AUTHOR:  Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.uni-kl.de}
7KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy
8OVERVIEW:
9@* The library contains several procedures for computing a/part of Schreyer resoltion (cf. [SFO]),
10   and some helpers for @code{derham.lib} (which requires resolutions over the homogenized Weyl algebra) for that purpose.
11@* The input for any resolution computation is a set of vectors @code{M} in form of a module over some basering @code{R}.
12   The helpers works both in the commutative and non-commutative setting (cf. [MO]), that is the ring @code{R} may be non-commutative,
13   in which case the ring ordering over it must be global. They produce/work with partial Schreyer resolutions of @code{(R^rank(M))/M}
14   in form of a specially constructed ring (endowed with a special ring ordering that will be extended in the
15   course of a resolution computation) containing a list of modules @code{RES} and a module @code{MRES}:
16@* @code{RES}: the list of modules contains the images of maps (also called syzygy modules) substituting the
17     computed beginning of a Schreyer resolution, that is, each syzygy module is given by a Groebner basis
18     with respect to the corresponding Schreyer ordering.
19@* @code{RES}: the list of modules which starts with a zero map given by @code{rank(M)} zero generators indicating that the image of
20     the first differential map is zero. The second map @code{RES[2]} is given by @code{M}, which indicates that
21     the resolution of @code{(R^rank(M))/M} is being computed.
22@* @code{MRES}: the module is a direct sum of modules from @code{RES} and thus comprises all computed differentials.
23@* Syzygies are shifted so that @code{gen(i)} is mapped to @code{MRES[i]} under the differential map.
24NOTE:
25@* Here, we call a free resolution a Schreyer resolution if each syzygy module is given by a Groebner basis
26     with respect to the corresponding Schreyer ordering.
27@* A Schreyer resolution can be much bigger than a minimal resolution of the same module, but may be easier to construct.
28@* The Schreyer ordering succesively extends the starting module ordering on @code{M} (defined in Singular by the basering @code{R})
29     and is extended to higher syzygies using the following definition:
30@*        a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ),
31@* where @code{d(a)} is the image of an under the differential (given by @code{MRES}),
32     and @code{comp(a)} is the module component, for any module terms @code{a} and @code{b} from the same higher syzygy module.
33NOTE:
34@* most comutations require the dynamic or built-in module @code{syzextra}, which will be auto-leaded on demand.
35PROCEDURES:
36  Sres(M,len)     helper for computing Schreyer resolution of module M of maximal length len
37  Ssyz(M)         helper for computing Schreyer resolution of module M of length 1
38  Scontinue(len)  helper for extending currently active resolution by (at most) len syszygies
39  s_res(M, len)   compute Schreyer resolution of module M of maximal length len via LiftTree method from [BMSS]
40REFERENCES:
41@*
42[BMSS] Burcin, E., Motsak, O., Schreyer, F.-O., Steenpass, A.: NEW ALGORITHMS TO COMPUTE SYZYGIES, 2014.
43@*
44[SFO]  Schreyer, F.O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrassschen Divisionssatz,
45       Master's thesis, Univ. Hamburg, 1980.
46@*
47[MO]   Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related
48       structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010.
49";
50
51static proc prepareSyz( module I, list # )
52{
53  int i;
54  int k = 0;
55  int r = nrows(I);
56  int c = ncols(I);
57
58
59  if( size(#) > 0 )
60  {
61    if( typeof(#[1]) == "int" || typeof(#[1]) == "bigint" )
62    {
63      k = #[1];
64    }
65  }
66
67  if( k < r )
68  {
69    "// *** Wrong k: ", k, " < nrows: ", r, " => setting k = r = ", r;
70    k = r;
71  }
72
73//   "k: ", k;  "c: ", c;   "I: ", I;
74
75  for( i = c; i > 0; i-- )
76  {
77    I[i] = I[i] + gen(k + i);
78  }
79
80//   Syzextra::DetailedPrint(I);
81
82  return(I);
83}
84
85static proc separateSyzGB( module J, int c )
86{
87  module II, G; vector v; int i;
88
89  J = simplify(J, 2);
90
91  for( i = ncols(J); i > 0; i-- )
92  {
93    v = J[i];
94    if(   Syzextra::leadcomp(v) > c )
95    {
96      II[i] = v;
97    } else
98    {
99      G[i] = v; // leave only gen(i): i <= c
100    }
101  }
102
103  II = simplify(II, 2);
104  G = simplify(G, 2);
105
106  return (list(G, II));
107}
108
109static proc splitSyzGB( module J, int c )
110{
111  module JJ; vector v, vv; int i;
112
113  for( i = ncols(J); i > 0; i-- )
114  {
115    v = J[i];
116
117    vv = 0;
118   
119    while(   Syzextra::leadcomp(v) <= c )
120    {
121      vv = vv + lead(v);
122      v  = v  - lead(v);
123    }
124
125    J[i] = vv;
126    JJ[i] = v;
127  }
128
129  J = simplify(J, 2);
130  JJ = simplify(JJ, 2);
131
132  return (list(J, JJ));
133}
134
135
136static proc Sinit(module M)
137{
138  def @save = basering;
139 
140  int @DEBUG = 0; // !system("with", "ndebug");
141  if( @DEBUG )
142  {
143    "Sinit::Input";
144    type(M);
145//      Syzextra::DetailedPrint(M);
146    attrib(M);
147  }
148
149  int @RANK = nrows(M); int @SIZE = ncols(M);
150
151  int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?!
152
153  if( !@IS_A_SB )
154  {
155    M = std(M); // this should be faster than computing std in S (later on)
156  }
157
158  def S =   Syzextra::MakeInducedSchreyerOrdering(1); // 1 puts history terms to the back
159  // TODO: NOTE: +1 causes trouble to Singular interpreter!!!???
160  setring S; // a new ring with a Schreyer ordering
161
162  if( @DEBUG )
163  {
164    "Sinit::StartingISRing";
165    basering;
166//      Syzextra::DetailedPrint(basering);
167  }
168
169  // Setup the leading syzygy^{-1} module to zero:
170  module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); 
171
172  module MRES = Z;
173 
174  list RES; RES[1] = Z;
175
176  module F = freemodule(@RANK);
177  intvec @V = deg(F[1..@RANK]);
178 
179  module M = imap(@save, M);
180 
181  attrib(M, "isHomog", @V);
182  attrib(M, "isSB", 1);
183
184 
185  if( @DEBUG )
186  {
187    "Sinit::SB_Input: ";
188    type(M);
189    attrib(M);
190    attrib(M, "isHomog");
191//      Syzextra::DetailedPrint(M);
192  }
193
194  if( @DEBUG )
195  {
196    // 0^th syz. property
197    if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 )
198    {
199      transpose( transpose(M) * transpose(MRES) );
200      "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!";
201        Syzextra::m2_end(666);
202    }
203  }
204
205  RES[size(RES)+1] = M; // list of all syzygy modules
206  MRES = MRES, M;
207
208  attrib(MRES, "isHomog", @V); 
209
210  attrib(S, "InducionLeads", lead(M));
211  attrib(S, "InducionStart", @RANK); 
212 
213  if( @DEBUG )
214  {
215    "Sinit::MRES";
216      Syzextra::DetailedPrint(MRES);
217    attrib(MRES, "isHomog");
218    attrib(S);
219  }
220
221  export RES;
222  export MRES;
223  return (S);
224}
225
226static proc Sstep()
227{
228  int @DEBUG = 0; // !system("with", "ndebug");
229
230  if( @DEBUG )
231  {
232    "Sstep::NextInducedRing";
233      Syzextra::DetailedPrint(basering);
234
235    attrib(basering, "InducionLeads");
236    attrib(basering, "InducionStart");
237
238      Syzextra::GetInducedData();
239  }
240
241  // syzygy step:
242
243/*
244  // is initial weights are all zeroes!
245  def L =  lead(M);
246  intvec @V = deg(M[1..ncols(M)]);  @W;  @V;  @W = @V;  attrib(L, "isHomog", @W); 
247    Syzextra::SetInducedReferrence(L, @RANK, 0);
248*/
249
250//  def L =  lead(MRES);
251//  @W = @W, @V;
252//  attrib(L, "isHomog", @W); 
253
254
255  // General setting:
256//    Syzextra::SetInducedReferrence(MRES, 0, 0); // limit: 0!
257  int @l = size(RES);
258
259  module M = RES[@l];
260
261  module L = attrib(basering, "InducionLeads");
262  int limit = attrib(basering, "InducionStart");
263
264//  L;  limit;
265 
266  int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?!
267
268/*
269  if( @RANK !=  nrows(M) )
270  {
271    type(MRES);
272    @RANK;
273    type(M);
274    pause();
275  }
276*/
277 
278  intvec @W = attrib(M, "isHomog");
279  intvec @V = deg(M[1..ncols(M)]);
280  @V = @W, @V;
281   
282  if( @DEBUG )
283  {
284    "Sstep::NextInput: ";
285    M;
286    deg(M[1..ncols(M)]); // no use of @W :(?
287    @RANK;   
288      Syzextra::DetailedPrint(MRES);
289    attrib(MRES, "isHomog"); @W;
290    deg(MRES[1..ncols(MRES)]);
291  }
292
293 
294     
295    Syzextra::SetInducedReferrence(L, limit, 0);
296 
297  def K = prepareSyz(M, @RANK);
298//  K;
299 
300//   attrib(K, "isHomog", @V);     Syzextra::DetailedPrint(K, 1000);
301
302//  pause();
303 
304  K =   Syzextra::idPrepare(K, @RANK); // std(K); // ?
305  K = simplify(K, 2);
306
307//  K;
308
309  module N = separateSyzGB(K, @RANK)[2]; // 1^st syz. module: vectors which start in lower part (comp >= @RANK)
310
311// "N_0: "; N;   Syzextra::DetailedPrint(N, 10);
312
313//  basering; print(@V); type(N);
314//  attrib(N, "isHomog", @V);  // TODO: fix "wrong weights"!!!? deg is wrong :(((
315  N = std(N);
316  attrib(N, "isHomog", @V);
317
318//  N;
319 
320  if( @DEBUG )
321  {
322    if( size(N) > 0 )
323    {
324      // next syz. property
325      if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 )
326      {
327        MRES;
328
329        "N: "; N;   Syzextra::DetailedPrint(N, 10);
330
331        "K:"; K;   Syzextra::DetailedPrint(K, 10);
332
333        "RANKS: ", @RANK;
334
335        "ERROR: transpose( transpose(N) * transpose(MRES) ) != 0!!!";
336        transpose( transpose(N) * transpose(MRES) );
337
338        "transpose(N) * transpose(MRES): ";
339        transpose(N) * transpose(MRES);
340          Syzextra::DetailedPrint(module(_), 2);
341          Syzextra::m2_end(666);
342      }
343    }
344  }
345 
346  RES[@l + 1] = N; // list of all syzygy modules
347 
348  MRES = MRES, N;
349  attrib(MRES, "isHomog", @V);
350
351
352  L = L, lead(N);
353  attrib(basering, "InducionLeads", L);
354
355  if( @DEBUG )
356  {
357    "Sstep::NextSyzOutput: ";
358      Syzextra::DetailedPrint(N);
359    attrib(N, "isHomog");
360  }
361
362}
363
364proc Scontinue(int l)
365"USAGE:  Scontinue(int len)
366RETURN:  nothing, instead it changes the currently active resolution
367PURPOSE: extends the currently active resolution by at most len syzygies
368ASSUME:  must be used within a ring returned by Sres or Ssyz
369EXAMPLE: example Scontinue; shows an example
370"
371{
372  def data =   Syzextra::GetInducedData();
373           
374  if( (!defined(RES)) || (!defined(MRES)) || (typeof(data) != "list") || (size(data) != 2) )
375  {
376    ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz");
377  }
378  for (;  (l != 0) && (size(RES[size(RES)]) > 0); l-- )
379  {
380    Sstep();
381  }
382}
383example
384{ "EXAMPLE:"; echo = 2;
385  ring r;
386  module M = maxideal(1); M;
387  def S = Ssyz(M); setring S; S;
388  "Only the first syzygy: ";
389  RES; MRES;
390  "More syzygies: ";
391  Scontinue(10);
392  RES; MRES;
393}
394
395proc Ssyz(module M)
396"USAGE:  Ssyz(module M)
397RETURN:  ring, containing a Schreyer resolution
398PURPOSE: computes a Schreyer resolution of M of length 1 (see the library overview)
399SEE ALSO: Sres
400EXAMPLE: example Ssyz; shows an example
401"
402{
403  def S = Sinit(M); setring S;
404 
405  Sstep(); // NOTE: what if M is zero?
406
407  return (S);
408}
409example
410{ "EXAMPLE:"; echo = 2;
411  ring r;
412  module M = maxideal(1); M;
413  def S = Ssyz(M); setring S; S;
414  "Only the first syzygy: ";
415  RES;
416  MRES; // Note gen(i)
417  kill S;
418  setring r; kill M;
419
420  module M = 0;
421  def S = Ssyz(M); setring S; S;
422  "Only the first syzygy: ";
423  RES;
424  MRES;
425}
426
427proc Sres(module M, int l)
428"USAGE:  Sres(module M, int len)
429RETURN:  ring, containing a Schreyer resolution
430PURPOSE: computes a Schreyer resolution of M of length at most len (see the library overview)
431NOTE:    If given len is zero then nvars(basering) + 1 is used instead.
