Changeset b9e63ba in git


Ignore:
Timestamp:
Feb 25, 2015, 1:51:29 PM (9 years ago)
Author:
Stephan Oberfranz <oberfran@…>
Branches:
(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
Children:
3976a5439418cd59683afac7809600f096099116
Parents:
36f0e5d294efb13b51fa672bf63ba263b67ef8b3f38979192ecdeb2303d71c85143896a67a0ca639
Message:
update

Merge branch 'spielwiese' of github.com:Singular/Sources into spielwiese
Files:
9 added
36 edited

Legend:

Unmodified
Added
Removed
  • Singular/LIB/gradedModules.lib

    r36f0e5 rb9e63ba  
    11///////////////////////////////////////////////////////////////////////////
    22version="version gradedModules.lib 4.0.1.1 Jan_2015 "; // $Id$
    3 category="General purpose?";
     3category="Commutative Algebra";
    44info="
    55LIBRARY: gradedModules.lib     Operations with graded modules/matrices/resolutions
    66AUTHORS:  Oleksandr Motsak <U@D>, where U=motsak, D=mathematik.uni-kl.de
    7 @*         Hanieh Keneshlou <hkeneshlou@yahoo.com>
     7@*        Hanieh Keneshlou <hkeneshlou@yahoo.com>
    88KEYWORDS: graded modules, graded homomorphisms, syzygies
    99OVERVIEW:
    10     The library contains several procedures for operations with graded modules/matrices/resolutions
    11     TODO!
     10    The library contains several procedures for constructing and manipulating graded modules/matrices/resolutions.
     11NOTE:
     12    set assumeLevel to positive integer value in order to auto-check all assumptions.
    1213REFERENCES:
    1314[MO]   Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related
    14        structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010 TODO!?
     15       structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010
    1516PROCEDURES:
    1617    grzero()        presentation of basering(0)^1
     
    3637static proc pad(int m, string s, string c){ string r = s; while( size(r) < m ){ r = c + r; } return(r); }
    3738static proc mstring( int m, string c){ if( m < 0 ) { return (c); }; return (string(m)); }
    38 static proc zstring( int m, int b, string c){ if(b) { return (c); }; return (string(m)); }
    3939// view helper
    40 static proc draw ( intmat D, intvec zc, int d )
     40static proc draw ( intmat D, int d )
    4141{
    4242//  print(D); return ();
     
    5050  {
    5151    head = head + pad(max, string(D[1 , c]), " ") + " ";
    52     foot = foot + pad(max, zstring(D[nr, c], zc[c - d], "?"), " ") + " ";
     52    foot = foot + pad(max, string(D[nr, c]), " ") + " ";
    5353  }
    5454  // last head/foot enties:
    5555  head = head + pad(max, string(D[1 , c]), " ");
    56   foot = foot + pad(max, zstring(D[nr, c], zc[c-d], "?"), " ");
     56  foot = foot + pad(max, string(D[nr, c]), " ");
    5757  // head/foot dash lines:
    5858  string dash  = repeat( (max + 1) * (nc - 2*d) , "-");
     
    7474}
    7575
    76 proc grview(def N)
    77 "
    78 PURPOSE: print the degree/grading data about the GRADED matrix/module/ideal N
     76proc grview(N)
     77"USAGE:  grview(M), graded object M
     78RETURN:  nothing
     79PURPOSE: print the degree/grading data about the GRADED matrix/module/ideal/mapping object M             
     80ASSUME:  M must be graded
     81EXAMPLE: example grsum; shows an example
    7982"
    8083{
     
    8992//  typeof( N ) ;  attrib( N );  attrib(N, "isHomog");
    9093
    91   ASSUME(0, /* input must be graded! */ typeof(attrib(N, "isHomog")) == "intvec" );
    92 
    9394  // input should be graded:
    94   intvec gr = attrib(N, "isHomog"); // grading weights?
    95   ASSUME(0, /* input must be correctly graded! */ nrows(N) == size(gr) );
    96 
    97 //  intvec gr = attrib( N, "isHomog" ); //  module(N); "grading: ", gr;
    98 
     95  ASSUME(1, grtest(N) );
     96 
     97  intvec G = grdeg(N);
    9998  matrix M = module(N);
     99 
    100100  int nc = ncols(M); int nr = nrows(M);
    101101  int r,c;
     
    103103  intmat D[nr+2*d][nc+2*d];
    104104
    105   module L = module(N); L = lead(L); vector v;
    106   int m = 1 + nvars(basering);
    107   intvec zc = 0:nc;
    108105  for( c = nc; c > 0; c-- )
    109106  {
    110107    D[1, c+d] = c; // top row indeces
    111     v = L[c];
    112     if( v != 0 )
    113     {
    114       D[nr+2*d, c+d] = deg(v) + gr[ leadexp(v)[m] ]; // bottom row with computed column induced degrees
    115     } else
    116     {
    117 //      D[nr+2*d, c+d] = 0; // TODO: 0/-1 is valid :(
    118       zc[c] = 1;
    119     }
    120   }
     108    D[nr+2*d, c+d] = G[c]; // deg(v) + gr[ leadexp(v)[m] ]; // bottom row with computed column induced degrees
     109  }
     110
     111  intvec gr = attrib(N, "isHomog"); // grading weights?
    121112
    122113  for( r = nr; r > 0; r-- )
     
    129120    D[r+d, nc+2*d] = r; // right-most block with indeces
    130121  }
    131   draw(D, zc, d); // print it nicely!
     122  draw(D, d); // print it nicely!
    132123}
    133124
     
    200191
    201192// Q@Wolfram: what should be done with zero gens!?
    202 proc grdeg( def M, list # )
    203 "graded degrees of gens(i.e. columns)"
    204 {
    205  // use initial grading if given
    206   if( size(#) == 1 )
    207   {
    208     def w = #[1];
    209     if( typeof(w) == "intvec" )
    210     {
    211       if( nrows(M) == size(w) )
    212       {
    213         attrib(M, "isHomog", w);
    214       }
    215     }
    216     kill w;
    217   }
    218 
     193proc grdeg(M)
     194"USAGE:  grdeg(M), graded object M
     195RETURN:  intvec of degrees
     196PURPOSE: graded degrees of columns (generators) of M
     197ASSUME:  M must be a graded object (matrix/module/ideal/mapping)
     198NOTE:    if M has zero cols it shoud have attrib(M,'degHomog') set.
     199EXAMPLE: example grsum; shows an example
     200"
     201{           
    219202  ASSUME(1, grtest(M) );
    220203
     204  if ( typeof(attrib(M, "degHomog")) == "intvec" )
     205  {   
     206    intvec t = attrib(M, "degHomog"); // graded degrees
     207    ASSUME(0, ncols(M) == size(t) );
     208
     209    return (t);
     210  }
     211 
     212  ASSUME(0, ncols(M) == size(M) );
     213 
    221214  def w = attrib(M, "isHomog"); // grading weights?
    222215
     
    230223  intvec c = leadexp(L[1..m])[n]; // their module-components
    231224
    232   w = intvec(-6665, w); // 0?????
    233   intvec gr = w[1+c]; // weights
     225//   w = intvec(-6665), w; // 0?????
     226  intvec gr = w[c]; //  + 1]; // weights?????
    234227
    235228  gr = gr + d; // finally we compute their graded degrees
    236229
    237   return (gr); // do we need g or w[c] ?
     230  return (gr);
    238231}
    239232
     
    257250  ASSUME(1, issorted(gr[pivot], s));
    258251
    259   module N = grobj(module(M[pivot]), w);  // reorder the starting ideal/module
     252  module N = grobj(module(M[pivot]), w, intvec(gr[pivot]));  // reorder the starting ideal/module
    260253
    261254//  "reorder: "; grview(N);
     
    264257}
    265258
     259static proc gtranspose(M)
     260"??????"
     261{   
     262  ASSUME(1, grtest(M) );
     263  return (  grobj(transpose(M), -grdeg(M), -attrib(M, "isHomog"))  );
     264}
     265
     266
    266267proc grtranspose(def M)
    267 "
    268 transpose graded module/map or a chain complex?...
     268"USAGE:  grtranspose(M), graded object or list M
     269RETURN:  same as input
     270PURPOSE: graded transpose of graded object or chain complex M
     271ASSUME:  M must be a graded object or a list of graded objects
     272EXAMPLE: example TestGRRes; shows an example
    269273"
    270274{
     
    293297    {
    294298//      grview(M[i]);
    295       L[j] = grtranspose(M[i]);
     299      L[j] = grtranspose( grobj( M[i], attrib(M[i], "isHomog")) );
    296300//      grview(L[j]);
    297301
     
    311315  ASSUME(1, grtest(M) );
    312316
    313   // TODO: something is wrong here:
    314 
    315317 intvec d; module N;
    316318
    317319 (N,d) = reorder(M, -1);
    318320
    319  kill M; module M = grobj(transpose(N), -d);
     321 kill M; module M = grobj(transpose(N), -d, -attrib(N, "isHomog"));
    320322
    321323// "b";  grview(M);
     
    334336}
    335337
    336 
    337 
    338338proc grorder(def M)
    339 "
    340 reorder graded module/map or a chain complex?...
     339"USAGE:  grorder(M), graded object or list M
     340RETURN:  same as input
     341PURPOSE: reorder/transform graded object or chain complex M into block form
     342ASSUME:  M must be a graded object or a list of graded objects
     343EXAMPLE: example TestGRRes; shows an example
    341344"
    342345{
     
    361364    {
    362365//      "i: ", i;      "A"; grview(M[i]);
    363       L[i] = grorder(M[i]);
     366      L[i] = grorder( grobj( M[i], attrib(M[i], "isHomog")) );
    364367//      "B"; grview(L[i]);
    365368      if( i < j )
     
    382385  (N,d) = reorder(M, 1); kill M;
    383386
    384   module M = grobj(transpose(N), -d); kill N,d;
     387  module M = grobj(transpose(N), -d, -attrib(N, "isHomog")); kill N,d;
    385388
    386389// "b";  grview(M);
     
    390393  (N,d) = reorder(M, -1); kill M;
    391394
    392   module M = grobj(transpose(N), -d);
     395  module M = grobj(transpose(N), -d, -attrib(N, "isHomog"));
    393396
    394397// "c";  grview(M);
     
    400403}
    401404
    402 proc TestGRRes(string Name, int version, ideal I )
    403 "
    404 test/output reordering res(I) & gr-traspose of res
     405proc TestGRRes(Name, J)
     406"USAGE:  TestGRRes(name, I), string name, ideal I
     407RETURN:  nothing
     408PURPOSE: compute/test/output/order/transpose a graded resolution of I
     409EXAMPLE: example TestGRRes; shows an example
    405410"
    406411{
     
    410415  " = Ring: ", string(basering);
    411416
    412   I = groebner(I); attrib(I, "isHomog", intvec(0));
     417  def I = grobj( groebner(J), intvec(0) ); // ASSUME: no zero entries in I!
    413418  ASSUME(0, grtest(I));
    414419//  " = Input degrees: "; grview(I);
     