432SEE ALSO: Ssyz
433EXAMPLE: example Sres; shows an example
434"
435{
436  def S = Sinit(M); setring S;
437
438  if (l == 0)
439  {
440    l = nvars(basering) + 1; // not really an estimate...?!
441  }
442 
443  Sstep(); l = l - 1;
444 
445  Scontinue(l);
446 
447  return (S);
448}
449example
450{ "EXAMPLE:"; echo = 2;
451  ring r;
452  module M = maxideal(1); M;
453  def S = Sres(M, 0); setring S; S;
454  RES;
455  MRES;
456  kill S;
457  setring r; kill M;
458
459  def A = nc_algebra(-1,0); setring A;
460  ideal Q = var(1)^2, var(2)^2, var(3)^2;
461  qring SCA = twostd(Q);
462  basering;
463
464  module M = maxideal(1);
465  def S = Sres(M, 2); setring S; S;
466  RES;
467  MRES;
468}
469
470
471
472// ================================================================== //
473
474
475LIB "general.lib"; // for sort
476
477static proc MySort(def M)
478" Sorts the given ideal or module wrt >_{(c, ds)}  (.<.<.<.<) "
479{
480  if( typeof( attrib(basering, "DEBUG") ) == "int" )
481  {
482    int @DEBUG = attrib(basering, "DEBUG");
483  } else
484  {
485    int @DEBUG = 0; // !system("with", "ndebug");
486  }
487
488  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
489  {
490    int @KERCHECK = attrib(basering, "KERCHECK");
491  } else
492  {
493    int @KERCHECK = @DEBUG;
494  }
495
496
497  if( @DEBUG )
498  {
499    "MySort:: Input: "; M;
500  }
501
502  def @N = M;
503 
504  if( size(M) > 0 )
505  {
506    Syzextra::Sort_c_ds(@N);
507
508    if( @KERCHECK )
509    {
510      def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed?
511      def @M = M;
512      @M = M[iv];
513
514      // 0^th syz. property
515      if( (size(@N) + size(@M)) > 0 )
516      {
517        if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 )
518        {
519          "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
520         
521          "@M:"; @M;
522          "@N:"; @N;
523
524          "module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ): ";
525          module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) );
526
527          "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!";
528            Syzextra::m2_end(666);
529        }
530      }
531    }
532  }
533
534  if( @DEBUG )
535  {
536    "MySort:: Ouput: "; @N;
537  }
538 
539  return (@N);
540}
541
542
543static proc SSinit(def M)
544{
545//  rtimer, "***TIMESNAP0 for SSinit: on level: [",-1,"] :: t: ", timer, ", r: ", rtimer;
546  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
547  {
548    ERROR("Sorry: need an ideal or a module for input");
549  }
550  def @save = basering;
551 
552  int @DEBUG = 0; // !system("with", "ndebug");
553
554  if( typeof( attrib(SSinit, "DEBUG") ) == "int" )
555  {
556    @DEBUG = attrib(SSinit, "DEBUG");
557  }
558
559  int @SYZCHECK = 0; // @DEBUG;
560
561  if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" )
562  {
563    @SYZCHECK = attrib(SSinit, "SYZCHECK");
564  }
565
566  int @KERCHECK = 0; // @DEBUG;
567
568  if( typeof( attrib(SSinit, "KERCHECK") ) == "int" )
569  {
570    @KERCHECK = attrib(SSinit, "KERCHECK");
571  }
572
573  int @IGNORETAILS = 0;
574
575  if( typeof( attrib(SSinit, "IGNORETAILS") ) == "int" )
576  {
577    @IGNORETAILS = attrib(SSinit, "IGNORETAILS");
578  }
579
580  int @TREEOUTPUT = 0;
581
582  if( typeof( attrib(SSinit, "TREEOUTPUT") ) == "int" )
583  {
584    @TREEOUTPUT = attrib(SSinit, "TREEOUTPUT");
585  }
586
587  int @RINGCHANGE = 0;
588
589  if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
590  {
591    @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
592  }
593
594
595  if( @DEBUG )
596  {
597    "SSinit::Input";
598    type(M);
599    attrib(M);
600  }
601
602  int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?!
603
604  if( !@IS_A_SB )
605  {
606    def opts = option(get);
607    option(redSB); option(redTail);
608    M = std(M);
609    option(set, opts);
610    kill opts;
611  }
612
613  M = simplify(M, 1 + 2 + 4 + 32);
614
615  if( @IGNORETAILS )
616  {
617    M = lead(M);
618   
619    if( @DEBUG )
620    {
621      "SSinit::Ignorring tails: M: ";
622      type(M);
623    }
624  }
625 
626  def @N = MySort(M); // TODO: replace with inplace sorting!!!
627  def LEAD = lead(@N);
628
629  if( @KERCHECK )
630  {
631    def @LEAD = lead(M);
632
633    // sort wrt neg.deg.rev.lex!
634    intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed!
635
636    M = M[iv_ds]; // sort M wrt ds on current leading terms
637    @LEAD = @LEAD[iv_ds];
638
639    if( size(module( matrix(@N) - matrix(M) )) > 0 )
640    {
641      "M:"; M;
642      "@N:"; @N;
643
644      "module( matrix(@N) - matrix(M) ): ";
645      module( matrix(@N) - matrix(M) );
646
647      "ERROR: wrong sorting (in SSnit): @N != M!!!";
648        Syzextra::m2_end(666);
649    }
650
651    if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 )
652    {
653      "LEAD:"; LEAD;
654      "@LEAD:"; @LEAD;
655
656      "module( matrix(@LEAD) - matrix(LEAD) ): ";
657      module( matrix(@LEAD) - matrix(LEAD) );
658
659      "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!";
660        Syzextra::m2_end(666);
661    }
662   
663  }
664
665  M = @N;
666 
667  def TAIL =   Syzextra::Tail(M);
668
669  int @RANK = nrows(M); int @SIZE = ncols(M);
670 
671  intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements
672 
673  // TODO: what about real modules? weighted ones?
674
675  if( @RINGCHANGE )
676  {
677    list @l = ringlist(@save);
678    int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]);
679    // NOTE: @wdeg will be ignored anyway :(
680    @l[3] = list(list("C", @z), list("lp", @wdeg));
681    kill @z, @m, @wdeg; // since these vars are ring independent!
682    def S = ring(@l); // --  Syzextra::MakeInducedSchreyerOrdering(1);
683    kill @l;
684    setring S; // ring with an easy divisibility test ("C, lex") // or not!???
685    if( @DEBUG )
686    {
687      "SSinit::NewRing(C,lex)?";
688      basering;
689        Syzextra::DetailedPrint(basering);
690    }
691  } else
692  { def S = basering; }
693
694  // Setup the leading syzygy^{-1} module to zero:
695  module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); 
696
697  if( !@RINGCHANGE )
698  {
699    if( defined(RES) )  { if( @DEBUG ){ "WARN: killing existing object: RES!"; }; kill RES; }
700    if( defined(MRES) ) { if( @DEBUG ){ "WARN: killing existing object: MRES!"; }; kill MRES; }
701    if( defined(LRES) ) { if( @DEBUG ){ "WARN: killing existing object: LRES!"; }; kill LRES; }
702    if( defined(TRES) ) { if( @DEBUG ){ "WARN: killing existing object: TRES!"; }; kill TRES; }
703  }
704
705  module MRES = Z;
706 
707  list RES;  RES[1] = Z;
708  list LRES; LRES[1] = Z;
709  list TRES; TRES[1] = Z;
710 
711  if( !defined(M) )
712  {
713    def M = imap(@save, M);
714  }
715
716  module F = freemodule(@RANK); intvec @V = deg(F[1..@RANK]); kill F;
717 
718  attrib(M, "isHomog", @V);
719  attrib(M, "isSB", 1);
720  attrib(M, "degrees", @DEGS); 
721 
722  if( !defined(LEAD) )
723  {
724    def LEAD = imap(@save, LEAD);
725  } 
726 
727  attrib(LEAD, "isHomog", @V);
728  attrib(LEAD, "isSB", 1); 
729 
730  if( !defined(TAIL) )
731  {
732    def TAIL = imap(@save, TAIL);
733  } 
734
735  if( @DEBUG )
736  {
737    "SSinit::(sorted) SB_Input: ";
738    type(M);
739    attrib(M);
740    attrib(M, "isHomog");
741  }
742
743  if( @SYZCHECK )
744  {
745    // 0^th syz. property
746    if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 )
747    {
748      transpose( transpose(M) * transpose(MRES) );
749      "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!";
750        Syzextra::m2_end(666);
751    }
752  }
753
754  RES [size(RES)+1] = M; // list of all syzygy modules
755  LRES[size(LRES)+1] = LEAD; // list of all syzygy modules
756  TRES[size(TRES)+1] = TAIL; // list of all syzygy modules
757 
758  MRES = MRES, M; //?
759
760  attrib(MRES, "isHomog", @V);
761 
762//  attrib(S, "InducionStart", @RANK);
763
764
765  if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" )
766  {
767    attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") );
768  } else
769  {
770    attrib(S, "LEAD2SYZ", 0);
771  }
772
773  if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" )
774  {
775    attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") );
776  } else
777  {
778    attrib(S, "TAILREDSYZ", 1);
779  }
780
781  if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" )
782  {
783    attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") );
784  } else
785  {
786    attrib(S, "HYBRIDNF", 0);
787  }
788
789  // maybe resetting existing ring attributes!
790  attrib(S, "DEBUG", @DEBUG);
791  attrib(S, "SYZCHECK", @SYZCHECK);
792  attrib(S, "KERCHECK", @KERCHECK);
793  attrib(S, "IGNORETAILS", @IGNORETAILS);
794  attrib(S, "TREEOUTPUT", @TREEOUTPUT);
795  attrib(S, "SYZNUMBER", 0);
796 
797  if( @DEBUG )
798  {
799    "SSinit::MRES";
800    MRES;
801//      Syzextra::DetailedPrint(MRES);
802    attrib(MRES, "isHomog");
803    attrib(S);
804  }
805
806  export RES;
807  export MRES;
808  export LRES;
809  export TRES;
810
811//  rtimer, "***TIMESNAP1 for SSinit: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
812 
813  return (S);
814}
815example
816{ "EXAMPLE:"; echo = 2;
817  ring R = 0, (w, x, y, z), dp;
818
819  def M = maxideal(1);
820  def S = SSinit(M); setring S; S;
821 
822  "Only the first initialization: ";
823  RES; LRES; TRES;
824  MRES;
825
826  kill S; setring R; kill M;
827 
828  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
829  def S = SSinit(M); setring S; S;
830
831  "Only the first initialization: ";
832  RES; LRES; TRES;
833  MRES;
834
835  kill S; setring R; kill M;
836}
837
838
839LIB "poly.lib"; // for lcm
840
841
842
843/// Compute L(Syz(L))
844static proc SSComputeLeadingSyzygyTerms(def L)
845{
846  if( typeof( attrib(basering, "DEBUG") ) == "int" )
847  {
848    int @DEBUG = attrib(basering, "DEBUG");
849  } else
850  {
851    int @DEBUG = 0; // !system("with", "ndebug");
852  }
853
854  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
855  {
856    int @SYZCHECK = attrib(basering, "SYZCHECK");
857  } else
858  {
859    int @SYZCHECK = @DEBUG;
860  }
861
862  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
863  {
864    int @KERCHECK = attrib(basering, "KERCHECK");
865  } else
866  {
867    int @KERCHECK = @DEBUG;
868  }
869
870  if( @DEBUG )
871  {
872    "SSComputeLeadingSyzygyTerms::Input: ";
873    L;
874  }
875
876  module SS =   Syzextra::ComputeLeadingSyzygyTerms(L);
877
878  if( @KERCHECK )
879  { 
880    int i, j, r;
881    int N = ncols(L);
882    def a, b;
883    poly aa, bb;
884
885    bigint c;
886
887    ideal M;
888
889    module S = 0;
890
891    for(i = 1; i <= N; i++)
892    {
893      a = L[i];
894      c =   Syzextra::leadcomp(a);
895      r = int(c);
896
897      aa =   Syzextra::leadmonomial(a);
898
899      M = 0;
900
901      for(j = i-1; j > 0; j--)
902      {
903        b = L[j];
904
905        if(   Syzextra::leadcomp(b) == c )
906        {
907          bb =   Syzextra::leadmonomial(b);
908
909          M[j] = (lcm(aa, bb) / aa);
910        }
911      }
912
913      // TODO: add quotient relations here...