    440445  assumeLevel = 5;
    441446
    442   string Name = "castelnuovo"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 5153xy2-98/23y3-101/51xyz+33/41y2z+99/79xz2+7136yz2-106/111z3+119/53xyu+34/57y2u-77/92xzu+84/73yzu-109/78z2u-27/56xu2+10023yu2+82/103zu2-34/25u3+3/2xyv-68/25y2v+12721xzv+4/63yzv-73/21z2v-7291xuv-91/53yuv-4/79zuv-34/91u2v-122/53xv2+123/70yv2-64/73zv2+44/65uv2+14/31v3,xy2-15202y3+10613xyz+13640y2z-107/103xz2+5292yz2+19/119z3-10042xyu+2770y2u+7957xzu+14008yzu+92/121z2u-92/51xu2+1178yu2+1/117zu2-12726u3+82/101xyv-92/17y2v-107/56xzv+14233yzv+79/28z2v+51/50xuv-31/5yuv+95/91zuv+19/108u2v+12151xv2-69/110yv2+37/89zv2-63/116uv2-88/23v3,-5153x2+37/23xy+8706y2-13160xz+68/115yz+5548z2-22/61xu-113/98yu+11818zu+2114u2-101/97xv+89/22yv-3355zv-113/5uv-5521v2;TestGRRes(Name, 2, I); kill R, Name, @p;  "";
    443 
    444   string Name = "ell.d8.g7"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = x2y2-47/69xy3+6059y4+78/85x2yz+55/124xy2z+13641y3z+8/17x2z2+7817xyz2-2746y2z2+85/124xz3+87yz3+13182z4+109/93x2yu-69/17xy2u+12089y3u+8769x2zu-53/36xyzu-14834y2zu+123/23xz2u+103/77yz2u-2344z3u-43/104x2u2-6198xyu2+47/115y2u2-39/19xzu2-29/24yzu2+51/89z2u2-65/37xu3-95/94yu3+11302zu3-53/57u4-2874x2yv+4347xy2v-25/77y3v+13819x2zv+29/34xyzv+474y2zv+33/107xz2v-3517yz2v+10617z3v+1834x2uv+54/113xyuv-8751y2uv+111/70xzuv-66/61yzuv+9195z2uv-14289xu2v-13/110yu2v+103/9zu2v+5113u3v+116/89x2v2+15142xyv2+13078y2v2-38/41xzv2-13/113yzv2-12824z2v2-57/11xuv2-114/17yuv2-125/31zuv2+11939u2v2+44/13xv3+56/69yv3+12/125zv3+643uv3+3530v4,-3454x2y-1285xy2-6182y3-8/69x2z+9/19xyz+64/49y2z+98/67xz2-13809yz2+21/44z3+77/47x2u+748xyu-41/77y2u+7318xzu+4217yzu+12562z2u-98/69xu2-14/85yu2+119/46zu2-61/121u3+5582x2v+108/77xyv-93/4y2v-65/49xzv-4135yzv+2477z2v+11114xuv+85/14yuv+51/125zuv-7572u2v-115/52xv2-7647yv2+4647zv2-5684uv2-1/55v3,3454x3-6645x2y-43/34xy2+14590y3+8/11x2z-117/112xyz+109/54y2z+6566xz2+23/57yz2-13078z3+95/61x2u+67/40xyu-4544y2u-95/72xzu-8/103yzu+100/77z2u+23/63xu2+69/61yu2-94/105zu2+8619u3+68/123x2v+8/117xyv+101/77y2v+124/125xzv+17/84yzv+23/67z2v+18/59xuv+3216yuv-77/59zuv-9/50u2v+96/109xv2-2491yv2+14089zv2+14067uv2-56/113v3;TestGRRes(Name, 2, I); kill R, Name, @p;  "";
    445 
    446   string Name = "ell.d7.g6"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 4971xy3+3/101y4-12318xy2z-12835y3z+97/98xyz2+63y2z2-8056xz3+23/91yz3-9662z4-7398xy2u+69/71y3u-53/68xyzu-49/67y2zu-113/122xz2u-9/61yz2u+71/88z3u+11358xyu2-38/29y2u2-10232xzu2+14490yzu2+2274z2u2+3501xu3+10427yu3-109/38zu3-99/5u4-6605xy2v-1555y3v-648xyzv-2083y2zv-61/41xz2v+75/17yz2v-69/55z3v-6104xyuv-9582y2uv+69/2xzuv-12551yzuv+47/49z2uv-118/13xu2v+34/105yu2v+105/41zu2v+6533u3v+122/25xyv2+2/43y2v2+16/61xzv2+11524yzv2+113/99z2v2-71/26xuv2+7809yuv2-4865zuv2-2122u2v2+53/118xv3-13209yv3-11106zv3-49/79uv3+3006v4,xy3+15492y4-13742xy2z+112/117y3z+6/47xyz2+28/41y2z2+71/111xz3+49/57yz3-61/44z4-11759xy2u+4242y3u-109/18xyzu+2260y2zu-6873xz2u-41/112yz2u+12574z3u-10939xyu2+119/38y2u2-62/33xzu2-3699yzu2+2651z2u2-13194xu3-15185yu3-11/116zu3-61/83u4-10094xy2v+13/4y3v-74/73xyzv+43/20y2zv-11547xz2v+53/43yz2v-92/93z3v+32/41xyuv+118/33y2uv-121/39xzuv-15913yzuv+53/11z2uv+97/76xu2v+85/29yu2v-5183zu2v+8520u3v+121/28xyv2+64/51y2v2-15810xzv2+1/43yzv2-6160z2v2+13988xuv2+9/40yuv2+123/4zuv2+15024u2v2+73/95xv3+80/97yv3+57/25zv3-109/81uv3-121/87v4,-4971x2+14389xy+1607y2+59/119xz+12020yz+103/122z2+8894xu+7091yu+54/19zu-50/77u2+28/25xv-113/56yv+68/29zv-14620uv+79/107v2;TestGRRes(Name, 2, I); kill R, Name, @p;  "";
    447 
    448   string Name = "k3.d7.g5"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = -97/108x2y-31/118xy2-73/61y3-79/14x2z-15930xyz-2324y2z+1842xz2+656yz2-8852z3-89/38x2u-102/43xyu+14719y2u+70/67xzu+7335yzu+27/56z2u-10744xu2-55/83yu2+120/73zu2+120/61u3-126/125x2v+691xyv-15385y2v+117/16xzv-17/97yzv+80/121z2v-48/119xuv+21/34yuv-103/65zuv-49/32u2v-41/42xv2+11/75yv2-502zv2-7583uv2+26/69v3,97/108x3+77/114x2y+71/21xy2+13679y3-1645x2z-1/33xyz-79/7y2z-52/53xz2+11940yz2-5800z3+109/13x2u-115/64xyu-125/56y2u-2365xzu+2103yzu+56/87z2u-84/79xu2+107/106yu2-79/70zu2-419u3+5354x2v+92/53xyv-32/19y2v+11/74xzv+4193yzv+45/79z2v-113/72xuv+17/71yuv+11164zuv-17/33u2v+103/66xv2+55/79yv2+118/15zv2-2646uv2+57/106v3,x3-61/113x2y-64/21xy2-107/8y3-13/60x2z+43/35xyz+41/114y2z-13683xz2-5829yz2+71/38z3+90/17x2u-39/29xyu+42/5y2u-61/55xzu+111/77yzu-87/100z2u+10735xu2-83/91yu2-4884zu2-7965u3-65/12x2v+109/86xyv+10606y2v-14164xzv-6678yzv+83/18z2v-93/10xuv+120/49yuv-1592zuv-8710u2v-73/57xv2+10762yv2-2956zv2-89/63uv2-12/7v3;TestGRRes(Name, 2, I); kill R, Name, @p;  "";
    449 
    450   string Name = "rat.d8.g6"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = -19/125x2y2-87/119xy3-97/21y4+36/53x2yz+2069xy2z-59/50y3z-65/33x2z2-14322xyz2+79/60y2z2-9035xz3-14890yz3+87/47z4-23/48x2yu+45/44xy2u+1972y3u+79/118x2zu-5173xyzu+115/121y2zu+1239xz2u-115/17yz2u-15900z3u-78/95x2u2+67/101xyu2-12757y2u2+12752xzu2+68/21yzu2+103/90z2u2-12917xu3+97/92yu3-24/49zu3-13/79u4-51/61x2yv-3103xy2v+77/117y3v+73/115x2zv-79/33xyzv+123/110y2zv+11969xz2v-31/95yz2v-123/95z3v-105/124x2uv+12624xyuv+2/63y2uv+6579xzuv+13/62yzuv+4388z2uv-12747xu2v-26/105yu2v-78/61zu2v-125/53u3v-5/71xyv2+62/77y2v2+21/44xzv2-9806yzv2+3/91z2v2+361xuv2+568yuv2+2926zuv2+53/38u2v2-14523yv3+2082zv3+113/115uv3,108/73x2y2+4028xy3+38/43y4-1944x2yz+39/80xy2z+8/109y3z+52/27x2z2+103/45xyz2+5834y2z2+63/101xz3+107/80yz3+1178z4-1/6x2yu+78/25xy2u-21/43y3u+50/71x2zu-14693xyzu+15074y2zu+9/103xz2u-7396yz2u-14493z3u+93/25x2u2+61/4xyu2-11306y2u2-79/81xzu2+59/82yzu2-5/106z2u2+89/71xu3-34/11yu3+15/103zu3-115/52u4-54/65x2yv+67/16xy2v-7/68y3v-10/13x2zv+32/85xyzv+1/91y2zv+107/118xz2v+7594yz2v-98/103z3v+9919x2uv-965xyuv+53/34y2uv+119/11xzuv-3400yzuv-8329z2uv+75/98xu2v-24yu2v+55/87zu2v-82/71u3v-73/115x2v2+85/19xyv2-213y2v2-7704xzv2-15347yzv2+14960z2v2+15065xuv2-125/17yuv2+32/83zuv2-14/73u2v2-21/44xv3+79/2yv3-61/32zv3+46/119uv3-2082v4,9/20x2y2+113/71xy3-88/65y4+9983x2yz-6722xy2z+87/68y3z+1893x2z2+65/32xyz2+51/55y2z2-102/53xz3+58/5yz3-7187z4-96/7x2yu-14/87xy2u-3532y3u+95/54x2zu+19/65xyzu-6728y2zu+31/121xz2u+73/106yz2u-91/5z3u-12928x2u2+707xyu2-55/48y2u2-96/25xzu2+15869yzu2-20/107z2u2-10030xu3-13786yu3-122/9zu3+19/59u4-7/52x2yv+101/74xy2v+83/6y3v-91/55x2zv-5266xyzv+85/61y2zv+126/95xz2v+56/51yz2v+13073z3v-50/21x2uv-13553xyuv-116/53y2uv+68/71xzuv-111/98yzuv-11037z2uv+68/121xu2v-124/53yu2v+54/55zu2v+5862u3v+12318x2v2-119/29xyv2+101/17y2v2-51/40xzv2-82/33yzv2-30/41z2v2-29/52xuv2+7817yuv2+8121zuv2-28/99u2v2+1125xv3-73/55yv3-14141zv3+8742uv3-1203v4,x2y2+11357xy3+295y4+144x2yz-31/54xy2z+89/119y3z+1/46x2z2+29/26xyz2+1384y2z2+1461xz3+113/91yz3+9494z4-7/32x2yu+12850xy2u-3626y3u-33/106x2zu-7/60xyzu-5935y2zu-8597xz2u+5527yz2u+1708z3u+6182x2u2-15780xyu2+4669y2u2-38/69xzu2+8412yzu2+9265z2u2-5679xu3-67/18yu3-34/67zu3-7178u4+113/56x2yv-3669xy2v+17/113y3v-87/35x2zv-4871xyzv-111/11y2zv-1131xz2v-72/13yz2v+838z3v-115/4x2uv+3395xyuv-43/68y2uv-82/13xzuv+7042yzuv-88/119z2uv+100/19xu2v+24/11yu2v+89/3zu2v+7395u3v-119/109x2v2+1/104xyv2+18/25y2v2+700xzv2-59/9yzv2-92/87z2v2+2486xuv2-67/103yuv2+1469zuv2-101/91u2v2-79/33xv3+10838yv3+81/4zv3-11843uv3+7204v4,19/125x3-15698x2y-22/117xy2-95/107y3+2027x2z-7750xyz+85/104y2z-15326xz2+31/101yz2+67/81z3-7879x2u-112/115xyu+124/81y2u+99/61xzu-7458yzu+40/33z2u-1502xu2+6591yu2-7/73zu2-42/95u3+93/83x2v-15/112xyv-84/95y2v+35/36xzv+5/24yzv-12768z2v+13232xuv-76/103yuv-79/52zuv-7217u2v+75/92xv2-49/64yv2+17/14zv2-6109uv2+1695v3;TestGRRes(Name, 2, I); kill R, Name, @p; "";
    451 
    452   string Name = "k3.d14.g19"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2, I); kill R, Name, @p;  "";
    453 
    454   string Name = "k3.d11.g11.ss0"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2, I); kill R, Name, @p; "";
    455 
    456   string Name = "ell.d10.g9"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2, I); kill R, Name, @p; "";
    457 
    458   string Name = "k3.d10.g9.quart2"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2, I); kill R, Name, @p; "";
    459 
    460   string Name = "rat.d10.g9.quart2"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2, I); kill R, Name, @p; "";
     447  // note: data from random generation 2
     448  string Name = "castelnuovo"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 5153xy2-98/23y3-101/51xyz+33/41y2z+99/79xz2+7136yz2-106/111z3+119/53xyu+34/57y2u-77/92xzu+84/73yzu-109/78z2u-27/56xu2+10023yu2+82/103zu2-34/25u3+3/2xyv-68/25y2v+12721xzv+4/63yzv-73/21z2v-7291xuv-91/53yuv-4/79zuv-34/91u2v-122/53xv2+123/70yv2-64/73zv2+44/65uv2+14/31v3,xy2-15202y3+10613xyz+13640y2z-107/103xz2+5292yz2+19/119z3-10042xyu+2770y2u+7957xzu+14008yzu+92/121z2u-92/51xu2+1178yu2+1/117zu2-12726u3+82/101xyv-92/17y2v-107/56xzv+14233yzv+79/28z2v+51/50xuv-31/5yuv+95/91zuv+19/108u2v+12151xv2-69/110yv2+37/89zv2-63/116uv2-88/23v3,-5153x2+37/23xy+8706y2-13160xz+68/115yz+5548z2-22/61xu-113/98yu+11818zu+2114u2-101/97xv+89/22yv-3355zv-113/5uv-5521v2;TestGRRes(Name, I); kill R, Name, @p;  "";
     449
     450  string Name = "ell.d8.g7"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = x2y2-47/69xy3+6059y4+78/85x2yz+55/124xy2z+13641y3z+8/17x2z2+7817xyz2-2746y2z2+85/124xz3+87yz3+13182z4+109/93x2yu-69/17xy2u+12089y3u+8769x2zu-53/36xyzu-14834y2zu+123/23xz2u+103/77yz2u-2344z3u-43/104x2u2-6198xyu2+47/115y2u2-39/19xzu2-29/24yzu2+51/89z2u2-65/37xu3-95/94yu3+11302zu3-53/57u4-2874x2yv+4347xy2v-25/77y3v+13819x2zv+29/34xyzv+474y2zv+33/107xz2v-3517yz2v+10617z3v+1834x2uv+54/113xyuv-8751y2uv+111/70xzuv-66/61yzuv+9195z2uv-14289xu2v-13/110yu2v+103/9zu2v+5113u3v+116/89x2v2+15142xyv2+13078y2v2-38/41xzv2-13/113yzv2-12824z2v2-57/11xuv2-114/17yuv2-125/31zuv2+11939u2v2+44/13xv3+56/69yv3+12/125zv3+643uv3+3530v4,-3454x2y-1285xy2-6182y3-8/69x2z+9/19xyz+64/49y2z+98/67xz2-13809yz2+21/44z3+77/47x2u+748xyu-41/77y2u+7318xzu+4217yzu+12562z2u-98/69xu2-14/85yu2+119/46zu2-61/121u3+5582x2v+108/77xyv-93/4y2v-65/49xzv-4135yzv+2477z2v+11114xuv+85/14yuv+51/125zuv-7572u2v-115/52xv2-7647yv2+4647zv2-5684uv2-1/55v3,3454x3-6645x2y-43/34xy2+14590y3+8/11x2z-117/112xyz+109/54y2z+6566xz2+23/57yz2-13078z3+95/61x2u+67/40xyu-4544y2u-95/72xzu-8/103yzu+100/77z2u+23/63xu2+69/61yu2-94/105zu2+8619u3+68/123x2v+8/117xyv+101/77y2v+124/125xzv+17/84yzv+23/67z2v+18/59xuv+3216yuv-77/59zuv-9/50u2v+96/109xv2-2491yv2+14089zv2+14067uv2-56/113v3;TestGRRes(Name, I); kill R, Name, @p;  "";
     451
     452  string Name = "ell.d7.g6"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 4971xy3+3/101y4-12318xy2z-12835y3z+97/98xyz2+63y2z2-8056xz3+23/91yz3-9662z4-7398xy2u+69/71y3u-53/68xyzu-49/67y2zu-113/122xz2u-9/61yz2u+71/88z3u+11358xyu2-38/29y2u2-10232xzu2+14490yzu2+2274z2u2+3501xu3+10427yu3-109/38zu3-99/5u4-6605xy2v-1555y3v-648xyzv-2083y2zv-61/41xz2v+75/17yz2v-69/55z3v-6104xyuv-9582y2uv+69/2xzuv-12551yzuv+47/49z2uv-118/13xu2v+34/105yu2v+105/41zu2v+6533u3v+122/25xyv2+2/43y2v2+16/61xzv2+11524yzv2+113/99z2v2-71/26xuv2+7809yuv2-4865zuv2-2122u2v2+53/118xv3-13209yv3-11106zv3-49/79uv3+3006v4,xy3+15492y4-13742xy2z+112/117y3z+6/47xyz2+28/41y2z2+71/111xz3+49/57yz3-61/44z4-11759xy2u+4242y3u-109/18xyzu+2260y2zu-6873xz2u-41/112yz2u+12574z3u-10939xyu2+119/38y2u2-62/33xzu2-3699yzu2+2651z2u2-13194xu3-15185yu3-11/116zu3-61/83u4-10094xy2v+13/4y3v-74/73xyzv+43/20y2zv-11547xz2v+53/43yz2v-92/93z3v+32/41xyuv+118/33y2uv-121/39xzuv-15913yzuv+53/11z2uv+97/76xu2v+85/29yu2v-5183zu2v+8520u3v+121/28xyv2+64/51y2v2-15810xzv2+1/43yzv2-6160z2v2+13988xuv2+9/40yuv2+123/4zuv2+15024u2v2+73/95xv3+80/97yv3+57/25zv3-109/81uv3-121/87v4,-4971x2+14389xy+1607y2+59/119xz+12020yz+103/122z2+8894xu+7091yu+54/19zu-50/77u2+28/25xv-113/56yv+68/29zv-14620uv+79/107v2;TestGRRes(Name, I); kill R, Name, @p;  "";
     453
     454  string Name = "k3.d7.g5"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = -97/108x2y-31/118xy2-73/61y3-79/14x2z-15930xyz-2324y2z+1842xz2+656yz2-8852z3-89/38x2u-102/43xyu+14719y2u+70/67xzu+7335yzu+27/56z2u-10744xu2-55/83yu2+120/73zu2+120/61u3-126/125x2v+691xyv-15385y2v+117/16xzv-17/97yzv+80/121z2v-48/119xuv+21/34yuv-103/65zuv-49/32u2v-41/42xv2+11/75yv2-502zv2-7583uv2+26/69v3,97/108x3+77/114x2y+71/21xy2+13679y3-1645x2z-1/33xyz-79/7y2z-52/53xz2+11940yz2-5800z3+109/13x2u-115/64xyu-125/56y2u-2365xzu+2103yzu+56/87z2u-84/79xu2+107/106yu2-79/70zu2-419u3+5354x2v+92/53xyv-32/19y2v+11/74xzv+4193yzv+45/79z2v-113/72xuv+17/71yuv+11164zuv-17/33u2v+103/66xv2+55/79yv2+118/15zv2-2646uv2+57/106v3,x3-61/113x2y-64/21xy2-107/8y3-13/60x2z+43/35xyz+41/114y2z-13683xz2-5829yz2+71/38z3+90/17x2u-39/29xyu+42/5y2u-61/55xzu+111/77yzu-87/100z2u+10735xu2-83/91yu2-4884zu2-7965u3-65/12x2v+109/86xyv+10606y2v-14164xzv-6678yzv+83/18z2v-93/10xuv+120/49yuv-1592zuv-8710u2v-73/57xv2+10762yv2-2956zv2-89/63uv2-12/7v3;TestGRRes(Name, I); kill R, Name, @p;  "";
     455
     456  string Name = "rat.d8.g6"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = -19/125x2y2-87/119xy3-97/21y4+36/53x2yz+2069xy2z-59/50y3z-65/33x2z2-14322xyz2+79/60y2z2-9035xz3-14890yz3+87/47z4-23/48x2yu+45/44xy2u+1972y3u+79/118x2zu-5173xyzu+115/121y2zu+1239xz2u-115/17yz2u-15900z3u-78/95x2u2+67/101xyu2-12757y2u2+12752xzu2+68/21yzu2+103/90z2u2-12917xu3+97/92yu3-24/49zu3-13/79u4-51/61x2yv-3103xy2v+77/117y3v+73/115x2zv-79/33xyzv+123/110y2zv+11969xz2v-31/95yz2v-123/95z3v-105/124x2uv+12624xyuv+2/63y2uv+6579xzuv+13/62yzuv+4388z2uv-12747xu2v-26/105yu2v-78/61zu2v-125/53u3v-5/71xyv2+62/77y2v2+21/44xzv2-9806yzv2+3/91z2v2+361xuv2+568yuv2+2926zuv2+53/38u2v2-14523yv3+2082zv3+113/115uv3,108/73x2y2+4028xy3+38/43y4-1944x2yz+39/80xy2z+8/109y3z+52/27x2z2+103/45xyz2+5834y2z2+63/101xz3+107/80yz3+1178z4-1/6x2yu+78/25xy2u-21/43y3u+50/71x2zu-14693xyzu+15074y2zu+9/103xz2u-7396yz2u-14493z3u+93/25x2u2+61/4xyu2-11306y2u2-79/81xzu2+59/82yzu2-5/106z2u2+89/71xu3-34/11yu3+15/103zu3-115/52u4-54/65x2yv+67/16xy2v-7/68y3v-10/13x2zv+32/85xyzv+1/91y2zv+107/118xz2v+7594yz2v-98/103z3v+9919x2uv-965xyuv+53/34y2uv+119/11xzuv-3400yzuv-8329z2uv+75/98xu2v-24yu2v+55/87zu2v-82/71u3v-73/115x2v2+85/19xyv2-213y2v2-7704xzv2-15347yzv2+14960z2v2+15065xuv2-125/17yuv2+32/83zuv2-14/73u2v2-21/44xv3+79/2yv3-61/32zv3+46/119uv3-2082v4,9/20x2y2+113/71xy3-88/65y4+9983x2yz-6722xy2z+87/68y3z+1893x2z2+65/32xyz2+51/55y2z2-102/53xz3+58/5yz3-7187z4-96/7x2yu-14/87xy2u-3532y3u+95/54x2zu+19/65xyzu-6728y2zu+31/121xz2u+73/106yz2u-91/5z3u-12928x2u2+707xyu2-55/48y2u2-96/25xzu2+15869yzu2-20/107z2u2-10030xu3-13786yu3-122/9zu3+19/59u4-7/52x2yv+101/74xy2v+83/6y3v-91/55x2zv-5266xyzv+85/61y2zv+126/95xz2v+56/51yz2v+13073z3v-50/21x2uv-13553xyuv-116/53y2uv+68/71xzuv-111/98yzuv-11037z2uv+68/121xu2v-124/53yu2v+54/55zu2v+5862u3v+12318x2v2-119/29xyv2+101/17y2v2-51/40xzv2-82/33yzv2-30/41z2v2-29/52xuv2+7817yuv2+8121zuv2-28/99u2v2+1125xv3-73/55yv3-14141zv3+8742uv3-1203v4,x2y2+11357xy3+295y4+144x2yz-31/54xy2z+89/119y3z+1/46x2z2+29/26xyz2+1384y2z2+1461xz3+113/91yz3+9494z4-7/32x2yu+12850xy2u-3626y3u-33/106x2zu-7/60xyzu-5935y2zu-8597xz2u+5527yz2u+1708z3u+6182x2u2-15780xyu2+4669y2u2-38/69xzu2+8412yzu2+9265z2u2-5679xu3-67/18yu3-34/67zu3-7178u4+113/56x2yv-3669xy2v+17/113y3v-87/35x2zv-4871xyzv-111/11y2zv-1131xz2v-72/13yz2v+838z3v-115/4x2uv+3395xyuv-43/68y2uv-82/13xzuv+7042yzuv-88/119z2uv+100/19xu2v+24/11yu2v+89/3zu2v+7395u3v-119/109x2v2+1/104xyv2+18/25y2v2+700xzv2-59/9yzv2-92/87z2v2+2486xuv2-67/103yuv2+1469zuv2-101/91u2v2-79/33xv3+10838yv3+81/4zv3-11843uv3+7204v4,19/125x3-15698x2y-22/117xy2-95/107y3+2027x2z-7750xyz+85/104y2z-15326xz2+31/101yz2+67/81z3-7879x2u-112/115xyu+124/81y2u+99/61xzu-7458yzu+40/33z2u-1502xu2+6591yu2-7/73zu2-42/95u3+93/83x2v-15/112xyv-84/95y2v+35/36xzv+5/24yzv-12768z2v+13232xuv-76/103yuv-79/52zuv-7217u2v+75/92xv2-49/64yv2+17/14zv2-6109uv2+1695v3;TestGRRes(Name, I); kill R, Name, @p; "";
     457
     458  string Name = "k3.d14.g19"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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I); kill R, Name, @p;  "";
     459
     460  string Name = "k3.d11.g11.ss0"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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I); kill R, Name, @p; "";
     461
     462  string Name = "ell.d10.g9"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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I); kill R, Name, @p; "";
     463
     464  string Name = "k3.d10.g9.quart2"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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I); kill R, Name, @p; "";
     465
     466  string Name = "rat.d10.g9.quart2"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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I); kill R, Name, @p; "";
    461467
    462468  if( defined(assumeLevel0) ){ assumeLevel = assumeLevel0; } else { kill assumeLevel; } // restore the state of aL
     