914
915      M = simplify(M, 1 + 2 + 32);
916
917      M = MySort(M);
918
919      S = S, M * gen(i);
920    }
921
922    S = MySort(simplify(S, 2));
923
924    if( (size(S) + size(SS)) > 0 )
925    {
926      if( size(module(matrix(S) - matrix(SS))) > 0 )
927      {
928        "ERROR: SSComputeLeadingSyzygyTerms: S != SS ";
929
930        "basering: "; basering;
931//          Syzextra::DetailedPrint(basering);
932
933        "S: ";  S;
934//          Syzextra::DetailedPrint(_, 1);
935        "SS: "; SS;
936//          Syzextra::DetailedPrint(_, 1);
937
938        "DIFF: ";
939        module(matrix(S) - matrix(SS));
940//          Syzextra::DetailedPrint(_, 2);     
941        print(matrix(S) - matrix(SS));
942          Syzextra::m2_end(666);
943      }
944    }
945  }
946
947 
948  if( @DEBUG )
949  {
950    "SSComputeLeadingSyzygyTerms::Output: ";
951    "SS: "; SS;
952  }
953 
954  if( size(SS) > 0 )
955  {
956    attrib(SS, "isSB", 1);
957  }
958 
959  return (SS);
960}
961
962/// Compute Syz(L), where L is a monomial (leading) module
963static proc SSCompute2LeadingSyzygyTerms(def L)
964{
965  if( typeof( attrib(basering, "DEBUG") ) == "int" )
966  {
967    int @DEBUG = attrib(basering, "DEBUG");
968  } else
969  {
970    int @DEBUG = 0; // !system("with", "ndebug");
971  }
972
973  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
974  {
975    int @SYZCHECK = attrib(basering, "SYZCHECK");
976  } else
977  {
978    int @SYZCHECK = @DEBUG;
979  }
980
981  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
982  {
983    int @KERCHECK = attrib(basering, "KERCHECK");
984  } else
985  {
986    int @KERCHECK = @DEBUG;
987  }
988
989  if( @DEBUG )
990  {
991    "SSCompute2LeadingSyzygyTerms::Input: ";
992    L;
993  }
994
995  module SS =   Syzextra::Compute2LeadingSyzygyTerms(L);
996
997  if( @DEBUG )
998  {
999    "SSCompute2LeadingSyzygyTerms::Syz(SS): "; SS;
1000  }
1001 
1002  if( @SYZCHECK )
1003  {
1004    if( size(SS) > 0 and size(L) > 0 )
1005    {
1006      if( size(module(transpose( transpose(SS) * transpose(L) ))) > 0 )
1007      {
1008        transpose( transpose(SS) * transpose(L) );
1009        "ERROR: transpose( transpose(SS) * transpose(L) ) != 0!!!";
1010          Syzextra::m2_end(666);
1011      }
1012    }
1013  }
1014   
1015  if( @KERCHECK )
1016  {
1017    int @TAILREDSYZ = 1;
1018    if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" )
1019    {
1020      @TAILREDSYZ = attrib(basering, "TAILREDSYZ");
1021    }
1022
1023    int i, j, r;
1024    int N = ncols(L);
1025    def a, b;
1026
1027    poly aa, bb, @lcm;
1028
1029    bigint c;
1030
1031    module M;
1032
1033    module S = 0;
1034
1035    for(i = 1; i <= N; i++)
1036    {
1037      a = L[i];
1038  //    "a: ", a;
1039      c =   Syzextra::leadcomp(a);
1040      r = int(c);
1041
1042      aa =   Syzextra::leadmonomial(a);
1043
1044      M = 0;
1045
1046      for(j = i-1; j > 0; j--)
1047      {
1048        b = L[j];
1049  //      "b: ", b;
1050
1051        if(   Syzextra::leadcomp(b) == c )
1052        {
1053          bb =   Syzextra::leadmonomial(b);
1054          @lcm = lcm(aa, bb);
1055
1056          M[j] = (@lcm / aa)* gen(i) - (@lcm / bb)* gen(j);
1057        }
1058      }
1059
1060      M = simplify(M, 2);
1061
1062      // TODO: add quotient relations here...
1063      S = S, M;
1064    }
1065
1066    if( @TAILREDSYZ )
1067    {
1068      // Make sure that 2nd syzygy terms are not reducible by 1st
1069      def opts = option(get);
1070      option(redSB); option(redTail);
1071      S = std(S); // binomial module
1072      option(set, opts);
1073      //  kill opts;
1074    } else
1075    {
1076      S = simplify(S, 2 + 32);
1077    }
1078
1079    S = MySort(S);
1080
1081    if( @DEBUG )
1082    {
1083      "SSCompute2LeadingSyzygyTerms::Syz(S): "; S;
1084    }
1085
1086    if( @SYZCHECK )
1087    {
1088      if( size(S) > 0 and size(L) > 0 )
1089      {
1090        if( size(module(transpose( transpose(S) * transpose(L) ))) > 0 )
1091        {
1092          transpose( transpose(S) * transpose(L) );
1093          "ERROR: transpose( transpose(S) * transpose(L) ) != 0!!!";
1094            Syzextra::m2_end(666);
1095        }
1096      }
1097    }
1098
1099    if(size(S) != size(SS))
1100    {
1101      "ERROR: SSCompute2LeadingSyzygyTerms: size(S) != size(SS)";
1102
1103      "basering: "; basering; //        Syzextra::DetailedPrint(basering);
1104
1105      "S: ";  S;
1106//        Syzextra::DetailedPrint(S, 2);
1107      "SS: "; SS;
1108//        Syzextra::DetailedPrint(SS, 2);
1109        Syzextra::m2_end(666);
1110    }   
1111
1112    if(size(S) > 0 && size(SS) > 0)
1113    {
1114      if( size(module(matrix(lead(S)) - matrix(lead(SS)))) > 0 )
1115      {
1116        "ERROR: SSCompute2LeadingSyzygyTerms: lead(S) != lead(SS) ";
1117
1118        "basering: ";  basering;
1119//          Syzextra::DetailedPrint(basering);
1120
1121        "lead(S ): "; lead(S );
1122//          Syzextra::DetailedPrint(_, 2);
1123        "lead(SS): "; lead(SS);
1124//          Syzextra::DetailedPrint(_, 2);
1125
1126        "DIFF: ";
1127        print( matrix(lead(S)) - matrix(lead(SS))  );
1128        module(matrix(lead(S)) - matrix(lead(SS)));
1129//          Syzextra::DetailedPrint(_ , 4);
1130          Syzextra::m2_end(666);
1131      }
1132
1133
1134      if( @TAILREDSYZ )
1135      {
1136      if( size(module(matrix(  Syzextra::Tail(S)) - matrix(  Syzextra::Tail(SS)))) > 0 )
1137      {
1138        "ERROR: SSCompute2LeadingSyzygyTerms: Tail(S) != Tail(SS) ";
1139
1140        "basering: ";  basering;
1141//          Syzextra::DetailedPrint(basering);
1142
1143        "Tail(S ): ";   Syzextra::Tail(S );
1144//          Syzextra::DetailedPrint(_, 2);
1145        "Tail(SS): ";   Syzextra::Tail(SS);
1146//          Syzextra::DetailedPrint(_, 2);
1147
1148        "DIFF: ";
1149        module( matrix(  Syzextra::Tail(S)) - matrix(  Syzextra::Tail(SS)) );
1150//          Syzextra::DetailedPrint(_, 4);
1151        print( matrix(  Syzextra::Tail(S)) - matrix(  Syzextra::Tail(SS)) );
1152          Syzextra::m2_end(666);
1153      }
1154      }
1155    }
1156  }
1157 
1158  module S2 =   Syzextra::Tail(SS);
1159  SS = lead(SS); // (C,lp) on base ring!
1160
1161  if( @SYZCHECK )
1162  {
1163    if( ncols(SS) != ncols(S2) ) // || size(SS) != ncols(SS) || size(S2) != ncols(S2)
1164    {
1165      "ERROR: SSCompute2LeadingSyzygyTerms: inappropriate S2 / SS: ";     
1166      type(SS);
1167      type(S2);
1168      L;
1169        Syzextra::m2_end(666);
1170    }
1171  } 
1172             
1173  if( @DEBUG )
1174  {
1175    "SSCompute2LeadingSyzygyTerms::Output: "; SS; S2;
1176  } 
1177 
1178  attrib(SS, "isSB", 1);
1179
1180  return (SS, S2);
1181}
1182
1183// -------------------------------------------------------- //
1184
1185/// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz?
1186static proc SSFindReducer(def product, def syzterm, def L, list #)
1187{
1188  if( typeof( attrib(basering, "DEBUG") ) == "int" )
1189  {
1190    int @DEBUG = attrib(basering, "DEBUG");
1191  } else
1192  {
1193    int @DEBUG = 0; // !system("with", "ndebug");
1194  }
1195
1196  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
1197  {
1198    int @SYZCHECK = attrib(basering, "SYZCHECK");
1199  } else
1200  {
1201    int @SYZCHECK = @DEBUG;
1202  }
1203
1204  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
1205  {
1206    int @KERCHECK = attrib(basering, "KERCHECK");
1207  } else
1208  {
1209    int @KERCHECK = @DEBUG;
1210  }
1211
1212
1213  if( @DEBUG )
1214  {
1215    "SSFindReducer::Input: ";
1216
1217    "syzterm: ", syzterm;
1218    "product: ", product;
1219//    "L: ", L;
1220//    "T: ", T;
1221    if( size(#) > 0 )
1222    {
1223//      "LSyz: ", #;
1224    }
1225  }
1226
1227
1228  if( @DEBUG && (syzterm != 0) )
1229  {
1230    def @@c =   Syzextra::leadcomp(syzterm); int @@r = int(@@c);
1231    def @@product =   Syzextra::leadmonomial(syzterm) * L[@@r];
1232
1233    if( @@product != product)
1234    {
1235      "product: ", product, ", @@product: ", @@product;
1236      "ERROR: 'syzterm' results in wrong product !!!???";
1237        Syzextra::m2_end(666);
1238    }
1239  }
1240
1241  if( typeof(#[1]) == "module" )
1242  {
1243    vector my =   Syzextra::FindReducer(product, syzterm, L/*, T*/, #[1]);
1244  } else
1245  {
1246    vector my =   Syzextra::FindReducer(product, syzterm, L/*, T*/);
1247  }
1248 
1249
1250  if( @KERCHECK )
1251  {
1252    bigint c =   Syzextra::leadcomp(product); int r = int(c);
1253
1254    def a, b, bb;
1255
1256    vector nf = [0];
1257
1258    // looking for an appropriate diviser
1259    for( int k = ncols(L); k > 0; k-- )
1260    {
1261      a = L[k];
1262      // with the same mod. component
1263      if(   Syzextra::leadcomp(a) == c )
1264      {
1265        b = - (  Syzextra::leadmonomial(product) /   Syzextra::leadmonomial(L[k]));
1266
1267        // which divides the product: looking for the 1st appropriate one!
1268        if( b != 0 )
1269        {
1270          bb = b * gen(k);
1271
1272          if (size(bb + syzterm) == 0) // cannot allow something like: a*gen(i) - a*gen(i)
1273          {
1274            nf = [0];
1275          } else
1276          {
1277            nf = bb;
1278          }
1279
1280          // new syz. term should not be in <LS = #>
1281          if( size(#) > 0 )
1282          {
1283            if( typeof(#[1]) == "module" )
1284            {
1285              nf = NF(bb, #[1]);
1286            }
1287          }
1288
1289          // while the complement (the fraction) is not reducible by leading syzygies
1290          if( nf != 0 ) // nf must be == bb!!!
1291          {
1292            /// TODO: save shortcut LM(m) * T[i] -> ?
1293
1294            // choose ANY such reduction... (with the biggest index?)
1295            break;
1296          }
1297        }
1298      }
1299    }
1300
1301    if( my != nf )
1302    {
1303      "ERROR in   Syzextra::FindReducer => ", my, " != nf: ", nf;
1304        Syzextra::m2_end(666);
1305    }
1306  }
1307
1308  if( @DEBUG )
1309  {
1310    "SSFindReducer::Output: ", my;
1311  }
1312 
1313  return (my);
1314}
1315
1316/// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ?