    467473// Q@Woflram?
    468474proc grzero()
    469 "presentation of S(0)^1
    470 TODO: can we return this as an undefined value?????
    471 "
    472 {
    473  return ( grobj(module([0]), intvec(0)) );
     475"USAGE:  grzero()
     476RETURN:  graded object representing S(0)^1
     477PURPOSE: compute presentation of S(0)^1
     478EXAMPLE: example grsum; shows an example
     479"
     480{
     481 return ( grobj(module([0]), intvec(0), intvec(0)) );
    474482}
    475483
    476484proc grpower(def A, int p)
    477 "
    478 compute A \oplus ... \opuls A (p-times)
     485"USAGE:  grpower(A, p), graded object A, int p > 0
     486RETURN:  graded direct power A^p
     487PURPOSE: compute the graded direct power A^p
     488NOTE:    the power p must be positive
     489EXAMPLE: example grsum; shows an example
    479490"
    480491{
     
    499510
    500511
    501 proc grsum(def A,def B)
    502 "
    503 direct sum of graded modules
     512proc grsum(A,B)
     513"USAGE:  grsum(A, B), graded objects A and B
     514RETURN:  graded direct sum of input objects
     515PURPOSE: compute the graded direct sum of A and B
     516EXAMPLE: example grsum; shows an example
    504517"
    505518{
     
    515528  module S = module(A), T;
    516529
    517   return(grobj(S, c));
     530  intvec da = grdeg(A);
     531  intvec db = grdeg(B);
     532  intvec dc = da, db;
     533
     534  return(grobj(S, c, dc));
    518535}
    519536example
     
    576593
    577594proc grshift( def M, int d)
    578 "
    579 shift graded module M by delta so that 1 is in M_d
    580 "
    581 {
     595"USAGE:  grshift(A, d), graded objects A, int d
     596RETURN:  shifted graded object
     597PURPOSE: shift the grading on A by d: A_i -> A_{i+/-d}?
     598EXAMPLE: example grsum; shows an example
     599"
     600{
     601  ASSUME(1, grtest(M) );
     602 
    582603  intvec a = attrib(M, "isHomog");
    583   return (grobj(M, intvec( a - intvec(d:size(a))) ));
    584 }
    585 
     604  a = a - intvec(d:size(a));
     605 
     606  intvec t = attrib(M, "degHomog");
     607  t = t - intvec(d:size(t));
     608 
     609  return (grobj(M, a, t));
     610}
     611
     612
     613static proc grisequal (def A, def B)
     614"USAGE:  grisequal(A, B), graded objects A and B
     615RETURN:  1 if A == B as graded objects, 0 otherwise
     616PURPOSE: test the equality of two graded object
     617NOTE: A and B should be literarly the same at the moment. TODO?
     618EXAMPLE: example grsum; shows an example
     619"
     620{
     621  ASSUME(1, grtest(A) );
     622  ASSUME(1, grtest(B) );
     623
     624  int ra = nrows(A);
     625  int rb = nrows(B);
     626
     627  intvec wa = attrib(A, "isHomog");
     628  intvec wb = attrib(B, "isHomog");
     629
     630  if( (ra != rb) || (ncols(A) != ncols(B)) ){ return (0); } // TODO: ???
     631
     632  intvec da = grdeg(A);
     633  intvec db = grdeg(B);
     634 
     635  return ( (da == db) && (wa == wb) &&
     636           (size(module(matrix(A) - matrix(B))) == 0)    ); // TODO: ???
     637}
     638
     639proc grtwist(int a, int d)
     640"USAGE:  grtwist(a,d), int a, d
     641RETURN:  graded object representing S(d)^a
     642PURPOSE: compute presentation of S(d)^a
     643EXAMPLE: example grsum; shows an example
     644"
     645{
     646  ASSUME(0, a > 0);
     647 
     648  module Z; Z[a] = [0];
     649  intvec w = -intvec(d:a);
     650  Z = grobj(Z, w, w); // will set the rank as well
     651  ASSUME(2, grisequal(Z, grpower( grshift(grzero(), d), a ) )); // optional check
     652  return(Z);
     653}
     654
     655proc grobj(def A, intvec w, list #)
     656"USAGE:  grobj(M, w[, d]), matrix/ideal/module M, intvec w, d
     657RETURN:  graded object with matrix presentation M, row weighting w [and total graded degrees d of columns]
     658PURPOSE: create a valid graded object with a given matrix presentation, weighting [and total graded degrees (in case of zero columns)]
     659EXAMPLE: example grsum; shows an example
     660"
     661{
     662  module M = module(A);
     663  ASSUME(0, size(w) >= nrows(M) );
     664 
     665  attrib(M, "rank", size(w));
     666  attrib(M, "isHomog", w);
     667
     668  if( size(#) > 0 )
     669  {
     670    ASSUME(0, typeof(#[1]) == "intvec" );
     671    ASSUME(0, size(#[1]) == ncols(M) );
     672    attrib(M, "degHomog", #[1]);
     673  }
     674  else
     675  {
     676    ASSUME(0, /* no zero cols please! */ size(M) == ncols(M) );
     677    attrib(M, "degHomog", grdeg(M));
     678  }   
     679
     680  ASSUME(0, grtest(M) );
     681  return (M);
     682}
    586683
    587684proc grtest(def N)
    588 "test if N is a matrix/module with matching isHomog attribute (intvec)"
     685"USAGE:  grtest(M), anyting M
     686RETURN:  1 if M is a valid graded object, 0 otherwise
     687PURPOSE: validate a graded object
     688NOTE: M should be an ideal or module or matrix, with weighting attribute
     689   'isHomog' and optionally total graded degrees attribute 'degHomog'.
     690   Attributes should be compatible with the presentation matrix.
     691EXAMPLE: example grsum; shows an example
     692"
    589693{
    590694  string t = typeof(N);
     
    595699
    596700  intvec gr = attrib(N, "isHomog"); // grading weights...
    597   if ( nrows(N) > size(gr) ) { return (0); };  // wrong number of rows?
     701  if ( nrows(N) != size(gr) ) { return (0); };  // wrong number of rows?
    598702
    599703//  if( attrib(N, "rank") != size(gr) ){ return (0); } // wrong rank :(
    600704
    601 
     705  if ( typeof(attrib(N, "degHomog")) == "intvec" )
     706  {
     707    intvec T = attrib(N, "degHomog"); // graded degrees
     708    if ( ncols(N) != size(T) ) { return (0); };  // wrong number of cols?
     709
     710    int k = nvars(basering) + 1; // index of mod. column in the leadexp
     711
     712    module L = lead(module(N)); vector v;
     713
     714    // checking T for non-zero N[i]
     715    int i = size(T);
     716   
     717    for (; i > 0; i-- )
     718    {
     719      v = L[i];
     720      if( v != 0 )
     721      {
     722        if( (deg(v) + gr[ leadexp(v)[k] ]) != T[i] ) { return (0); };  // wrong T[i]       
     723      }
     724    }
     725
     726    // TODO: check t on nonzero cols...
     727  } else
     728  {
     729    if( ncols(N) != size(N) ) { return (0); };
     730  }
     731 
    602732//  if( !homog(N) ) { return (0); };  // N should be homogenous
    603733
    604 
    605734  return (1);
    606735}
    607 
    608 proc grisequal (def A, def B)
    609 "TODO"
    610 {
    611   ASSUME(1, grtest(A) );
    612   ASSUME(1, grtest(B) );
    613 
    614   int ra = nrows(A);
    615   int rb = nrows(B);
    616 
    617   intvec wa = attrib(A, "isHomog");
    618   intvec wb = attrib(B, "isHomog");
    619 
    620   if( (ra != rb) || (ncols(A) != ncols(B)) ){ return (0); } // TODO: ???
    621   return ( (wa == wb) &&
    622            (size(module(matrix(A) - matrix(B))) == 0)    ); // TODO: ???
    623 }
    624 
    625 proc grtwist(int a, int d)
    626 "
    627 matrix presentation for twisted polynomial ring S(d)^a
    628 "
    629 {
    630   module Z; Z[a] = [0];
    631   Z = grobj(Z, -intvec(d:a)); // will set the rank as well
    632 
    633   ASSUME(2, grisequal(Z, grpower( grshift(grzero(), d), a ) )); // optional check
    634   return(Z);
    635 }
    636 
    637 proc grobj(def A, intvec w)
    638 ""
    639 {
    640   module M = module(A);
    641   ASSUME(0, size(w) >= nrows(M) );
    642   attrib(M, "rank", size(w));
    643   attrib(M, "isHomog", w);
    644   ASSUME(1, grtest(M) );
    645   return (M);
    646 }
    647 
     736   
    648737
    649738static proc align( def A, int d)
  • Singular/LIB/grwalk.lib

    rf38979 rb9e63ba  
    255255}
    256256
    257 proc gwalk(ideal Go, list #)
    258 "SYNTAX: gwalk(ideal i);
    259          gwalk(ideal i, intvec v, intvec w);
     257proc gwalk(ideal Go, int reduction,int printout, list #)
     258"SYNTAX: gwalk(ideal i, int reduction, int printout);
     259         gwalk(ideal i, int reduction, int printout, intvec v, intvec w);
    260260TYPE:    ideal
    261261PURPOSE: compute the standard basis of the ideal, calculated via
     
    274274   string ord_str =   OSCTW[2];
    275275   intvec curr_weight   =   OSCTW[3]; /* original weight vector */
    276    intvec target_weight =   OSCTW[4]; /* terget weight vector */
     276   intvec target_weight =   OSCTW[4]; /* target weight vector */
    277277   kill OSCTW;
    278278   option(redSB);
     
    284284   //print("//** help ring = " + string(basering));
    285285   ideal G = fetch(xR, Go);
    286    G = system("Mwalk", G, curr_weight, target_weight,basering);
     286   G = system("Mwalk", G, curr_weight, target_weight,basering,reduction,printout);
    287287
    288288   setring xR;
     
    299299  //** compute a Groebner basis of I w.r.t. lp.
    300300  ring r = 32003,(z,y,x), lp;
    301   ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
    302   gwalk(I);
     301  ideal I = zy2+yx2+yx+3,
     302            z3x+y3+zyx-yx2-yx-3,
     303            z2yx3-y5+z2yx2+y3x2+y2x3+y3x+y2x2+3z2x+3y2+3yx,
     304            zyx5+y6-y4x2-y3x3+2zyx4-y4x-y3x2+zyx3-3z2yx+3zx3-3y3-3y2x+3zx2,
     305            yx7-y7+y5x2+y4x3+3yx6+y5x+y4x2+3yx5-6zyx3+yx4+3x5+3y4+3y3x-6zyx2+6x4+3x3-9zx;
     306  gwalk(I,0,1);
    303307}
    304308
     
    346350}
    347351
    348 proc fwalk(ideal Go, list #)
    349 "SYNTAX: fwalk(ideal i);
    350          fwalk(ideal i, intvec v, intvec w);
     352proc fwalk(ideal Go, int reduction, int printout, list #)
     353"SYNTAX: fwalk(ideal i,int reductioin);
     354         fwalk(ideal i, int reduction intvec v, intvec w);
    351355TYPE:    ideal
    352356PURPOSE: compute the standard basis of the ideal w.r.t. the
     
    372376
    373377   ideal G = fetch(xR, Go);
    374    G = system("Mfwalk", G, curr_weight, target_weight);
     378   G = system("Mfwalk", G, curr_weight, target_weight, reduction, printout);
    375379
    376380   setring xR;
     
    387391    ring r = 32003,(z,y,x), lp;
    388392    ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
    389     fwalk(I);
     393    int reduction = 1;
     394    int printout = 1;
     395    fwalk(I,reduction,printout);
    390396}
    391397
     
    437443}
    438444
    439 proc pwalk(ideal Go, int n1, int n2, list #)
    440 "SYNTAX: pwalk(int d, ideal i, int n1, int n2);
    441          pwalk(int d, ideal i, int n1, int n2, intvec v, intvec w);
     445proc pwalk(ideal Go, int n1, int n2, int reduction, int printout, list #)
     446"SYNTAX: pwalk(int d, ideal i, int n1, int n2, int reduction, int printout);
     447         pwalk(int d, ideal i, int n1, int n2, int reduction, int printout, intvec v, intvec w);
    442448TYPE:    ideal
    443449PURPOSE: compute the standard basis of the ideal, calculated via
     
    477483  ideal G = fetch(xR, Go);
    478484
    479   G = system("Mpwalk", G, n1, n2, curr_weight, target_weight,nP);
    480 
     485  G = system("Mpwalk",G,n1,n2,curr_weight,target_weight,nP,reduction,printout);
     486 
    481487  setring xR;
    482   //kill Go;
     488  //kill Go; //unused
    483489
    484490  keepring basering;
     
    492498    ring r = 32003,(z,y,x), lp;
    493499    ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
    494     //I = std(I);
    495     //ring rr = 32003,(z,y,x),lp;
    496     //ideal I = fetch(r,I);
    497     pwalk(I,2,2);
     500    int reduction = 1;
     501    int printout = 2;
     502    pwalk(I,2,2,reduction,printout);
    498503}
    499504
  • Singular/LIB/modwalk.lib

    • Property mode changed from 100644 to 100755
    rf38979 rb9e63ba  
    1616
    1717PROCEDURES:
     18modpWalk(ideal,int,int,int[,int,int,int,int])    standard basis conversion of I in prime characteristic
    1819modWalk(ideal,int,int[,int,int,int,int]);        standard basis conversion of I using modular methods (chinese remainder)
    1920";
     
    2930////////////////////////////////////////////////////////////////////////////////
    3031
    31 static proc modpWalk(def II, int p, int variant, list #)
     32proc modpWalk(def II, int p, int variant, int reduction, list #)
    3233"USAGE:  modpWalk(I,p,#); I ideal, p integer, variant integer
    3334ASSUME:  If size(#) > 0, then
     
    8081    }
    8182  }
     83<<<<<<< HEAD
     84=======
    8285
    8386//-------------------------  make i homogeneous  -----------------------------
     
    106109  }
    107110
     111>>>>>>> f533f6f7667328bccb271b19b2f603aaebe41596
    108112//-------------------------  compute a standard basis mod p  -----------------------------
    109 
    110113  if(variant == 1)
    111114  {
    112115    if(size(#)>0)
    113116    {
    114       i = rwalk(i,radius,pert_deg,#);
    115      // rwalk(i,radius,pert_deg,#); std(i);
     117      i = rwalk(i,radius,pert_deg,reduction,#);
    116118    }
    117119    else
    118120    {
    119       i = rwalk(i,radius,pert_deg);
     121      i = rwalk(i,radius,pert_deg,reduction);
    120122    }
    121123  }
     
    124126    if(size(#) == 2)
    125127    {
    126       i = gwalk(i,#);
     128      i = gwalk(i,reduction,#);
    127129    }
    128130    else
    129131    {
    130       i = gwalk(i);
     132      i = gwalk(i,reduction);
    131133    }
    132134  }
     
    135137    if(size(#) == 2)
    136138    {
    137       i = frandwalk(i,radius,#);
     139      i = frandwalk(i,radius,reduction,#);
    138140    }
    139141    else
    140142    {
    141       i = frandwalk(i,radius);
     143      i = frandwalk(i,radius,reduction);
    142144    }
    143145  }
     
    157159    if(size(#) == 2)
    158160    {
    159      i=prwalk(i,radius,pert_deg,pert_deg,#);
     161     i=prwalk(i,radius,pert_deg,pert_deg,reduction,#);
    160162    }
    161163    else
    162164    {
    163       i=prwalk(i,radius,pert_deg,pert_deg);
     165      i=prwalk(i,radius,pert_deg,pert_deg,reduction);
    164166    }
    165167  }
     
    168170    if(size(#) == 2)
    169171    {
    170       i=pwalk(i,pert_deg,pert_deg,#);
     172      i=pwalk(i,pert_deg,pert_deg,reduction,#);
    171173    }
    172174    else
    173175    {
     176<<<<<<< HEAD
     177      i=pwalk(i,pert_deg,pert_deg,reduction);
     178=======
    174179      i=pwalk(i,pert_deg,pert_deg);
    175180    }
     
    189194        kill HomR;
    190195      }
    191     }
    192   }
     196>>>>>>> f533f6f7667328bccb271b19b2f603aaebe41596
     197    }
     198  }
     199
    193200  setring R0;
    194201  return(list(fetch(@r,i),p));
     
    204211  ring ra = 0,x(1..4),(a(a),lp);
    205212  ideal I = std(cyclic(4));
     213  int reduction = 1;
    206214  ring rb = 0,x(1..4),(a(b),lp);
    207215  ideal I = imap(ra,I);
    208   modpWalk(I,p,1,a,b);
     216  modpWalk(I,p,1,reduction,a,b);
    209217  std(I);
    210218}
     
    212220////////////////////////////////////////////////////////////////////////////////
    213221
    214 proc modWalk(def II, int variant, list #)
     222proc modWalk(def II, int variant, int reduction, list #)
    215223"USAGE:  modWalk(II); II ideal or list(ideal,int)
    216224ASSUME:  If variant =
     
    487495  if(n2 > 4)
    488496  {
    489   //  L[5] = prime(random(an,en));
     497    L[5] = prime(random(an,en));
    490498  }
    491499  if(printlevel >= 10)
     
    504512    for(i=1; i<=size(L); i++)
    505513    {
    506       Arguments[i] = list(II,L[i],variant,list(curr_weight,target_weight));
     514      Arguments[i] = list(II,L[i],variant,reduction,list(curr_weight,target_weight));
    507515    }
    508516  }
     
    511519    for(i=1; i<=size(L); i++)
    512520    {
    513       Arguments[i] = list(II,L[i],variant);
     521      Arguments[i] = list(II,L[i],variant,reduction);
    514522    }
    515523  }
     
    528536//-------------------  Now all leading ideals are the same  --------------------
    529537//-------------------  Lift results to basering via farey  ---------------------
    530 
    531538    tt = timer; rt = rtimer;
    532539    N = T2[1];
     
    545552
    546553//----------------  Test if we already have a standard basis of I --------------
    547 
    548554    tt = timer; rt = rtimer;
    549     pTest = pTestSB(I,J,L,variant);
    550     //pTest = primeTestSB(I,J,L,variant);
     555    pTest = primeTest(J, prime(random(1000000000,2134567879)));
    551556    if(printlevel >= 10)
    552557    {
     
    596601    }
    597602//--------------  We do not already have a standard basis of I, therefore do the main computation for more primes  --------------
    598 
    599603    T1 = H;
    600604    T2 = N;
     
    613617      for(i=j; i<=size(L); i++)
    614618      {
    615         //Arguments[i-j+1] = list(II,L[i],variant,list(curr_weight,target_weight));
    616         Arguments[size(Arguments)+1] = list(II,L[i],variant,list(curr_weight,target_weight));
     619        Arguments[size(Arguments)+1] = list(II,L[i],variant,reduction,list(curr_weight,target_weight));
    617620      }
    618621    }
     
    621624      for(i=j; i<=size(L); i++)
    622625      {
    623         //Arguments[i-j+1] = list(II,L[i],variant);
    624         Arguments[size(Arguments)+1] = list(II,L[i],variant);
     626        Arguments[size(Arguments)+1] = list(II,L[i],variant,reduction);
    625627      }
    626628    }
     
    632634    for(i=1; i<=size(PP); i++)
    633635    {
    634       //P[size(P) + 1] = PP[i];
    635636      T1[size(T1) + 1] = PP[i][1];
    636637      T2[size(T2) + 1] = bigint(PP[i][2]);
     
    649650  echo = 2;
    650651  ring R=0,(x,y,z),lp;
    651   ideal I=-x+y2z-z,xz+1,x2+y2-1;
    652   // I is a standard basis in dp
    653   ideal J = modWalk(I,1);
     652  ideal I= y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
     653  int reduction = 0;
     654  ideal J = modWalk(I,1,1);
    654655  J;
    655656}
     
    772773  return(J);
    773774}
    774 //////////////////////////////////////////////////////////////////////////////////
    775 static proc primeTestSB(def II, ideal J, list L, int variant, list #)
    776 "USAGE:  primeTestSB(I,J,L,variant,#); I,J ideals, L intvec of primes, variant int
    777 RETURN:  1 (resp. 0) if for a randomly chosen prime p that is not in L
    778          J mod p is (resp. is not) a standard basis of I mod p
    779 EXAMPLE: example primeTestSB; shows an example
    780 "
    781 {
    782 if(typeof(II) == "ideal")
    783   {
    784   ideal I = II;
    785   int radius = 2;
    786   }
    787 if(typeof(II) == "list")
    788   {
    789   ideal I = II[1];
    790   int radius = II[2];
    791   }
    792 
    793 int i,j,k,p;
    794 def R = basering;
    795 list r = ringlist(R);
    796 
    797 while(!j)
    798   {
    799   j = 1;
    800   p = prime(random(1000000000,2134567879));
    801   for(i = 1; i <= size(L); i++)
    802     {
    803     if(p == L[i])
    804       {
    805       j = 0;
    806       break;
    807       }
    808     }
    809   if(j)
    810     {
    811     for(i = 1; i <= ncols(I); i++)
    812       {
    813       for(k = 2; k <= size(I[i]); k++)
    814         {
    815         if((denominator(leadcoef(I[i][k])) mod p) == 0)
    816           {
    817           j = 0;
    818           break;
    819           }
    820         }
    821       if(!j)
    822         {
    823         break;
    824         }
    825       }
    826     }
    827   if(j)
    828     {
    829     if(!primeTest(I,p))
    830       {
    831       j = 0;
    832       }
    833     }
    834   }
    835 r[1] = p;
    836 def @R = ring(r);
    837 setring @R;
    838 ideal I = imap(R,I);
    839 ideal J = imap(R,J);
    840 attrib(J,"isSB",1);
    841 
    842 int t = timer;
    843 j = 1;
    844 if(isIncluded(I,J) == 0)
    845   {
    846   j = 0;
    847   }
    848 if(printlevel >= 11)
    849   {
    850   "isIncluded(I,J) takes "+string(timer - t)+" seconds";
    851   "j = "+string(j);
    852   }
    853 t = timer;
    854 if(j)
    855   {
    856   if(size(#) > 0)
    857     {
    858     ideal K = modpWalk(I,p,variant,#)[1];
    859     }
    860   else
    861     {
    862     ideal K = modpWalk(I,p,variant)[1];
    863     }
    864   t = timer;
    865   if(isIncluded(J,K) == 0)
    866     {
    867     j = 0;
    868     }
    869   if(printlevel >= 11)
    870     {
    871     "isIncluded(K,J) takes "+string(timer - t)+" seconds";
    872     "j = "+string(j);
    873     }
    874   }
    875 setring R;
    876 
    877 return(j);
    878 }
    879 example
    880 { "EXAMPLE:"; echo = 2;
    881    intvec L = 2,3,5;
    882    ring r = 0,(x,y,z),lp;
    883    ideal I = x+1,x+y+1;
    884    ideal J = x+1,y;
    885    primeTestSB(I,I,L,1);
    886    primeTestSB(I,J,L,1);
    887 }
    888 
    889 ////////////////////////////////////////////////////////////////////////////////
    890 static proc pTestSB(ideal I, ideal J, list L, int variant, list #)
    891 "USAGE:  pTestSB(I,J,L,variant,#); I,J ideals, L intvec of primes, variant int
    892 RETURN:  1 (resp. 0) if for a randomly chosen prime p that is not in L
    893          J mod p is (resp. is not) a standard basis of I mod p
    894 EXAMPLE: example pTestSB; shows an example
    895 "
    896 {
    897    int i,j,k,p;
    898    def R = basering;
    899    list r = ringlist(R);
    900 
    901    while(!j)
    902    {
    903       j = 1;
    904       p = prime(random(1000000000,2134567879));
    905       for(i = 1; i <= size(L); i++)
    906       {
    907          if(p == L[i]) { j = 0; break; }
    908       }
    909       if(j)
    910       {
    911          for(i = 1; i <= ncols(I); i++)
    912          {
    913             for(k = 2; k <= size(I[i]); k++)
    914             {
    915                if((denominator(leadcoef(I[i][k])) mod p) == 0) { j = 0; break; }
    916             }
    917             if(!j){ break; }
    918          }
    919       }
    920       if(j)
    921       {
    922          if(!primeTest(I,p)) { j = 0; }
    923       }
    924    }
    925    r[1] = p;
    926    def @R = ring(r);
    927    setring @R;
    928    ideal I = imap(R,I);
    929    ideal J = imap(R,J);
    930    attrib(J,"isSB",1);
    931 
    932    int t = timer;
    933    j = 1;
    934    if(isIncluded(I,J) == 0) { j = 0; }
    935 
    936    if(printlevel >= 11)
    937    {
    938       "isIncluded(I,J) takes "+string(timer - t)+" seconds";
    939       "j = "+string(j);
    940    }
    941 
    942    t = timer;
    943    if(j)
    944    {
    945       if(size(#) > 0)
    946       {
    947          ideal K = modpStd(I,p,variant,#[1])[1];
    948       }
    949       else
    950       {
    951          ideal K = groebner(I);
    952       }
    953       t = timer;
    954       if(isIncluded(J,K) == 0) { j = 0; }
    955 
    956       if(printlevel >= 11)
    957       {
    958          "isIncluded(J,K) takes "+string(timer - t)+" seconds";
    959          "j = "+string(j);
    960       }
    961    }
    962    setring R;
    963    return(j);
    964 }
    965 example
    966 { "EXAMPLE:"; echo = 2;
    967    intvec L = 2,3,5;
    968    ring r = 0,(x,y,z),dp;
    969    ideal I = x+1,x+y+1;
    970    ideal J = x+1,y;
    971    pTestSB(I,I,L,2);
    972    pTestSB(I,J,L,2);
    973 }
     775
    974776////////////////////////////////////////////////////////////////////////////////
    975777static proc mixedTest()
  • Singular/LIB/normal.lib