1317static proc SSReduceTerm(poly m, def t, def syzterm, def L, def T, list #)
1318{
1319  if( typeof( attrib(basering, "DEBUG") ) == "int" )
1320  {
1321    int @DEBUG = attrib(basering, "DEBUG");
1322  } else
1323  {
1324    int @DEBUG = 0; // !system("with", "ndebug");
1325  }
1326
1327
1328  if( @DEBUG )
1329  {
1330    "SSReduce::Input: ";
1331
1332    "syzterm: ", syzterm;
1333    "mult: ", m;
1334    "term: ", t;
1335//    "L: ", L;
1336//    "T: ", T;
1337    if( size(#) > 0 )
1338    {
1339//      "LSyz: ", #;
1340    }
1341//    "attrib(LS, 'isSB')", attrib(LS, "isSB");
1342  }
1343
1344  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
1345  {
1346    int @KERCHECK = attrib(basering, "KERCHECK");
1347  } else
1348  {
1349    int @KERCHECK = @DEBUG;
1350  }
1351 
1352  if( typeof( attrib(basering, "SYZCHECK") ) == "int" )
1353  {
1354    int @SYZCHECK = attrib(basering, "SYZCHECK");
1355  } else
1356  {
1357    int @SYZCHECK = @DEBUG;
1358  }
1359
1360  if( @SYZCHECK && (syzterm != 0) )
1361  {
1362    def @@c =   Syzextra::leadcomp(syzterm); int @@r = int(@@c);
1363    poly @@m =   Syzextra::leadmonomial(syzterm); def @@t = L[@@r];
1364
1365    if( (@@m != m) || (@@t != t))
1366    {
1367      "m: ", m, ", t: ", t;
1368      "@@m: ", @@m, ", @@t: ", @@t;
1369      "ERROR: 'syzterm' results in wrong m * t !!!";
1370        Syzextra::m2_end(666);
1371    }
1372  }
1373
1374  if( typeof(#[1]) == "module" )
1375  {
1376    vector ss =   Syzextra::ReduceTerm(m, t, syzterm, L, T, #[1]);
1377  } else
1378  {
1379    vector ss =   Syzextra::ReduceTerm(m, t, syzterm, L, T);
1380  }
1381
1382  if( @KERCHECK )
1383  {
1384    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");
1385 
1386    vector s = 0;
1387
1388    if( size(t) > 0 )
1389    {
1390      def product = m * t;
1391
1392      s = SSFindReducer(product, syzterm, L, #);
1393
1394      if( size(s) != 0 )
1395      {
1396        poly @b =   Syzextra::leadmonomial(s);
1397
1398        def @c =   Syzextra::leadcomp(s); int k = int(@c);
1399
1400        if( @TREEOUTPUT ){ "\CHILD{", (s), "}{", ( @b*L[k]), "}"; }
1401
1402        s = s + SSTraverseTail(@b, T[k], L, T, #); // !!!   
1403      }
1404    }
1405   
1406    if( s != ss )
1407    {
1408      "ERROR in   Syzextra::ReduceTerm => old: ", s, " != ker: ", ss;
1409      "m: ", m;
1410      "t: ", t;
1411      "syzterm: ", syzterm;
1412       L; T; #;
1413        Syzextra::m2_end(666);
1414    } 
1415  }
1416
1417  if( @DEBUG )
1418  {
1419    "SSReduceTerm::Output: ", ss;
1420  }
1421 
1422  return (ss);
1423}
1424
1425
1426// TODO: store m * @tail -.-^-.-^-.--> ?
1427static proc SSTraverseTail(poly m, def @tail, def L, def T, list #)
1428{
1429  if( typeof( attrib(basering, "DEBUG") ) == "int" )
1430  {
1431    int @DEBUG = attrib(basering, "DEBUG");
1432  } else
1433  {
1434    int @DEBUG = 0; // !system("with", "ndebug");
1435  }
1436
1437  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
1438  {
1439    int @KERCHECK = attrib(basering, "KERCHECK");
1440  } else
1441  {
1442    int @KERCHECK = @DEBUG;
1443  }
1444 
1445
1446  if( @DEBUG )
1447  {
1448    "SSTraverse::Input: ";
1449
1450    "mult: ", m;
1451    "tail: ", @tail; // T[i];
1452
1453    if( size(#) > 0 )
1454    {
1455//      "LSyz: "; #[1];
1456    }
1457  }
1458
1459  if( typeof(#[1]) == "module" )
1460  {
1461    vector ss =   Syzextra::TraverseTail(m, @tail, L, T, #[1]);
1462  } else
1463  {
1464    vector ss =   Syzextra::TraverseTail(m, @tail, L, T);
1465  }
1466
1467  if( @KERCHECK )
1468  {
1469    vector s = 0;
1470
1471    def @l, @p;
1472    @p = @tail;
1473
1474  // iterate tail-terms in ANY order!
1475    while( size(@p) > 0 )
1476    {
1477      @l = lead(@p);
1478      s = s + SSReduceTerm(m, @l, [0], L, T, #); // :(
1479      @p = @p - @l;
1480    }
1481   
1482    if( s != ss )
1483    {
1484      "ERROR in   Syzextra::TraverseTail => old: ", s, " != ker: ", ss;
1485      "m: ", m;
1486      "@tail: ", @tail;
1487      L; T; #;
1488        Syzextra::m2_end(666);
1489    } 
1490  }
1491
1492  if( @DEBUG )
1493  {
1494    "SSTraverseTail::Output: ", ss;
1495  }
1496 
1497  return (ss);
1498}
1499
1500// -------------------------------------------------------- //
1501
1502static proc SSSchreyerSyzygyNF(vector syz_lead, vector syz_2, def L, def T, list #)
1503"  Hybrid Syzygy computation: 'reduce' spoly by eliminating _any_ terms while discurding terms of lower order!
1504   Return the tail syzygy (without: syz_lead, starting with: syz_2)"
1505{
1506  if( typeof( attrib(basering, "DEBUG") ) == "int" )
1507  {
1508    int @DEBUG = attrib(basering, "DEBUG");
1509  } else
1510  {
1511    int @DEBUG = 0; // !system("with", "ndebug");
1512  }
1513
1514  if( @DEBUG )
1515  {
1516    "SSSchreyerSyzygyNF::Input: ";
1517
1518    "syzygy_lead: ", syz_lead;
1519    "syzygy 2nd : ", syz_2;
1520//    L; T;
1521    if( size(#) > 0 )
1522    {
1523//      "LSyz: "; #[1];
1524    }
1525  }
1526
1527  if( typeof( attrib(basering, "KERCHECK") ) == "int" )
1528  {
1529    int @KERCHECK = attrib(basering, "KERCHECK");
1530  } else
1531  {
1532    int @KERCHECK = @DEBUG;
1533  }
1534
1535  if( typeof(#[1]) == "module" )
1536  {
1537    def my =   Syzextra::SchreyerSyzygyNF(syz_lead, syz_2, L, T, #[1]);
1538  } else
1539  {
1540    def my =   Syzextra::SchreyerSyzygyNF(syz_lead, syz_2, L, T);
1541  }
1542
1543  if( @KERCHECK )
1544  {
1545    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");
1546   
1547    def spoly =   Syzextra::leadmonomial(syz_lead) * T[int(  Syzextra::leadcomp(syz_lead))]
1548              +   Syzextra::leadmonomial(syz_2)    * T[int(  Syzextra::leadcomp(syz_2))];
1549
1550    vector @tail = syz_2;
1551   
1552    poly @b; int k;
1553
1554    while (size(spoly) > 0)
1555    {
1556      syz_2 = SSFindReducer(lead(spoly), 0, L, #); spoly =   Syzextra::Tail(spoly);
1557
1558      if( size(syz_2) != 0)
1559      {         
1560        @b =   Syzextra::leadmonomial(syz_2);
1561        k =  int(  Syzextra::leadcomp(syz_2));
1562       
1563        if( @TREEOUTPUT ){ "\CHILD{", (syz_2), "}{", ( lead(spoly)), "}"; }
1564       
1565        spoly = spoly + @b * T[k];
1566        @tail = @tail + syz_2;
1567       
1568      }
1569    }
1570   
1571    if( my != @tail )
1572    {
1573      "ERROR in   Syzextra::SchreyerSyzygyNF => old: ", @tail, " != ker: ", my;
1574     
1575      "syzygy_lead: ", syz_lead;
1576      "syzygy 2nd : ", syz_2;
1577     
1578      L; T; #;
1579        Syzextra::m2_end(666);
1580    }
1581  }
1582
1583  if( @DEBUG )
1584  {
1585    "SSSchreyerSyzygyNF::Output: ", my;
1586  }
1587 
1588  return (my);
1589}
1590
1591
1592
1593// -------------------------------------------------------- //
1594
1595// module (N, LL, TT) = SSComputeSyzygy(L, T);
1596// Compute Syz(L ++ T) = N = LL ++ TT
1597static proc SSComputeSyzygy(def L, def T)
1598{
1599//  rtimer, "***TIMESNAP0 for   Syzextra::ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1600  int @DEBUG    = attrib(basering, "DEBUG");
1601  int @KERCHECK = attrib(basering, "KERCHECK");
1602  int @SYZCHECK = attrib(basering, "SYZCHECK");
1603
1604  if( @DEBUG )
1605  {
1606    "SSComputeSyzygy::Input";
1607    "basering: ", basering; attrib(basering);
1608//      Syzextra::DetailedPrint(basering);
1609
1610//    "iCompShift: ", iCompShift;
1611
1612    "L: "; L;
1613    "T: "; T;
1614  }
1615
1616//  option(prot);
1617//  rtimer, "***TIME for   Syzextra::ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1618  list @res=  Syzextra::ComputeSyzygy(L,T);
1619//  rtimer, "***TIME for   Syzextra::ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1620//  option(noprot); // TODO: restore!
1621
1622
1623  module @LL = @res[1]; module @TT = @res[2];
1624
1625  if( @KERCHECK )
1626  {
1627    int @SYZCHECK    = attrib(basering, "SYZCHECK");
1628    int @LEAD2SYZ    = attrib(basering, "LEAD2SYZ");
1629    int @TAILREDSYZ  = attrib(basering, "TAILREDSYZ");
1630    int @HYBRIDNF    = attrib(basering, "HYBRIDNF");
1631    int @IGNORETAILS = attrib(basering, "IGNORETAILS");
1632    int @TREEOUTPUT  = attrib(basering, "TREEOUTPUT");
1633
1634    int @SYZNUMBER   = attrib(basering,"SYZNUMBER");
1635   
1636    if( @HYBRIDNF == 2 )
1637    {
1638      if( @SYZNUMBER < 3 ){ @HYBRIDNF = 1; } else { @HYBRIDNF = 0; }
1639    }
1640   
1641    module LL;
1642
1643    /// Get the critical leading syzygy terms
1644    if( @LEAD2SYZ ) // & 2nd syz. term
1645    {
1646      module LL2;
1647      (LL, LL2) = SSCompute2LeadingSyzygyTerms(L);
1648    } else
1649    {
1650      LL = SSComputeLeadingSyzygyTerms(L);
1651    }
1652
1653    if( ncols(LL) != ncols(@LL) )
1654    {
1655      "ERROR in SSComputeSyzygy: wrong leading syzygies!?";
1656      "";
1657      L; T;
1658      "";
1659      type(LL);
1660      type(@LL);
1661        Syzextra::m2_end(666);
1662    }
1663
1664    if( size( module( matrix(LL) - matrix(@LL) ) ) != 0 )
1665    {
1666      "ERROR in SSComputeSyzygy: wrong leading syzygies!?";
1667      "";
1668      L; T;
1669      "";
1670      type(LL);
1671      type(@LL);
1672        Syzextra::m2_end(666);
1673    }
1674
1675    module TT, SYZ;
1676
1677    vector a, a2; bigint c; int r; poly aa;
1678
1679    if( size(LL) > 0 )
1680    {
1681      list LS;
1682
1683      if( @TAILREDSYZ)
1684      {
1685        LS = list(LL);
1686      }
1687
1688      vector @tail = 0;
1689
1690//      for(int k = 1; k <= ncols(LL); k++ )
1691      for(int k = ncols(LL); k > 0; k-- )
1692      {
1693        // leading syz. term:
1694        a = LL[k];
1695       
1696        if( !@IGNORETAILS )
1697        {
1698          c =   Syzextra::leadcomp(a); r = int(c); aa =   Syzextra::leadmonomial(a);
1699         
1700          if( @TREEOUTPUT ){ "\ROOT{", (lead(a)), "}"; }
1701         
1702          // NF reduction:
1703          if( @HYBRIDNF == 0 ) // Traverse approach:
1704          {
1705            @tail = SSTraverseTail(aa, T[r], L, T, LS);
1706
1707            // get the 2nd syzygy term...