    r36f0e5 rb9e63ba  
    36703670   }
    36713671
     3672   // check for 0-ideal
     3673   if (size(id)==0)
     3674   {
     3675     list result=list(ideal(1)),list(intvec(0),int(0));
     3676     // delta invariant,total delta invariant
     3677     if (wring)
     3678     {
     3679       result[3]=result[2]; // pair(delta invariants , total delta invariant)
     3680       result[2]=result[1];
     3681       def BR = basering;
     3682       list rl = ringlist(basering);
     3683       def rng = ring(rl);
     3684       setring rng;
     3685       ideal norid = 0;
     3686       ideal normap = maxideal(1);
     3687       export(norid);
     3688       export(normap);
     3689       setring BR;
     3690       result[1] = list(rng);
     3691     }
     3692     return (result);
     3693   }
     3694
    36723695   kill #;
    36733696   list #;
     
    38563879
    38573880   ideal J = mstdid[1];         //J is the SB of I
     3881   if (J[1]==1) { return(ideal(0));}
    38583882   ideal I = mstdid[2];
    38593883   int h = n-dim(J);            //codimension of V(I), I is a prime ideal
  • Singular/LIB/polymake.lib

    r36f0e5 rb9e63ba  
    4242  newtonPolytopeLP()  computes the lattice points of the Newton polytope
    4343  normalFanL()         computes the normal fan of a polytope
    44   groebnerFan()       computes the Groebner fan of a polynomial
     44  groebnerFanP()       computes the Groebner fan of a polynomial
    4545
    4646PROCEDURES USING TOPCOM:
     
    436436/////////////////////////////////////////////////////////////////////////////
    437437
    438 proc groebnerFan (poly f)
    439 "USAGE:  groebnerFan(f);  f poly
     438proc groebnerFanP (poly f)
     439"USAGE:  groebnerFanP(f);  f poly
    440440RETURN:  list, the ith entry of L[1] contains information about the ith cone
    441441               in the Groebner fan dual to the ith vertex in the Newton
     
    460460        TU Berlin and Michael Joswig, so it only works if polymake is installed;
    461461        see http://www.math.tu-berlin.de/polymake/
    462 EXAMPLE: example groebnerFan;   shows an example"
     462EXAMPLE: example groebnerFanP;   shows an example"
    463463{
    464464  int i,j;
     
    497497   poly f=y3+x2+xy+2xz+yz+z2+1;
    498498   // the Newton polytope of f is
    499    list gf=groebnerFan(f);
     499   list gf=groebnerFanP(f);
    500500   // the exponent vectors of f are ordered as follows
    501501   gf[4];
  • Singular/LIB/rwalk.lib

    • Property mode changed from 100644 to 100755
    rf38979 rb9e63ba  
    1010rwalk(ideal,int,int[,intvec,intvec]);   standard basis of ideal via Random Walk algorithm
    1111rwalk(ideal,int[,intvec,intvec]);       standard basis of ideal via Random Perturbation Walk algorithm
    12 frwalk(ideal,int[,intvec,intvec]);      standard basis of ideal via Random Fractal Walk algorithm
     12frandwalk(ideal,int[,intvec,intvec]);      standard basis of ideal via Random Fractal Walk algorithm
    1313";
    1414
     
    141141 * Random Walk  *
    142142 ****************/
    143 proc rwalk(ideal Go, int radius, int pert_deg, list #)
     143proc rwalk(ideal Go, int radius, int pert_deg, int reduction, int printout, list #)
    144144"SYNTAX: rwalk(ideal i, int radius);
    145145         if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
     146         intermediate Groebner bases are not reduced if reduction = 0
    146147TYPE:    ideal
    147148PURPOSE: compute the standard basis of the ideal, calculated via
     
    178179
    179180ideal G = fetch(xR, Go);
    180 G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg, basering);
     181G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg, reduction, printout);
    181182
    182183setring xR;
     
    196197  int radius = 1;
    197198  int perturb_deg = 2;
    198   rwalk(I,radius,perturb_deg);
     199  int reduction = 0;
     200  int printout = 1;
     201  rwalk(I,radius,perturb_deg,reduction,printout);
    199202}
    200203
     
    202205 * Perturbation Walk with random element *
    203206 *****************************************/
    204 proc prwalk(ideal Go, int radius, int o_pert_deg, int t_pert_deg, list #)
     207proc prwalk(ideal Go, int radius, int o_pert_deg, int t_pert_deg, int reduction, int printout, list #)
    205208"SYNTAX: rwalk(ideal i, int radius);
    206209         if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
     
    227230  OSCTW= OrderStringalp_NP("al", #);
    228231  }
     232int nP = OSCTW[1];
    229233string ord_str = OSCTW[2];
    230234intvec curr_weight = OSCTW[3]; // original weight vector
     
    238242
    239243ideal G = fetch(xR, Go);
    240 G = system("Mprwalk", G, curr_weight, target_weight, radius, o_pert_deg, t_pert_deg, basering);
     244G = system("Mprwalk", G, curr_weight, target_weight, radius, o_pert_deg, t_pert_deg,
     245           nP, reduction, printout);
    241246
    242247setring xR;
     
    257262  int o_perturb_deg = 2;
    258263  int t_perturb_deg = 2;
    259   prwalk(I,radius,o_perturb_deg,t_perturb_deg);
     264  int reduction = 0;
     265  int printout = 2;
     266  prwalk(I,radius,o_perturb_deg,t_perturb_deg,reduction,printout);
    260267}
    261268
     
    263270 * Fractal Walk with random element *
    264271 ************************************/
    265 proc frandwalk(ideal Go, int radius, list #)
    266 "SYNTAX: frwalk(ideal i, int radius);
    267          frwalk(ideal i, int radius, intvec v, intvec w);
     272proc frandwalk(ideal Go, int radius, int reduction, int printout, list #)
     273"SYNTAX: frwalk(ideal i, int radius, int reduction, int printout);
     274         frwalk(ideal i, int radius, int reduction, int printout, intvec v, intvec w);
    268275TYPE:    ideal
    269276PURPOSE: compute the standard basis of the ideal, calculated via
     
    299306   ideal G = fetch(xR, Go);
    300307   int pert_deg = 2;
    301    G = system("Mfrwalk", G, curr_weight, target_weight, radius);
     308
     309   G = system("Mfrwalk", G, curr_weight, target_weight, radius, reduction, printout);
    302310
    303311   setring xR;
     
    314322    ring r = 0,(z,y,x), lp;
    315323    ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
    316     frandwalk(I,2);
    317 }
     324    int reduction = 0;
     325    frandwalk(I,2,0,1);
     326}
  • Singular/LIB/swalk.lib

    • Property mode changed from 100644 to 100755
  • Singular/dyn_modules/gfanlib/Makefile.am

    r36f0e5 rb9e63ba  
    11ACLOCAL_AMFLAGS = -I ../../m4
    22
    3 SOURCES = singularWishlist.h gfanlib_exceptions.h callgfanlib_conversion.cc callgfanlib_conversion.h bbcone.cc bbcone.h bbfan.cc bbfan.h bbpolytope.cc bbpolytope.h gfan.h gitfan.cc gitfan.h std_wrapper.cc std_wrapper.h tropicalVarietyOfPolynomials.h tropicalVarietyOfPolynomials.cc ppinitialReduction.cc ppinitialReduction.h containsMonomial.cc containsMonomial.h adjustWeights.cc adjustWeights.h tropicalStrategy.cc tropicalStrategy.h initial.cc initial.h witness.cc witness.h lift.cc lift.h flip.cc flip.h tropicalCurves.cc tropicalCurves.h groebnerCone.cc groebnerCone.h startingCone.cc startingCone.h tropicalTraversal.cc tropicalTraversal.h tropicalVarietyOfIdeals.cc tropicalVarietyOfIdeals.h tropicalVariety.cc tropicalVariety.h tropical.cc tropical.h gfanlib.cc
     3SOURCES = singularWishlist.h gfanlib_exceptions.h callgfanlib_conversion.cc callgfanlib_conversion.h bbcone.cc bbcone.h bbfan.cc bbfan.h bbpolytope.cc bbpolytope.h gfan.h gitfan.cc gitfan.h std_wrapper.cc std_wrapper.h tropicalVarietyOfPolynomials.h tropicalVarietyOfPolynomials.cc ppinitialReduction.cc ppinitialReduction.h containsMonomial.cc containsMonomial.h adjustWeights.cc adjustWeights.h tropicalStrategy.cc tropicalStrategy.h initial.cc initial.h witness.cc witness.h lift.cc lift.h flip.cc flip.h tropicalCurves.cc tropicalCurves.h groebnerCone.cc groebnerCone.h startingCone.cc startingCone.h tropicalTraversal.cc tropicalTraversal.h tropicalVarietyOfIdeals.cc tropicalVarietyOfIdeals.h tropicalVariety.cc tropicalVariety.h groebnerFan.cc groebnerFan.h groebnerComplex.cc groebnerComplex.h tropical.cc tropical.h gfanlib.cc
    44
    55MY_CPPFLAGS = -I${srcdir} -I${top_srcdir} -I${top_builddir} \
  • Singular/dyn_modules/gfanlib/bbcone.cc

    r36f0e5 rb9e63ba  
    16661666
    16671667  return relativeInteriorPoints;
     1668}
     1669
     1670
     1671/***
     1672 * Computes a relative interior point and an outer normal vector for each facet of zc
     1673 **/
     1674std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc, const std::set<gfan::ZVector> &exceptThesePoints, const bool onlyLowerHalfSpace)
     1675{
     1676  gfan::ZMatrix inequalities = zc.getFacets();
     1677  gfan::ZMatrix equations = zc.getImpliedEquations();
     1678  int r = inequalities.getHeight();
     1679  int c = inequalities.getWidth();
     1680
     1681  /* our cone has r facets, if r==0 return empty matrices */
     1682  gfan::ZMatrix relativeInteriorPoints = gfan::ZMatrix(0,c);
     1683  gfan::ZMatrix outerFacetNormals = gfan::ZMatrix(0,c);
     1684  if (r==0)
     1685    return std::make_pair(relativeInteriorPoints,outerFacetNormals);
     1686
     1687  /* next we iterate over each of the r facets,
     1688   * build the respective cone and add it to the list
     1689   * this is the i=0 case */
     1690  gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c);
     1691  gfan::ZMatrix newEquations = equations;
     1692  newEquations.appendRow(inequalities[0]);
     1693  gfan::ZCone facet = gfan::ZCone(newInequalities,newEquations);
     1694  gfan::ZVector interiorPoint = facet.getRelativeInteriorPoint();
     1695  if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
     1696  {
     1697    if (exceptThesePoints.count(interiorPoint)==0)
     1698    {
     1699      relativeInteriorPoints.appendRow(interiorPoint);
     1700      outerFacetNormals.appendRow(-inequalities[0]);
     1701    }
     1702  }
     1703
     1704  /* these are the cases i=1,...,r-2 */
     1705  for (int i=1; i<r-1; i++)
     1706  {
     1707    newInequalities = inequalities.submatrix(0,0,i,c);
     1708    newInequalities.append(inequalities.submatrix(i+1,0,r,c));
     1709    newEquations = equations;
     1710    newEquations.appendRow(inequalities[i]);
     1711    facet = gfan::ZCone(newInequalities,newEquations);
     1712    interiorPoint = facet.getRelativeInteriorPoint();
     1713    if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
     1714    {
     1715      if (exceptThesePoints.count(interiorPoint)==0)
     1716      {
     1717        relativeInteriorPoints.appendRow(interiorPoint);
     1718        outerFacetNormals.appendRow(-inequalities[i]);
     1719      }
     1720    }
     1721  }
     1722
     1723  /* this is the i=r-1 case */
     1724  newInequalities = inequalities.submatrix(0,0,r-1,c);
     1725  newEquations = equations;
     1726  newEquations.appendRow(inequalities[r-1]);
     1727  facet = gfan::ZCone(newInequalities,newEquations);
     1728  interiorPoint = facet.getRelativeInteriorPoint();
     1729  if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
     1730  {
     1731    if (exceptThesePoints.count(interiorPoint)==0)
     1732    {
     1733      relativeInteriorPoints.appendRow(interiorPoint);
     1734      outerFacetNormals.appendRow(-inequalities[r-1]);
     1735    }
     1736  }
     1737
     1738  return std::make_pair(relativeInteriorPoints,outerFacetNormals);
    16681739}
    16691740
  • Singular/dyn_modules/gfanlib/bbcone.h

    r36f0e5 rb9e63ba  
    2121gfan::ZCone liftUp(const gfan::ZCone &zc);
    2222gfan::ZMatrix interiorPointsOfFacets(const gfan::ZCone &zc, const std::set<gfan::ZVector> &exceptThese=std::set<gfan::ZVector>());
     23std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc, const std::set<gfan::ZVector> &exceptThesePoints=std::set<gfan::ZVector>(), const bool onlyLowerHalfSpace=false);
    2324
    2425#endif
  • Singular/dyn_modules/gfanlib/groebnerCone.cc

    r36f0e5 rb9e63ba  
    444444
    445445/***
    446  * Computes a relative interior point and an outer normal vector for each facet of zc
    447  **/
    448 static std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc)
    449 {
    450   gfan::ZMatrix inequalities = zc.getFacets();
    451   gfan::ZMatrix equations = zc.getImpliedEquations();
    452   int r = inequalities.getHeight();
    453   int c = inequalities.getWidth();
    454 
    455   /* our cone has r facets, if r==0 return empty matrices */
    456   gfan::ZMatrix relativeInteriorPoints = gfan::ZMatrix(0,c);
    457   gfan::ZMatrix outerFacetNormals = gfan::ZMatrix(0,c);
    458   if (r==0)
    459     return std::make_pair(relativeInteriorPoints,outerFacetNormals);
    460 
    461   /* next we iterate over each of the r facets,
    462    * build the respective cone and add it to the list
    463    * this is the i=0 case */
    464   gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c);
    465   gfan::ZMatrix newEquations = equations;
    466   newEquations.appendRow(inequalities[0]);
    467   gfan::ZCone facet = gfan::ZCone(newInequalities,newEquations);
    468   relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
    469   assume(zc.contains(relativeInteriorPoints[0]) && !zc.containsRelatively(relativeInteriorPoints[0]));
    470   outerFacetNormals.appendRow(-inequalities[0]);
    471 
    472   /* these are the cases i=1,...,r-2 */
    473   for (int i=1; i<r-1; i++)
    474   {
    475     newInequalities = inequalities.submatrix(0,0,i,c);
    476     newInequalities.append(inequalities.submatrix(i+1,0,r,c));
    477     newEquations = equations;
    478     newEquations.appendRow(inequalities[i]);
    479     facet = gfan::ZCone(newInequalities,newEquations);
    480     relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
    481     assume(zc.contains(relativeInteriorPoints[i]) && !zc.containsRelatively(relativeInteriorPoints[i]));
    482     outerFacetNormals.appendRow(-inequalities[i]);
    483   }
    484 
    485   /* this is the i=r-1 case */
    486   newInequalities = inequalities.submatrix(0,0,r-1,c);
    487   newEquations = equations;
    488   newEquations.appendRow(inequalities[r-1]);
    489   facet = gfan::ZCone(newInequalities,newEquations);
    490   relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
    491   assume(zc.contains(relativeInteriorPoints[r-1]) && !zc.containsRelatively(relativeInteriorPoints[r-1]));
    492   outerFacetNormals.appendRow(-inequalities[r-1]);
    493 
    494   return std::make_pair(relativeInteriorPoints,outerFacetNormals);
    495 }
    496 
    497 
    498 /***
    499446 * Returns a complete list of neighboring Groebner cones.
    500447 **/
     
    565512    {
    566513      gfan::ZCone zc = sigma->getPolyhedralCone();
    567       assume(isCompatible(zf,&zc));
     514      // assume(isCompatible(zf,&zc));
    568515      zf->insert(zc);
    569516    }
  • Singular/dyn_modules/gfanlib/initial.cc

    r36f0e5 rb9e63ba  
    1212  {
    1313    if (!w[i].fitsInInt())
     14    {
     15      WerrorS("wDeg: overflow in weight vector");
    1416      throw 0; // weightOverflow;
     17    }
    1518    d += p_GetExp(p,i+1,r)*w[i].toInt();
    1619  }
  • Singular/dyn_modules/gfanlib/ppinitialReduction.cc

    r36f0e5 rb9e63ba  
    121121}
    122122
     123bool p_xLeadmonomDivisibleBy(const poly g, const poly f, const ring r)
     124{
     125  poly gx = p_Head(g,r);
     126  poly fx = p_Head(f,r);
     127  p_SetExp(gx,1,0,r);
     128  p_SetExp(fx,1,0,r);
     129  p_Setm(gx,r);
     130  p_Setm(fx,r);
     131  bool b = p_LeadmonomDivisibleBy(gx,fx,r);
     132  p_Delete(&gx,r);
     133  p_Delete(&fx,r);
     134  return b;
     135}
     136
     137void pReduceInhomogeneous(poly &g, const number p, const ring r)
     138{
     139  if (g==NULL)
     140    return;
     141  p_Test(g,r);
     142
     143  poly toBeChecked = pNext(g);
     144  pNext(g) = NULL; poly gEnd = g;
     145  poly gCache;
     146
     147  number coeff, pPower; int power; poly subst;
     148  while(toBeChecked)
     149  {
     150    for (gCache = g; gCache; pIter(gCache))
     151      if (p_xLeadmonomDivisibleBy(gCache,toBeChecked,r)) break;
     152    if (gCache)
     153    {
     154      n_Power(p,p_GetExp(toBeChecked,1,r)-p_GetExp(gCache,1,r),&pPower,r->cf);
     155      coeff = n_Mult(p_GetCoeff(toBeChecked,r),pPower,r->cf);
     156      p_SetCoeff(gCache,n_Add(p_GetCoeff(gCache,r),coeff,r->cf),r);
     157      n_Delete(&pPower,r->cf); n_Delete(&coeff,r->cf);
     158      toBeChecked=p_LmDeleteAndNext(toBeChecked,r);
     159    }
     160    else
     161    {
     162      if (n_DivBy(p_GetCoeff(toBeChecked,r),p,r->cf))
     163      {
     164        power=1;
     165        coeff=n_Div(p_GetCoeff(toBeChecked,r),p,r->cf);
     166        while (n_DivBy(coeff,p,r->cf))
     167        {
     168          power++;
     169          number coeff0 = n_Div(coeff,p,r->cf);
     170          n_Delete(&coeff,r->cf);
     171          coeff = coeff0;
     172          coeff0 = NULL;
     173          if (power<1)
     174          {
     175            WerrorS("pReduce: overflow in exponent");
     176            throw 0;
     177          }
     178        }
     179        subst=p_LmInit(toBeChecked,r);
     180        p_AddExp(subst,1,power,r);
     181        p_SetCoeff(subst,coeff,r);
     182        p_Setm(subst,r); p_Test(subst,r);
     183        toBeChecked=p_LmDeleteAndNext(toBeChecked,r);
     184        toBeChecked=p_Add_q(toBeChecked,subst,r);
     185        p_Test(toBeChecked,r);
     186      }
     187      else
     188      {
     189        pNext(gEnd)=toBeChecked;
     190        pIter(gEnd); pIter(toBeChecked);
     191        pNext(gEnd)=NULL;
     192        p_Test(g,r);
     193      }
     194    }
     195  }
     196  p_Test(g,r);
     197  divideByCommonGcd(g,r);
     198  return;
     199}
     200
    123201void ptNormalize(poly* gStar, const number p, const ring r)
    124202{
  • Singular/dyn_modules/gfanlib/ppinitialReduction.h

    r36f0e5 rb9e63ba  
    1010bool isOrderingLocalInT(const ring r);
    1111void pReduce(ideal &I, const number p, const ring r);
     12void pReduceInhomogeneous(poly &g, const number p, const ring r);
    1213bool ppreduceInitially(ideal I, const ring r, const number p);
    1314/* BOOLEAN ppreduceInitially(leftv res, leftv args); */
  • Singular/dyn_modules/gfanlib/startingCone.cc

    r36f0e5 rb9e63ba  
    55#include <lift.h>
    66#include <groebnerCone.h>
    7 // #include <neighbours.h>
    87#include <tropicalStrategy.h>
    98#include <tropicalCurves.h>
     
    1413
    1514
    16 /***
    17  * checks whether sigma is contained in the tropical variety
    18  * by testing whether the initial Ideal with respect to the interior point
    19  * is monomial free.
    20  **/
    21 // static bool checkContainmentInTropicalVariety(const groebnerCone sigma)
    22 // {
    23 //   ideal I = sigma.getPolynomialIdeal();
    24 //   ring r = sigma.getPolynomialRing();
    25 //   const tropicalStrategy* currentStrategy = sigma.getTropicalStrategy();
    26 
    27 //   gfan::ZCone zc = sigma.getPolyhedralCone();
    28 //   gfan::ZMatrix zm = zc.extremeRays();
    29 //   for (int i=0; i<zm.getHeight(); i++)
    30 //   {
    31 //     gfan::ZVector w = zm[i];
    32 //     if (currentStrategy->isValuationNonTrivial() && w[0].sign()==0)
    33 //       continue;
    34 //     poly s = currentStrategy->checkInitialIdealForMonomial(I,r,w);
    35 //     if (s)
    36 //     {
    37 //       p_Delete(&s,r);
    38 //       return false;
    39 //     }
    40 //   }
    41 
    42 //   zm = zc.generatorsOfLinealitySpace();
    43 //   for (int i=0; i<zm.getHeight(); i++)
    44 //   {
    45 //     gfan::ZVector w = zm[i];
    46 //     if (currentStrategy->isValuationNonTrivial() && w[0].sign()==0)
    47 //       continue;
    48 //     poly s = currentStrategy->checkInitialIdealForMonomial(I,r,w);
    49 //     if (s)
    50 //     {
    51 //       p_Delete(&s,r);
    52 //       return false;
    53 //     }
    54 //   }
    55 
    56 //   return true;
    57 // }
    58 
    59 
    60 // static bool checkOneCodimensionalLinealitySpace(const groebnerCone sigma)
    61 // {
    62 //   gfan::ZCone zc = sigma.getPolyhedralCone();
    63 //   int linDim = zc.dimensionOfLinealitySpace();
    64 //   int dim = zc.dimension();
    65 //   return (linDim+1)==dim;
    66 // }
     15groebnerCone groebnerStartingCone(const tropicalStrategy& currentStrategy)
     16{
     17  groebnerCone sigma(currentStrategy.getStartingIdeal(), currentStrategy.getStartingRing(), currentStrategy);
     18  return sigma;
     19}
    6720
    6821
  • Singular/dyn_modules/gfanlib/startingCone.h

    r36f0e5 rb9e63ba  
    55#include <tropicalStrategy.h>
    66
     7groebnerCone groebnerStartingCone(const tropicalStrategy& currentStrategy);
    78groebnerCone tropicalStartingCone(const tropicalStrategy& currentCase);
    89
  • Singular/dyn_modules/gfanlib/tropical.cc

    r36f0e5 rb9e63ba  
    55#include <bbcone.h>
    66#include <ppinitialReduction.h>
    7 // #include <ttinitialReduction.h>
    87#include <containsMonomial.h>
    98#include <initial.h>
    109#include <witness.h>
    1110#include <tropicalCurves.h>
    12 // #include <neighbours.h>
    1311#include <tropicalStrategy.h>
    1412#include <startingCone.h>
     13#include <groebnerFan.h>
     14#include <groebnerComplex.h>
    1515#include <tropicalVariety.h>
    1616
     17int tropicalVerboseLevel = 0;
    1718
    1819gfan::ZCone homogeneitySpace(ideal I, ring r)
     