1708            if( @LEAD2SYZ ) // with the 2nd syz. term:
1709            {     
1710              a2 = LL2[k]; c =   Syzextra::leadcomp(a2); r = int(c); aa =   Syzextra::leadmonomial(a2);
1711             
1712              if( @TREEOUTPUT ){ "\CHILD{", (lead(a2)), "}{", ( aa*L[r]), "}"; }
1713             
1714              @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS);
1715            } else
1716            {
1717              @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS);
1718            }
1719
1720          } else // Hybrid approach:
1721          {
1722
1723            // get the 2nd syzygy term...
1724            if( @LEAD2SYZ )
1725            {
1726              a2 = LL2[k];
1727            } else
1728            {
1729              a2 = SSFindReducer( aa * L[r], a, L, LS);
1730            }
1731
1732            if ( (@SYZCHECK || @DEBUG) )
1733            {
1734              if( size(a2) == 0 ) // if syzterm == 0!!!!
1735              {
1736                "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!";
1737                  Syzextra::m2_end(666);
1738              }
1739            }
1740           
1741            if( @TREEOUTPUT ){ "\CHILD{", (a2), "}{", ( aa*L[r]), "}"; }
1742
1743            @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS);
1744          }
1745        } // else @tail remains zero!
1746
1747        TT[k] = @tail;
1748        SYZ[k] = a + @tail;
1749
1750        if ( TT[k] != @TT[k] )
1751        {
1752          "ERROR in SSComputeSyzygy: wrong tail syzygy!?";
1753          "INPUT";
1754          L; T;
1755          "LEADING SYZYGY TERMS";
1756          type(LL);
1757         
1758          "CURRENT TAILS";
1759          type(TT);
1760          type(@TT);
1761         
1762          "WRONG TAIL [", k, "]:";
1763          type(TT[k]);
1764          type(@TT[k]);
1765
1766//          "IMAGES:";
1767//              transpose( transpose(N) * transpose(MRES) );             
1768         
1769            Syzextra::m2_end(666);
1770        }
1771
1772      } // FOR
1773    }
1774
1775    if( ncols(TT) != ncols(@TT) )
1776    {
1777      "ERROR in SSComputeSyzygy: wrong tail syzygies!?";
1778      "";
1779      L; T;
1780      "";
1781      type(LL);
1782      type(@LL);
1783      "";
1784      type(TT);
1785      type(@TT);
1786        Syzextra::m2_end(666);
1787    }
1788
1789    if( size( module( matrix(TT) - matrix(@TT) ) ) != 0 )
1790    {
1791      "ERROR in SSComputeSyzygy: wrong tail syzygies!?";
1792      "";
1793      TT; @TT;
1794      "";
1795      L; T;
1796      "";
1797      type(LL);
1798      type(@LL);
1799        Syzextra::m2_end(666);
1800    }   
1801   
1802  }
1803
1804  module @SYZ;
1805 
1806  for(int @k = ncols(@LL); @k > 0; @k-- )
1807  {
1808    @SYZ[@k] = @LL[@k] + @TT[@k];
1809  }
1810 
1811  if( @DEBUG )
1812  {
1813    "SSComputeSyzygy::Output";
1814
1815//    "SYZ: "; @SYZ;
1816    "LL: "; @LL;
1817    "TT: "; @TT;
1818  }
1819
1820//  rtimer, "***TIMESNAP1 for   Syzextra::ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1821  return (@SYZ, @LL, @TT);
1822}
1823
1824// resolution/syzygy step:
1825static proc SSstep()
1826{
1827//  rtimer, "***TIMESNAP0 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1828 
1829  int @DEBUG = attrib(basering, "DEBUG");
1830  int @SYZCHECK = attrib(basering, "SYZCHECK");
1831
1832  if( @DEBUG )
1833  {
1834    "SSstep::NextInducedRing";
1835    "basering: ", basering; attrib(basering);
1836  }
1837
1838/*
1839  // is initial weights are all zeroes!
1840  def L =  lead(M);
1841  intvec @V = deg(M[1..ncols(M)]);  @W;  @V;  @W = @V;  attrib(L, "isHomog", @W); 
1842    Syzextra::SetInducedReferrence(L, @RANK, 0);
1843*/
1844
1845//  def L =  lead(MRES);
1846//  @W = @W, @V;
1847//  attrib(L, "isHomog", @W); 
1848
1849
1850  // General setting:
1851//    Syzextra::SetInducedReferrence(MRES, 0, 0); // limit: 0!
1852  int @l = size(RES);
1853
1854  def M =  RES[@l];
1855
1856  def L = LRES[@l];
1857  def T = TRES[@l];
1858
1859
1860  //// TODO: wrong !!!!!
1861  int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?!
1862
1863 
1864
1865/*
1866  if( @RANK !=  nrows(M) )
1867  {
1868    type(MRES);
1869    @RANK;
1870    type(M);
1871    pause();
1872  }
1873*/
1874 
1875  intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V;
1876   
1877  if( @DEBUG )
1878  {
1879    "Sstep::NextInput: ";
1880    M;
1881    L;
1882    @V;
1883    @RANK;
1884//      Syzextra::DetailedPrint(MRES);
1885    attrib(MRES, "isHomog");
1886  }
1887
1888     
1889  // TODO: N  = SYZ( M )!!!
1890  module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/);
1891
1892  // shift syz.comp by @RANK:
1893  module Z;
1894  Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL);   LL = transpose(Z);
1895  Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT);   TT = transpose(Z);
1896  Z = 0; Z[@RANK] = 0; Z = Z, transpose(N);     N = transpose(Z);
1897
1898
1899  if( @SYZCHECK )
1900  {
1901    if( size(N) > 0 )
1902    {
1903      // next syz. property
1904      if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 )
1905      {
1906        "MRES", MRES;
1907
1908        "N: "; N; //   Syzextra::DetailedPrint(N, 2);
1909
1910        "LL:"; LL; //   Syzextra::DetailedPrint(LL, 1);
1911        "TT:"; TT; //   Syzextra::DetailedPrint(TT, 10);
1912
1913        "RANKS: ", @RANK;
1914
1915        "transpose( transpose(N) * transpose(MRES) ) != 0!!!";
1916        transpose( transpose(N) * transpose(MRES) );
1917
1918        "transpose(N) * transpose(MRES): ";
1919        transpose(N) * transpose(MRES);
1920        //   Syzextra::DetailedPrint(module(_), 2);
1921          Syzextra::m2_end(666);
1922      }
1923    }
1924  }
1925
1926  attrib(N, "isHomog", @V);
1927
1928  // TODO: correct the following:
1929  intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :(
1930
1931 
1932  attrib(N, "degrees", @DEGS);
1933 
1934   RES[@l + 1] = N; // list of all syzygy modules
1935  LRES[@l + 1] = LL; // list of all syzygy modules
1936  TRES[@l + 1] = TT; // list of all syzygy modules
1937
1938  MRES = MRES, N;
1939 
1940  attrib(MRES, "isHomog", @V);
1941
1942//  L = L, lead(N);  attrib(basering, "InducionLeads", L);
1943
1944  if( @DEBUG )
1945  {
1946    "SSstep::NextSyzOutput: ";
1947    N;
1948//      Syzextra::DetailedPrint(N);
1949    attrib(N);
1950  }
1951
1952  int ss = attrib(basering, "SYZNUMBER");
1953  attrib(basering, "SYZNUMBER", ss + 1 );
1954
1955//  rtimer, "***TIMESNAP1 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1956}
1957
1958static proc SScontinue(int l)
1959"USAGE:  SScontinue(l)
1960RETURN:  nothing, instead it changes RES and MRES variables in the current ring
1961PURPOSE: computes further (at most l) syzygies
1962NOTE:    must be used within a ring returned by Sres or Ssyz. RES and MRES are
1963         explained in Sres
1964EXAMPLE: example Scontinue; shows an example
1965"
1966{
1967//  rtimer, "***TIMESNAP0 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1968
1969  /// TODO!
1970//  def data =   Syzextra::GetInducedData();
1971
1972  if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */
1973  {
1974    ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz");
1975  }
1976  for (;  (l != 0) && (size(RES[size(RES)]) > 0); l-- )
1977  {
1978    SSstep();
1979  }
1980 
1981//  rtimer, "***TIMESNAP1 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer;
1982
1983}
1984example
1985{ "EXAMPLE:"; echo = 2;
1986  ring r;
1987  module M = maxideal(1); M;
1988  def S = SSsyz(M); setring S; S;
1989  "Only the first syzygy: ";
1990  RES; MRES;
1991  "More syzygies: ";
1992  SScontinue(10);
1993  RES; MRES;
1994}
1995
1996static proc SSsyz(def M)
1997"USAGE:  SSsyz(M)
1998RETURN:  ring, containing a list of modules RES and a module MRES
1999PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)?
2000NOTE:    The output is explained in Sres
2001EXAMPLE: example Ssyz; shows an example
2002"
2003{
2004  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
2005  {
2006    ERROR("Sorry: need an ideal or a module for input");
2007  }
2008
2009  def SS = SSinit(M); setring SS;
2010 
2011  SSstep(); // NOTE: what if M is zero?
2012
2013  return (SS);
2014}
2015example
2016{ "EXAMPLE:"; echo = 2;
2017  ring r;
2018
2019/*  ideal M = 0;
2020  def S = SSsyz(M); setring S; S;
2021  "Only the first syzygy: ";
2022  RES; LRES; TRES;
2023  MRES;
2024 
2025  kill S; setring r; kill M;
2026*/ 
2027
2028  ideal M = maxideal(1); M;
2029
2030  def S = SSres(M, 0); setring S; S;
2031  MRES;
2032  print(_);
2033  RES;
2034
2035  kill S; setring r; kill M;
2036
2037  kill r;
2038 
2039  ring R = 0, (w, x, y, z), dp;
2040  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
2041 
2042  def S = SSres(M, 0); setring S; S;
2043  "";
2044  LRES;
2045  "";
2046  TRES;
2047  "";
2048  MRES;
2049  print(_);
2050  RES;
2051}
2052
2053static proc SSres(def M, int l)
2054"USAGE:  SSres(I, l)
2055RETURN:  ring, containing a list of modules RES and a module MRES
2056PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer
2057         induced ordering with gen(i) > gen(j) if i > j, provided both gens
2058         are from the same syzygy level.???
2059NOTE:    RES contains the images of maps subsituting the beginning of the
2060         Schreyer free resolution of baseRing^r/M, while MRES is a sum of
2061         these images in a big free sum, containing all the syzygy modules.
2062         The syzygy modules are shifted so that gen(i) correspons to MRES[i].
2063         The leading zero module RES[0] indicates the fact that coker of the
2064         first map is zero. The number of zeroes inducates the rank of input.
2065NOTE:    If l == 0 then l is set to be nvars(basering) + 1
2066EXAMPLE: example SSres; shows an example
2067"
2068{
2069  if( (typeof(M) != "module") && (typeof(M) != "ideal") )
2070  {
2071    ERROR("Sorry: need an ideal or a module for input");
2072  }
2073/*
2074  "KERCHECK: ", attrib(SSinit, "KERCHECK");
2075  "SYZCHECK: ", attrib(SSinit, "SYZCHECK");
2076  "DEBUG: ", attrib(SSinit, "DEBUG");
2077  "HYBRIDNF: ", attrib(SSinit, "HYBRIDNF");
2078  "TAILREDSYZ: ", attrib(SSinit, "TAILREDSYZ");
2079  "LEAD2SYZ: ", attrib(SSinit, "LEAD2SYZ");
2080*/
2081 
2082  def SS = SSinit(M); setring SS;
2083/* 
2084  "KERCHECK: ", attrib(SS, "KERCHECK");
2085  "SYZCHECK: ", attrib(SS, "SYZCHECK");
2086  "DEBUG: ", attrib(SS, "DEBUG");
2087  "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
2088  "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
2089  "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
2090  "";
2091  "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
2092  "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
2093*/
2094  if (l == 0)
2095  {
2096    l = nvars(basering) + 2; // not really an estimate...?!
2097  }
2098
2099  SSstep(); l = l - 1;
2100
2101  SScontinue(l);
2102/*
2103  "KERCHECK: ", attrib(SS, "KERCHECK");
2104  "SYZCHECK: ", attrib(SS, "SYZCHECK");
2105  "DEBUG: ", attrib(SS, "DEBUG");
2106  "HYBRIDNF: ", attrib(SS, "HYBRIDNF");
2107  "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ");
2108  "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ");
2109  "";
2110  "IGNORETAILS: ", attrib(SS, "IGNORETAILS");
2111  "SYZNUMBER: ", attrib(SS, "SYZNUMBER");
2112*/ 
2113  return (SS);
2114}
2115example
2116{ "EXAMPLE:"; echo = 2;
2117  ring r;
2118  module M = maxideal(1); M;
2119  def S = SSres(M, 0); setring S; S;
2120  RES;
2121  MRES;
2122}
2123
2124static proc SRES_betti2(SRES SR, def a)
2125{
2126  def R = SR.r; setring R;
2127  return ( betti(SR.rsltn, a) );
2128}
2129
2130static proc SRES_betti1(SRES SR)
2131{
2132  def R = SR.r; setring R;
2133  return ( betti(SR.rsltn) ); 
2134}
2135
2136static proc SRES_print(SRES SR)
2137{
2138  def R = SR.r; setring R;
2139  "Schreyer resolution: ";
2140  SR.rsltn; //  print ();
2141  "over the ring: "; R;
2142}
2143
2144static proc SRES_minres(SRES SR)
2145{
2146  def save = basering;
2147  SRES S;
2148  def R = SR.r; S.r = R;
2149  setring R;
2150  S.rsltn = minres(SR.rsltn); // in target ring :(
2151  return (S);
2152}
2153
2154
2155// cannot be automatically used via overloading :(
2156proc SRES_list(def SR)
2157"USAGE:  SRES_list(resolution)
2158RETURN:  list
2159PURPOSE: convert given resolution to a list
2160NOTE:    result is over basering
2161SEE ALSO: s_res, resolution
2162EXAMPLE: example s_res; shows an example
2163"
2164{
2165  if( typeof(SR) != "SRES" )
2166  {
2167    list @@@L = SR;
2168    return (@@@L);
2169  }
2170 
2171  def save = basering; 
2172  def R = SR.r;
2173
2174//    if( 0 )  // ( save == R ) // TODO: not implemented :(((
2175//    {      list L = SR.rsltn;      return (L);    }
2176   
2177  setring R;
2178 
2179  list @@@L = SR.rsltn;
2180  setring save; 
2181  return (imap( R, @@@L ));
2182}
2183
2184static proc mod_init()
2185{
2186  int @DEBUG = 0; // !system("with", "ndebug"); //    "om_ndebug?: ", system("with", "om_ndebug");
2187
2188  if( @DEBUG )  {    listvar(Top);  }
2189
2190  if( !defined(SRES) )
2191  {
2192      load("syzextra.so");
2193
2194      if( @DEBUG ){        listvar(Syzextra);      }
2195     
2196//      exportto(Top,   Syzextra::ClearContent); //      exportto(Top,   Syzextra::ClearDenominators);     exportto(Schreyer,   Syzextra::noop);
2197//      exportto(Schreyer,   Syzextra::leadrawexp); //      exportto(Schreyer,   Syzextra::ISUpdateComponents);
2198//      exportto(Schreyer,   Syzextra::GetAMData);//      exportto(Schreyer,   Syzextra::SetSyzComp);
2199//      exportto(Schreyer,   Syzextra::MakeSyzCompOrdering); //      exportto(Schreyer,   Syzextra::reduce_syz);//      exportto(Schreyer,   Syzextra::p_Content);
2200
2201//    exportto(Schreyer,   Syzextra::DetailedPrint);
2202//    exportto(Schreyer,   Syzextra::m2_end);
2203//    exportto(Schreyer,   Syzextra::leadmonomial);
2204//    exportto(Schreyer,   Syzextra::leadcomp);
2205//    exportto(Schreyer,   Syzextra::SetInducedReferrence);
2206//    exportto(Schreyer,   Syzextra::GetInducedData);
2207//    exportto(Schreyer,   Syzextra::MakeInducedSchreyerOrdering);
2208//    exportto(Schreyer,   Syzextra::idPrepare);   
2209//    exportto(Schreyer,   Syzextra::ProfilerStart);   exportto(Schreyer,   Syzextra::ProfilerStop);
2210//    exportto(Schreyer,   Syzextra::NumberStatsInit); exportto(Schreyer,   Syzextra::NumberStatsPrint);   
2211//    exportto(Schreyer,   Syzextra::Tail);
2212//    exportto(Schreyer,   Syzextra::ComputeLeadingSyzygyTerms);
2213//    exportto(Schreyer,   Syzextra::Compute2LeadingSyzygyTerms);
2214//    exportto(Schreyer,   Syzextra::Sort_c_ds);   
2215//    exportto(Schreyer,   Syzextra::FindReducer);
2216//    exportto(Schreyer,   Syzextra::ReduceTerm);
2217//    exportto(Schreyer,   Syzextra::TraverseTail);   
2218//    exportto(Schreyer,   Syzextra::SchreyerSyzygyNF);
2219//    exportto(Schreyer,   Syzextra::ComputeSyzygy);
2220//    exportto(Schreyer,   Syzextra::ComputeResolution);
2221   
2222    // TODO: SSres - return SRESOLUTION?
2223    newstruct("SRES","ring r,resolution rsltn"); // http://www.singular.uni-kl.de/Manual/latest/sing_179.htm#SEC218
2224//      system("install","SRES","string",SRES_string, 1);
2225    system("install","SRES","print",SRES_print, 1);
2226    system("install","SRES","betti",SRES_betti1, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
2227    system("install","SRES","betti",SRES_betti2, 2); // http://www.singular.uni-kl.de/Manual/latest/sing_260.htm#SEC299
2228    system("install","SRES","minres",SRES_minres, 1); // http://www.singular.uni-kl.de/Manual/latest/sing_344.htm#SEC383
2229    system("install","SRES","list", SRES_list, 1); // will never work :(((
2230
2231//    exportto(Top, s_res); //   Syzextra::GetInducedData);
2232
2233    if( @DEBUG )    {      listvar(Top);      listvar(Schreyer);    }
2234  }
2235}
2236
2237
2238static proc testallSexamples()
2239{
2240  example Ssyz;
2241  example Scontinue;
2242  example Sres; 
2243}
2244
2245static proc testallSSexamples()
2246{
2247  example SSsyz;
2248  example SScontinue;
2249  example SSres; 
2250}
2251example
2252{ "EXAMPLE:"; echo = 2;
2253  testallSexamples();
2254  testallSSexamples();
2255}
2256
2257static proc  StartResTesting(list #)
2258{
2259  int @treeout = attrib(SSinit, "TREEOUTPUT");
2260 
2261  if( defined(@save_res_list) )
2262  { ERROR("Sorry: existing global variable @save_res_list - run StopAddResTesting before another Start!!!"); }
2263 
2264  string @save_res_desc = string(#);
2265 
2266  if( !@treeout )
2267  {
2268    ">>>>>>>>> {{{{{{{{{ STARTING TESTING ('" + @save_res_desc + "') :::::::::::: ";
2269  } else
2270  {
2271    "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
2272  }
2273 
2274  list @save_res_list = list();
2275  export @save_res_list;
2276  export @save_res_desc;
2277}
2278
2279static proc  StopResTesting()
2280{
2281  int @treeout = attrib(SSinit, "TREEOUTPUT");
2282 
2283  if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
2284  { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }
2285
2286  if( !defined(@save_res_list) || !defined(@save_res_desc) )
2287  { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }
2288
2289  int i, j;
2290  int f = 0;
2291  def m, mm;
2292
2293  if( !@treeout )
2294  {
2295  for (i = size(@save_res_list); i > 0; i--)
2296  {
2297    "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];
2298  }
2299 
2300  }
2301 
2302  for (i = size(@save_res_list); i > 1; i--)
2303  {
2304    m = @save_res_list[i][4];
2305   
2306    for (j = i-1; j > 0; j--)
2307    {
2308      mm = @save_res_list[j][4];
2309      if( (nrows(m) != nrows(mm)) || (ncols(m) != ncols(mm)) )
2310      {
2311        "ERROR: SIZE(Betti[j: ", j, "]) != SIZE(Betti[i: ", i, "]):";
2312        "j: ", j;
2313        print( @save_res_list[j][4], "betti");
2314        print(@save_res_list[j]);
2315       
2316        "i: ", i;
2317        print( @save_res_list[i][4], "betti");
2318        print(@save_res_list[i]);
2319
2320        f = 1;
2321
2322      } else
2323      {
2324        if( m != mm )
2325        {
2326          "ERROR: Betti[j: ", j, "] != Betti[i: ", i, "]:";
2327          "j: ", j;
2328          print( @save_res_list[j][4], "betti");
2329          print(@save_res_list[j]);
2330
2331          "i: ", i;
2332          print( @save_res_list[i][4], "betti");
2333          print(@save_res_list[i]);
2334
2335          f = 1;
2336        };
2337      };
2338 
2339    };
2340 
2341  };
2342 
2343  if( f )
2344  {
2345    print(@save_res_list);
2346    "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
2347   
2348    "ERROR: There were some wrong betti numbers... ";
2349//      Syzextra::m2_end(666);   
2350  } else
2351  {
2352    if( !@treeout )
2353    {
2354      "BETTI: "; print( @save_res_list[1][4], "betti");
2355    }
2356  }
2357
2358  kill @save_res_list;
2359   
2360  if( !@treeout )
2361  {
2362    "<<<<<<<<< }}}}}}}}}  STOP TESTING (", @save_res_desc,  ") !!!!!!!!!!!! ";
2363  } else
2364  {
2365//    "{ \"Example\": \"" + @save_res_desc + "\", \"computations\": [";
2366    "] },";
2367  }
2368  kill @save_res_desc;
2369}
2370
2371static proc StartAddResTest(string method, string desc)
2372{
2373  int @treeout = attrib(SSinit, "TREEOUTPUT");
2374 
2375  if( !defined(@save_res_list) )
2376  { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); }
2377
2378  if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) )
2379  { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); }
2380 
2381 
2382  def @save_opts = option(get); export @save_opts;
2383  def @save_method = method; export @save_method;
2384  def @save_desc = desc; export @save_desc;
2385 
2386  if( !@treeout )
2387  {
2388    "< START RES TEST{{{ ", @save_method, ", with:", @save_desc, " ... ";
2389  } else
2390  {
2391//    Print("{ \"RESOLUTION: HYBRIDNF:%d, TAILREDSYZ: %d, LEAD2SYZ: %d, IGNORETAILS: %d\": [\n",
2392//       attributes.__HYBRIDNF__, attributes.__TAILREDSYZ__, attributes.__LEAD2SYZ__, attributes.__IGNORETAILS__);
2393    " { \"RESOLUTION: " + @save_method + ", with: " + @save_desc + "\": [";
2394  }
2395}
2396
2397
2398static proc StopAddResTest(def RR, intmat S, int @t, int @m)
2399{
2400  int @treeout = attrib(SSinit, "TREEOUTPUT");
2401 
2402  if( !(defined(@save_opts) && defined(@save_method) && defined(@save_desc)) )
2403  { ERROR("Sorry: no global variables - run StartAddResTest beforehand!!!"); }
2404
2405  list @l = list(@save_method, @save_desc, option(get), S, @t, @m);
2406 
2407//  RR, 
2408//  print(S, "betti");
2409 
2410  if( !@treeout )
2411  {
2412    "> -STOP RES TEST}}} ", @save_method, ", with:", @save_desc, ", Timer:", @t; option();
2413  } else
2414  {
2415    " ] },";
2416  }
2417
2418 
2419  option(set, @save_opts); kill @save_opts;
2420
2421  kill @save_method; kill @save_desc;
2422 
2423  @save_res_list[1 + size(@save_res_list)] = @l;
2424}
2425
2426
2427static proc SCheck(def S)
2428{
2429  setring S; // for checking...
2430
2431  module M = MRES;
2432  if( ncols(M) < nrows(M) )
2433  {
2434    M[nrows(M)] = 0;
2435  } else
2436  {
2437    M = transpose(M);
2438    if( ncols(M) < nrows(M) )
2439    {
2440      M[nrows(M)] = 0;
2441    }
2442    M = transpose(M);
2443  }
2444
2445  if( nrows(M) != ncols(M) )
2446  {
2447    "ERROR: non-square M!!!";
2448      Syzextra::m2_end(666);
2449  }
2450
2451  if( size(module( M*M )) > 0 )
2452  {
2453    "ERROR: module( M*M ) != 0!!!";
2454    module( M*M );
2455
2456    "MRES': "; M; print(M);
2457
2458      Syzextra::m2_end(666);
2459  }
2460//  "MRES': "; M; print(M);
2461
2462  if( size(RES[1]) != 0 )
2463  {
2464    "ERROR: wrong starting zero module!!!";
2465      Syzextra::m2_end(666);
2466  }
2467
2468//  RES;
2469/* 
2470  MRES;
2471  RES;
2472  "";
2473  LRES;
2474  "";
2475  TRES;
2476*/ 
2477}
2478
2479//// TODO: SSres(0) fails..!!!??
2480static proc TestSSres(def I)
2481{
2482  def save = basering;
2483  int @t,@m,r,rr,i;
2484  string name =
2485    "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
2486    ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
2487    ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));
2488
2489  int @PROFILE = attrib(SSinit, "PROFILE");
2490  if(@PROFILE){ string @prof = "SSres_" + @save_res_desc + "_" + name + ".prof"; }
2491
2492  StartAddResTest(
2493   "SSres",
2494   "minres + betti(,1) + mods: {" + name + "}"
2495  );
2496 
2497  option(redSB); option(redTail);
2498  if(@PROFILE){  Syzextra::ProfilerStart(@prof);}
2499  timer=0;rtimer=0;def R=SSres(I,0);@m=rtimer;
2500  if(@PROFILE){  Syzextra::ProfilerStop();}
2501  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;
2502//    Syzextra::DetailedPrint(RR,0);
2503  SCheck(R);
2504  StopAddResTest(RR, S, @t,@m);
2505  kill S, RR; setring save; kill R;
2506}
2507
2508proc s_res(def I, int l)
2509"USAGE:  s_res(ideal/module M, int len)
2510RETURN:  resolution object or SRES
2511PURPOSE: compute a Schreyer resolution of M of length at most len (see [BMSS])
2512NOTE:    If given len is zero then nvars(basering) + 1 is used instead.
2513@* This functions is not related to other helpers from this library.
2514@* One can switch on computation protocol and statistic (depending on the build) by setting the @code{prot} option.
2515@* Further recognized switches are the following attributes of @code{Schreyer::SSinit} procedure:
2516LEAD2SYZ, TAILREDSYZ, HYBRIDNF
2517DEBUG, ...
2518SEE ALSO: sres
2519EXAMPLE: example s_res; shows an example
2520"
2521{
2522  int @prot = (find(option(),"prot") != 0) && (defined(  Syzextra::NumberStatsInit)) && (defined(  Syzextra::NumberStatsPrint));
2523  def @save = basering;
2524 
2525  int @RINGCHANGE = 0;
2526
2527  if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
2528  {
2529    @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
2530  }
2531 
2532  def R=SSinit(I);
2533  if( @RINGCHANGE ){ setring R; }
2534 
2535  int @l = size(RES);
2536  if(@prot){   Syzextra::NumberStatsInit(); }
2537  def rsltn =   Syzextra::ComputeResolution(RES[@l], LRES[@l], TRES[@l], l);
2538  if(@prot){   Syzextra::NumberStatsPrint("Number statistic for s_res with   Syzextra::ComputeResolution"); }
2539 
2540  if( !@RINGCHANGE )
2541  {
2542    return (rsltn); // ret
2543  }
2544 
2545  SRES ret; ret.r = R; ret.rsltn = rsltn; 
2546  return (ret);
2547}
2548example
2549{ "EXAMPLE:"; echo = 2;
2550  ring R;
2551  module M = maxideal(1); M;
2552  def  rs = s_res(M, 0);
2553  print(rs);
2554  print(betti(rs, 0)); // non-minimal betties
2555  print(SRES_list(rs));
2556  print(betti(rs, 1)); //minimal betties
2557  print(minres(rs));
2558}
2559
2560static proc s_res_bm(def I)
2561{
2562  int @prot = (find(option(),"prot") != 0) && (defined(  Syzextra::NumberStatsInit)) && (defined(  Syzextra::NumberStatsPrint));
2563  def @save = basering;
2564 
2565  int @RINGCHANGE = 0;
2566
2567  if( typeof( attrib(SSinit, "RINGCHANGE") ) == "int" )
2568  {
2569    @RINGCHANGE = attrib(SSinit, "RINGCHANGE");
2570  }
2571  int t,tt,sum;
2572 
2573t=rtimer;def R=SSinit(I);tt=rtimer;
2574
2575  "%% Setup(SSinit) TIME:", tt - t; // if(@prot){ } ?
2576  int sum = (tt-t);
2577
2578  if( @RINGCHANGE ){ setring R; }
2579 
2580  int @l = size(RES);
2581  module N, L, T, LL, TT;
2582  L = LRES[@l];
2583  T = TRES[@l];
2584
2585 
2586  int ss = attrib(basering, "SYZNUMBER");
2587 
2588  while ( 1 )
2589  {
2590    if(@prot){   Syzextra::NumberStatsInit(); }
2591
2592//  SSstep():
2593t=rtimer;(N,LL,TT)=SSComputeSyzygy(L,T);tt=rtimer;
2594   
2595    @l = @l + 1;
2596    if(@prot){   Syzextra::NumberStatsPrint("Number statistic for SSComputeSyzygy["+string(@l-2)+"]"); }
2597    "%% SSstep[",@l-2, "] TIME:", tt - t;  // if(@prot){ } ?
2598    sum = sum + (tt-t);
2599   
2600    if( (size(LL) == 0) || (size(N) == 0) ) { break; }
2601    L = LL; T = TT; RES[@l] = N; // LRES[@l] = LL; TRES[@l] = TT;
2602
2603    ss = ss + 1; attrib(basering, "SYZNUMBER", ss );   
2604  }
2605 
2606  "%% Whole Resolution (with "+string(@l)+"syzygies) TIME:", sum;  // if(@prot){ } ?
2607  resolution rsltn = list(RES[2..size(RES)]);
2608 
2609  if( !@RINGCHANGE )
2610  {
2611    return (rsltn); // ret
2612  }
2613 
2614  SRES ret; ret.r = R; ret.rsltn = rsltn;
2615  return (ret);
2616}
2617
2618
2619static proc s_syz(def I)
2620{
2621  def R=SSinit(I); setring R;
2622  int @l = size(RES); //   def M =  RES[@l];
2623  module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(LRES[@l], TRES[@l]);
2624  SSYZ ret; ret.r = R; ret.szg = N; // Schreyer::  Syzextra::ComputeResolution(RES[2], LRES[2], TRES[2], 0);
2625  return (ret);
2626}
2627
2628static proc TestSSSres(def I)
2629{
2630  def save = basering;
2631  int @t,@m,r,rr,i;
2632  string name =
2633    "LEAD2SYZ:"  +string(attrib(SSinit,"LEAD2SYZ")) +
2634    ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) +
2635    ",HYBRIDNF:"  +string(attrib(SSinit,"HYBRIDNF"));
2636
2637  int @PROFILE = attrib(SSinit, "PROFILE");
2638  if(@PROFILE){ string @prof = "SSSres_" + @save_res_desc + "_" + name + ".prof"; }
2639
2640  StartAddResTest(
2641   "SSSres",
2642   "minres + betti(,1) + mods: {" + name + "}"
2643  );
2644 
2645  option(redSB); option(redTail);
2646  if(@PROFILE){  Syzextra::ProfilerStart(@prof);}
2647  timer=0;rtimer=0;def R=SSinit(I);setring R;def RR=  Syzextra::ComputeResolution(RES[2], LRES[2], TRES[2], 0);
2648@m=rtimer;
2649  if(@PROFILE){  Syzextra::ProfilerStop();}
2650RR=minres(RR); def S=betti(RR,1);@t=rtimer;
2651//    Syzextra::DetailedPrint(RR,0);  print(RR);  print(S, "betti");
2652  SCheck(R);
2653  StopAddResTest(RR, S, @t,@m);
2654  kill S, RR; setring save; kill R;
2655}
2656
2657
2658static proc TestSres(def I)
2659{
2660  def save = basering;
2661  int @t,r,rr,i,@m;
2662  StartAddResTest(
2663  "Sres",
2664  "minres + betti(,1)"
2665  );
2666  option(redSB); option(redTail);
2667  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;
2668  SCheck(R);
2669  StopAddResTest(RR, S, @t,@m); 
2670  kill S, RR; setring save; kill R;
2671}
2672
2673
2674static proc Testsres(def M)
2675{
2676  int @t,@m;
2677  StartAddResTest("sres", "no minres + betti(,1)");
2678  option(redSB);option(redTail);
2679  timer=0;rtimer=0;def RR=sres(groebner(M),0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
2680  StopAddResTest(RR, S, @t,@m); kill S, RR;
2681}
2682
2683static proc Testlres(def M)
2684{
2685  int @t,@m;
2686  StartAddResTest("lres", "no minres + betti(,1)");
2687  option(redSB);option(redTail);
2688  timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
2689  StopAddResTest(RR, S, @t,@m); kill S, RR;
2690
2691  StartAddResTest("lres", "minres + betti()");
2692  option(redSB);option(redTail);
2693  timer=0;rtimer=0;def RR=lres(M,0);@m=rtimer;def S=betti(minres(RR));@t=rtimer;
2694  StopAddResTest(RR, S, @t,@m);
2695  kill S, RR;
2696}
2697
2698
2699static proc Testnres(def M)
2700{
2701  int @t,@m;
2702  StartAddResTest("nres", "no minres + betti(,1)");
2703 
2704  option(redSB); option(redTail);
2705  timer=0;rtimer=0;def RR=nres(M,0);@m=rtimer;def S=betti(RR,1);@t=rtimer;
2706 
2707  StopAddResTest(RR, S, @t,@m); kill S, RR;
2708}
2709
2710static proc TestSSresAttribs(def M, list #)
2711{
2712  M = groebner(M);
2713 
2714  StartResTesting(#);
2715
2716  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
2717  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);
2718
2719 // WRONG???! LEAD2SYZ?
2720//  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
2721//  attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSSres(M);
2722
2723  int @treeout = attrib(SSinit, "TREEOUTPUT");
2724  if( !@treeout )
2725  {
2726   Testlres(M); Testnres(M);
2727//   Testsres(M); //   TestSres(M); // too long for the last medium test :(
2728  }
2729 
2730  StopResTesting();
2731}
2732
2733static proc TestSSresAttribs2tr(def M, list #)
2734{
2735  M = groebner(M);
2736 
2737  StartResTesting(#);
2738 
2739  attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSSres(M);
2740  Testlres(M); 
2741
2742  StopResTesting();
2743}
2744
2745static proc testSimple(list #)
2746{
2747  def DEBUG = 0;
2748  if(size(#) > 0) { DEBUG = #[1]; }
2749
2750  system("--min-time", "0.01");
2751  system("--ticks-per-sec", 100);
2752
2753//  option(prot);
2754
2755  // TODO: only for now!!
2756  attrib(SSinit, "DEBUG", (DEBUG > 0) );
2757  attrib(SSinit, "SYZCHECK", (DEBUG > 0) );
2758  attrib(SSinit, "KERCHECK", (DEBUG > 0) );
2759
2760  attrib(SSinit, "TREEOUTPUT", 0);
2761  attrib(SSinit, "PROFILE", 0);
2762  attrib(SSinit, "IGNORETAILS", 0); // not only frame
2763
2764  int @treeout = attrib(SSinit, "TREEOUTPUT");
2765 
2766  if( @treeout)
2767  {
2768    monitor("SimpleTests.json", "o");
2769    "{ \"SimpleTests\": [";
2770  } else { option(prot); }
2771 
2772
2773  ring r; ideal M = maxideal(1);
2774  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2775  kill r;
2776
2777  ring r = 0, (a, b, c, d), lp; ideal M = maxideal(1);
2778  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2779  kill r;
2780
2781  ring R = 0, (w, x, y, z), dp;
2782  ideal M = w^2 - x*z,  w*x - y*z,  x^2 - w*y, x*y - z^2, y^2 - w*z;
2783  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2784  kill R;
2785
2786
2787  ring r = 0, (a, b, c, d, e, f), dp; ideal M = maxideal(1);
2788  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2789  kill r; 
2790
2791
2792  ring r = 0, (x, y), lp; ideal M = x2, xy, y2;  // Schreyer conterexample???
2793  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2794  kill r;
2795
2796  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?
2797  TestSSresAttribs(M, "\\\\GENERATED{" + string(M) + "} in " + string(basering));
2798  kill r;
2799
2800 
2801  ring AGR = (101), (a, b, c, d), dp;
2802  // simple: AGR@101n3d002s004%1:
2803  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;
2804  TestSSresAttribs(M, "simple: AGR@101n3d002s004%1");
2805
2806  // medium: AGR@101n3d004s009%1;
2807  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;
2808  TestSSresAttribs(M, "medium: AGR@101n3d004s009%1");
2809
2810  if( @treeout)
2811  {
2812    "] }";
2813    monitor("");
2814  }
2815
2816}
2817
2818static proc testAGR(list #)
2819{
2820  def DEBUG = 0;
2821  if(size(#) > 0) { DEBUG = #[1]; }
2822
2823  system("--min-time", "0.01");
2824  system("--ticks-per-sec", 100);
2825
2826  attrib(SSinit, "DEBUG", 0);
2827  attrib(SSinit, "SYZCHECK", (DEBUG > 0));
2828  attrib(SSinit, "KERCHECK", 0);
2829  attrib(SSinit, "TREEOUTPUT", 0);
2830  attrib(SSinit, "PROFILE", 0);
2831  attrib(SSinit, "IGNORETAILS", 0); // not only frame
2832 
2833  option(prot);
2834
2835  ring AGR = (101), (a, b, c, d), dp; AGR;
2836  // lengthy: AGR@101n3d008s058%3, kernel only!
2837  ideal M = 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2838  TestSSresAttribs2tr(M, "AGR@101n3d008s058%3");
2839
2840  // AGR@101n3d010s010%3, a bit slower...
2841  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;
2842  TestSSresAttribs2tr(M, "AGR@101n3d010s010%3"); 
2843  kill AGR;
2844
2845  ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR;
2846  // AGR@101n7d005s010%2, medium: <= 2
2847  ideal M =
2848f*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,
2849b^5+17*h^5,a^5+17*h^5,h^6;
2850  TestSSresAttribs2tr(M, "AGR@101n7d005s010%2");
2851  kill AGR;
2852
2853// from Andreas...tooo long!?
2854
2855  ring AGR = (101), (a,b,c,d,e), dp; AGR;
2856
2857  // AGR101n4d007s021%4
2858  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,
2859a*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,
2860a^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,
2861a^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,
2862b^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,
2863a*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,
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2865a^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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2872a^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,
2873b^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,
2874a*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,
2875a^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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2882b^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,
2883a*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,
2884a^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,
2885a^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,
2886a^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,
2887a^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,
2888e^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,
2889b*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,
2890a*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,
2891c^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,
2892a*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,
2893c^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,
2894c^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,
2895b^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,
2896b^2*c^2*e^2, a*b*c^2*e^2;
2897  TestSSresAttribs2tr(M, "AGR101n4d007s021%4");
2898/*
2899options:  1 1 0 :  Time:  5/9/10 (35 without LCM)
2900options:  1 1 1 :  Time:  6/8/25
2901lres  Time:  5
2902nres  Time:  5
2903sres  Time:  693
2904*/
2905
2906  kill M;
2907
2908
2909
2910  // AGR101n4d008s020%1, too big?
2911  ideal M =
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2958a^4*b^2-31*a^4*d^2+30*a^3*b*d^2-42*a^2*b^2*d^2-32*a*b^3*d^2-38*b^4*d^2-49*a^3*c*d^2-4*a^2*b*c*d^2-45*a*b^2*c*d^2+8*b^3*c*d^2+44*a^2*c^2*d^2+21*a*b*c^2*d^2-13*b^2*c^2*d^2-16*a*c^3*d^2+31*b*c^3*d^2-42*c^4*d^2+49*a^3*d^3+44*a^2*b*d^3+a*b^2*d^3+47*b^3*d^3-31*a^2*c*d^3+42*a*b*c*d^3-34*b^2*c*d^3-44*a*c^2*d^3-3*b*c^2*d^3-14*c^3*d^3+24*a^2*d^4+12*a*b*d^4+14*b^2*d^4-32*a*c*d^4+16*b*c*d^4+40*c^2*d^4+8*a*d^5+5*b*d^5+35*c*d^5+2*d^6+7*a^5*e+a^4*b*e-24*a^3*b^2*e-25*a^2*b^3*e-8*a*b^4*e-46*b^5*e+12*a^4*c*e-49*a^3*b*c*e+47*a^2*b^2*c*e-22*a*b^3*c*e-22*b^4*c*e+31*a^3*c^2*e-48*a^2*b*c^2*e-46*a*b^2*c^2*e+28*b^3*c^2*e-5*a^2*c^3*e+42*a*b*c^3*e-9*b^2*c^3*e+13*a*c^4*e+23*b*c^4*e-29*c^5*e+9*a^4*d*e+9*a^3*b*d*e+3*a^2*b^2*d*e+47*a*b^3*d*e+31*b^4*d*e-25*a^3*c*d*e-37*a*b^2*c*d*e-23*b^3*c*d*e+18*a^2*c^2*d*e+8*a*b*c^2*d*e-15*b^2*c^2*d*e-40*a*c^3*d*e+26*b*c^3*d*e-29*c^4*d*e+20*a^3*d^2*e-25*a^2*b*d^2*e+41*a*b^2*d^2*e+10*b^3*d^2*e-12*a^2*c*d^2*e+38*a*b*c*d^2*e-30*b^2*c*d^2*e-49*b*c^2*d^2*e-34*c^3*d^2*e+14*a^2*d^3*e+45*a*b*d^3*e-29*b^2*d^3*e-23*a*c*d^3*e+33*b*c*d^3*e-23*c^2*d^3*e-36*a*d^4*e+29*b*d^4*e+22*c*d^4*e+45*d^5*e-46*a^4*e^2-37*a^3*b*e^2-36*a^2*b^2*e^2-23*a*b^3*e^2-4*b^4*e^2+31*a^3*c*e^2+45*a^2*b*c*e^2-34*a*b^2*c*e^2+6*b^3*c*e^2-38*a^2*c^2*e^2-26*a*b*c^2*e^2-5*b^2*c^2*e^2-24*a*c^3*e^2-28*b*c^3*e^2+20*c^4*e^2+25*a^3*d*e^2+14*a^2*b*d*e^2+a*b^2*d*e^2+18*b^3*d*e^2+12*a^2*c*d*e^2+32*a*b*c*d*e^2+17*b^2*c*d*e^2+50*a*c^2*d*e^2-12*b*c^2*d*e^2-46*c^3*d*e^2+4*a^2*d^2*e^2-29*a*b*d^2*e^2-16*b^2*d^2*e^2+38*a*c*d^2*e^2+3*b*c*d^2*e^2-19*c^2*d^2*e^2+50*a*d^3*e^2+23*b*d^3*e^2+5*c*d^3*e^2+47*d^4*e^2-38*a^3*e^3-31*a^2*b*e^3+14*a*b^2*e^3-43*b^3*e^3+22*a^2*c*e^3+26*a*b*c*e^3-28*b^2*c*e^3-49*a*c^2*e^3+15*c^3*e^3-40*a^2*d*e^3+5*a*b*d*e^3-20*b^2*d*e^3-40*a*c*d*e^3+35*b*c*d*e^3+17*c^2*d*e^3-8*a*d^2*e^3-6*b*d^2*e^3+3*c*d^2*e^3-7*d^3*e^3+45*a^2*e^4-49*a*b*e^4+45*b^2*e^4-25*a*c*e^4+b*c*e^4-33*c^2*e^4-44*a*d*e^4+30*b*d*e^4-26*c*d*e^4+42*d^2*e^4+14*b*e^5-3*c*e^5-47*d*e^5+22*e^6,
2959a^5*b-48*a^4*d^2-33*a^3*b*d^2-34*a^2*b^2*d^2-14*a*b^3*d^2-29*b^4*d^2-7*a^3*c*d^2-13*a^2*b*c*d^2+15*a*b^2*c*d^2+27*b^3*c*d^2+49*a^2*c^2*d^2-a*b*c^2*d^2+46*b^2*c^2*d^2+37*a*c^3*d^2+20*b*c^3*d^2-27*c^4*d^2+33*a^3*d^3+30*a^2*b*d^3+32*a*b^2*d^3+b^3*d^3-47*a^2*c*d^3-2*a*b*c*d^3-36*b^2*c*d^3-7*a*c^2*d^3-23*b*c^2*d^3-41*c^3*d^3-43*a^2*d^4-4*a*b*d^4+14*b^2*d^4+38*a*c*d^4+41*b*c*d^4+27*c^2*d^4-33*a*d^5-50*b*d^5+8*c*d^5+42*d^6-21*a^5*e+46*a^4*b*e+6*a^3*b^2*e+22*a^2*b^3*e+2*a*b^4*e-15*b^5*e+50*a^4*c*e-40*a^2*b^2*c*e+49*a*b^3*c*e+5*b^4*c*e+a^3*c^2*e+47*a^2*b*c^2*e-36*a*b^2*c^2*e+25*b^3*c^2*e-36*a^2*c^3*e+46*a*b*c^3*e+24*b^2*c^3*e-9*a*c^4*e+39*b*c^4*e-40*c^5*e+29*a^4*d*e-49*a^3*b*d*e+16*a^2*b^2*d*e+7*a*b^3*d*e-30*b^4*d*e+42*a^3*c*d*e+22*a^2*b*c*d*e-49*a*b^2*c*d*e+19*b^3*c*d*e-23*a^2*c^2*d*e+7*a*b*c^2*d*e+2*b^2*c^2*d*e-2*a*c^3*d*e-2*b*c^3*d*e+5*c^4*d*e+35*a^3*d^2*e-47*a^2*b*d^2*e-28*a*b^2*d^2*e+5*b^3*d^2*e+45*a^2*c*d^2*e+7*a*b*c*d^2*e+3*b^2*c*d^2*e+33*a*c^2*d^2*e-37*b*c^2*d^2*e+26*c^3*d^2*e-18*a*b*d^3*e-42*b^2*d^3*e-22*a*c*d^3*e-46*b*c*d^3*e-25*c^2*d^3*e+6*a*d^4*e-50*b*d^4*e+22*c*d^4*e-4*d^5*e-42*a^4*e^2+43*a^3*b*e^2+39*a^2*b^2*e^2+12*a*b^3*e^2-20*b^4*e^2+2*a^3*c*e^2+27*a^2*b*c*e^2-21*a*b^2*c*e^2+36*b^3*c*e^2+47*a^2*c^2*e^2-41*a*b*c^2*e^2-23*b^2*c^2*e^2+34*a*c^3*e^2-29*b*c^3*e^2-46*c^4*e^2+15*a^3*d*e^2+4*a^2*b*d*e^2-13*a*b^2*d*e^2+43*b^3*d*e^2-7*a^2*c*d*e^2+4*a*b*c*d*e^2-37*a*c^2*d*e^2-34*b*c^2*d*e^2+20*c^3*d*e^2-5*a^2*d^2*e^2-42*a*b*d^2*e^2+14*b^2*d^2*e^2+9*a*c*d^2*e^2-19*b*c*d^2*e^2+15*c^2*d^2*e^2-35*a*d^3*e^2+24*b*d^3*e^2-35*c*d^3*e^2-14*d^4*e^2-27*a^3*e^3-39*a^2*b*e^3-44*a*b^2*e^3-6*b^3*e^3-30*a^2*c*e^3+47*a*b*c*e^3-26*b^2*c*e^3+9*a*c^2*e^3+16*b*c^2*e^3+37*c^3*e^3-49*a^2*d*e^3+19*a*b*d*e^3+44*b^2*d*e^3-9*a*c*d*e^3-41*b*c*d*e^3+29*c^2*d*e^3-43*a*d^2*e^3+33*b*d^2*e^3-2*c*d^2*e^3-15*d^3*e^3-4*a^2*e^4-46*a*b*e^4+15*b^2*e^4+21*a*c*e^4+13*b*c*e^4+38*c^2*e^4-20*a*d*e^4+16*b*d*e^4-9*c*d*e^4-19*d^2*e^4+14*a*e^5-33*b*e^5+34*c*e^5+16*d*e^5-24*e^6,
2960a^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,
2961e^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,
2962b*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,
2963a*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,
2964c^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,
2965a*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,
2966c^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,
2967c^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,
2968b^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,
2969b^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,
2970a^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,
2971c*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,
2972b^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,
2973a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2;
2974//  M;
2975  TestSSresAttribs2tr(M, "AGR101n4d008s020%1_big");
2976/*
2977options:  1 1 0 :  Time:  29/32/73/92 (316 without LCM)
2978options:  1 1 1 :  Time:  32/34/43/202
2979lres  Time:  24
2980nres  Time:  19
2981sres  Time:  71
2982*/
2983  kill M;
2984
2985  kill AGR;
2986
2987  ring AGR = (101), (a,b,c,d,e,f), dp; AGR;
2988
2989  // AGR@101n5d005s016%1, new, medium difficulty?
2990  ideal M =
2991b*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;
2992  TestSSresAttribs(M, "AGR@101n5d005s016%1");
2993  kill M;
2994}
2995
2996static proc testAGRhard(list #)
2997{
2998  def DEBUG = 0;
2999  if(size(#) > 0) { DEBUG = #[1]; }
3000
3001  system("--min-time", "0.01");
3002  system("--ticks-per-sec", 100);
3003
3004  attrib(SSinit, "DEBUG", 0);
3005  attrib(SSinit, "SYZCHECK", (DEBUG > 0));
3006  attrib(SSinit, "KERCHECK", 0);
3007  attrib(SSinit, "TREEOUTPUT", 0);
3008  attrib(SSinit, "PROFILE", 0);
3009 
3010  option(prot);
3011  // AGR@101n5d006s016%1, new, hard
3012  ring AGR = (101), (a,b,c,d,e,f), dp; AGR;
3013  ideal M =
3014b*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;
3015  TestSSresAttribs2tr(M, "AGR@101n5d006s016%1_hard");
3016 kill M;
3017}
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