    5152{
    5253  leftv u = args;
     54  if ((u != NULL) && (u->Typ() == POLY_CMD))
     55  {
     56    leftv v = u->next;
     57    if (v == NULL)
     58    {
     59      poly g = (poly) u->Data();
     60      ideal I = idInit(1);
     61      I->m[0] = g;
     62      res->rtyp = coneID;
     63      res->data = (void*) new gfan::ZCone(homogeneitySpace(I,currRing));
     64      I->m[0] = NULL;
     65      id_Delete(&I,currRing);
     66      return FALSE;
     67    }
     68  }
    5369  if ((u != NULL) && (u->Typ() == IDEAL_CMD))
    5470  {
     
    107123{
    108124  leftv u = args;
     125  if ((u != NULL) && (u->Typ() == POLY_CMD))
     126  {
     127    leftv v = u->next;
     128    if (v == NULL)
     129    {
     130      poly g = (poly) u->Data();
     131      ideal I = idInit(1);
     132      I->m[0] = g;
     133      res->rtyp = coneID;
     134      res->data = (void*) new gfan::ZCone(lowerHomogeneitySpace(I,currRing));
     135      I->m[0] = NULL;
     136      id_Delete(&I,currRing);
     137      return FALSE;
     138    }
     139  }
    109140  if ((u != NULL) && (u->Typ() == IDEAL_CMD))
    110141  {
     
    181212{
    182213  leftv u = args;
     214  if ((u != NULL) && (u->Typ() == POLY_CMD))
     215  {
     216    leftv v = u->next;
     217    if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
     218    {
     219      try
     220      {
     221        poly g = (poly) u->Data();
     222        ideal I = idInit(1);
     223        I->m[0] = g;
     224        gfan::ZVector* weightVector;
     225        if (v->Typ() == INTVEC_CMD)
     226        {
     227          intvec* w0 = (intvec*) v->Data();
     228          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
     229          w1->inpTranspose();
     230          weightVector = bigintmatToZVector(*w1);
     231          delete w1;
     232        }
     233        else
     234        {
     235          bigintmat* w1 = (bigintmat*) v->Data();
     236          weightVector = bigintmatToZVector(*w1);
     237        }
     238        res->rtyp = coneID;
     239        res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
     240        delete weightVector;
     241        I->m[0] = NULL;
     242        id_Delete(&I,currRing);
     243        return FALSE;
     244      }
     245      catch (const std::exception& ex)
     246      {
     247        Werror("ERROR: %s",ex.what());
     248        return TRUE;
     249      }
     250    }
     251  }
    183252  if ((u != NULL) && (u->Typ() == IDEAL_CMD))
    184253  {
     
    186255    if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
    187256    {
    188       ideal I = (ideal) u->Data();
    189       gfan::ZVector* weightVector;
    190       if (v->Typ() == INTVEC_CMD)
    191       {
    192         intvec* w0 = (intvec*) v->Data();
    193         bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
    194         w1->inpTranspose();
    195         weightVector = bigintmatToZVector(*w1);
    196         delete w1;
    197       }
    198       else
    199       {
    200         bigintmat* w1 = (bigintmat*) v->Data();
    201         weightVector = bigintmatToZVector(*w1);
    202       }
    203       res->rtyp = coneID;
    204       res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
    205       delete weightVector;
    206       return FALSE;
     257      try
     258      {
     259        ideal I = (ideal) u->Data();
     260        gfan::ZVector* weightVector;
     261        if (v->Typ() == INTVEC_CMD)
     262        {
     263          intvec* w0 = (intvec*) v->Data();
     264          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
     265          w1->inpTranspose();
     266          weightVector = bigintmatToZVector(*w1);
     267          delete w1;
     268        }
     269        else
     270        {
     271          bigintmat* w1 = (bigintmat*) v->Data();
     272          weightVector = bigintmatToZVector(*w1);
     273        }
     274        res->rtyp = coneID;
     275        res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
     276        delete weightVector;
     277        return FALSE;
     278      }
     279      catch (const std::exception& ex)
     280      {
     281        Werror("ERROR: %s",ex.what());
     282        return TRUE;
     283      }
    207284    }
    208285  }
     
    243320{
    244321  leftv u = args;
     322  if ((u != NULL) && (u->Typ() == POLY_CMD))
     323  {
     324    leftv v = u->next;
     325    if (v == NULL)
     326    {
     327      try
     328      {
     329        poly g = (poly) u->Data();
     330        ideal I = idInit(1);
     331        I->m[0] = g;
     332        res->rtyp = coneID;
     333        res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
     334        I->m[0] = NULL;
     335        id_Delete(&I,currRing);
     336        return FALSE;
     337      }
     338      catch (const std::exception& ex)
     339      {
     340        Werror("ERROR: %s",ex.what());
     341        return TRUE;
     342      }
     343    }
     344  }
    245345  if ((u != NULL) && (u->Typ() == IDEAL_CMD))
    246346  {
     
    248348    if (v == NULL)
    249349    {
    250       ideal I = (ideal) u->Data();
    251       res->rtyp = coneID;
    252       res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
    253       return FALSE;
     350      try
     351      {
     352        ideal I = (ideal) u->Data();
     353        res->rtyp = coneID;
     354        res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
     355        return FALSE;
     356      }
     357      catch (const std::exception& ex)
     358      {
     359        Werror("ERROR: %s",ex.what());
     360        return TRUE;
     361      }
    254362    }
    255363  }
     
    293401    if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
    294402    {
    295       ideal I = (ideal) u->Data();
    296       gfan::ZVector* weightVector;
    297       if (v->Typ() == INTVEC_CMD)
    298       {
    299         intvec* w0 = (intvec*) v->Data();
    300         bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
    301         w1->inpTranspose();
    302         weightVector = bigintmatToZVector(*w1);
    303         delete w1;
    304       }
    305       else
    306       {
    307         bigintmat* w1 = (bigintmat*) v->Data();
    308         weightVector = bigintmatToZVector(*w1);
    309       }
    310       res->rtyp = IDEAL_CMD;
    311       res->data = (void*) initial(I, currRing, *weightVector);
    312       delete weightVector;
    313       return FALSE;
     403      try
     404      {
     405        ideal I = (ideal) u->Data();
     406        gfan::ZVector* weightVector;
     407        if (v->Typ() == INTVEC_CMD)
     408        {
     409          intvec* w0 = (intvec*) v->Data();
     410          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
     411          w1->inpTranspose();
     412          weightVector = bigintmatToZVector(*w1);
     413          delete w1;
     414        }
     415        else
     416        {
     417          bigintmat* w1 = (bigintmat*) v->Data();
     418          weightVector = bigintmatToZVector(*w1);
     419        }
     420        res->rtyp = IDEAL_CMD;
     421        res->data = (void*) initial(I, currRing, *weightVector);
     422        delete weightVector;
     423        return FALSE;
     424      }
     425      catch (const std::exception& ex)
     426      {
     427        Werror("ERROR: %s",ex.what());
     428        return TRUE;
     429      }
    314430    }
    315431  }
     
    326442  p->iiAddCproc("","lowerHomogeneitySpace",FALSE,lowerHomogeneitySpace);
    327443  p->iiAddCproc("","initial",FALSE,initial);
     444  p->iiAddCproc("","tropicalVariety",FALSE,tropicalVariety);
     445  p->iiAddCproc("","groebnerFan",FALSE,groebnerFan);
     446  p->iiAddCproc("","groebnerComplex",FALSE,groebnerComplex);
     447#ifndef NDEBUG
    328448  // p->iiAddCproc("","tropicalNeighbours",FALSE,tropicalNeighbours);
    329 #ifndef NDEBUG
    330449  // p->iiAddCproc("","initial0",FALSE,initial0);
    331450  p->iiAddCproc("","pReduceDebug",FALSE,pReduceDebug);
     
    362481  p->iiAddCproc("","nonPositiveTropicalStartingPoint",FALSE,nonPositiveTropicalStartingPoint);
    363482  p->iiAddCproc("","tropicalStartingCone",FALSE,tropicalStartingCone);
    364   p->iiAddCproc("","tropicalVariety",FALSE,tropicalVariety);
    365483#endif //NDEBUG
    366484  // p->iiAddCproc("","ppreduceInitially",FALSE,ppreduceInitially);
  • Singular/dyn_modules/gfanlib/tropical.h

    r36f0e5 rb9e63ba  
    44#include "Singular/ipid.h"
    55
     6
     7extern int tropicalVerboseLevel;
     8
     9
    610gfan::ZCone homogeneitySpace(ideal I, ring r);
    711void tropical_setup(SModulFunctions* p);
  • Singular/dyn_modules/gfanlib/tropicalCurves.cc

    r36f0e5 rb9e63ba  
    7070
    7171  /* construct a new ordering as describe above */
    72   bool overflow;
     72  bool overflow = false;
    7373  s->order[0] = ringorder_a;
    7474  s->block0[0] = 1;
     
    9797
    9898  if (overflow)
    99     throw 0; //todo: use a proper custom exception
     99  {
     100    WerrorS("genericlyWeightedOrdering: overflow in weight vector");
     101    throw 0; // weightOverflow;
     102  }
    100103
    101104  /* complete the ring and return it */
  • Singular/dyn_modules/gfanlib/tropicalStrategy.cc

    r36f0e5 rb9e63ba  
    134134  extraReductionAlgorithm(noExtraReduction)
    135135{
    136   assume(rField_is_Q(r) || rField_is_Zp(r));
     136  assume(rField_is_Q(r) || rField_is_Zp(r) || rField_is_Ring_Z(r));
    137137  if (!completelyHomogeneous)
    138138  {
     
    225225  omFreeSize(shiftByOne,(n+1)*sizeof(int));
    226226
    227   // ring origin = currRing;
    228   // rChangeCurrRing(startingRing);
    229   // ideal startingIdeal = kNF(pt,startingRing->qideal,J);
    230   // rChangeCurrRing(origin);
    231   ideal startingIdeal = J; J = NULL;
     227  ring origin = currRing;
     228  rChangeCurrRing(startingRing);
     229  ideal startingIdeal = kNF(pt,startingRing->qideal,J); // mathematically redundant,
     230  rChangeCurrRing(origin);                              // but helps with upcoming std computation
     231  // ideal startingIdeal = J; J = NULL;
    232232  assume(startingIdeal->m[k]==NULL);
    233233  startingIdeal->m[k] = pt->m[0];
     
    271271  /* map the input ideal into the new polynomial ring */
    272272  startingIdeal = constructStartingIdeal(J,s,uniformizingParameter,startingRing);
     273  reduce(startingIdeal,startingRing);
    273274
    274275  linealitySpace = homogeneitySpace(startingIdeal,startingRing);
  • Singular/dyn_modules/gfanlib/tropicalTraversal.cc

    r36f0e5 rb9e63ba  
    33#include <tropicalCurves.h>
    44
    5 std::vector<bool> checkNecessaryFlips(const groebnerCones &tropicalVariety, const groebnerCones &workingList,
    6                                       const gfan::ZVector &interiorPoint, const gfan::ZMatrix &normalVectors)
     5std::vector<bool> checkNecessaryTropicalFlips(const groebnerCones &tropicalVariety, const groebnerCones &workingList,
     6                                              const gfan::ZVector &interiorPoint, const gfan::ZMatrix &normalVectors)
    77{
    88  int k = normalVectors.getHeight();
     
    7272        id_Delete(&inI,sigma.getPolynomialRing());
    7373
    74         std::vector<bool> needToFlip = checkNecessaryFlips(tropicalVariety,workingList,interiorPoint,normalVectors);
     74        std::vector<bool> needToFlip = checkNecessaryTropicalFlips(tropicalVariety,workingList,interiorPoint,normalVectors);
    7575        for (int j=0; j<normalVectors.getHeight(); j++)
    7676        {
     
    8888    workingList.erase(sigma);
    8989    tropicalVariety.insert(sigma);
    90     // std::cout << "tropicalVariety.size():" << tropicalVariety.size() << std::endl;
    91     // std::cout << "workingList.size():" << workingList.size() << std::endl;
     90    if (printlevel > 0)
     91      Print("cones finished: %lu   cones in working list: %lu\n",
     92      (unsigned long)tropicalVariety.size(), (unsigned long)workingList.size());
    9293  }
    9394  return tropicalVariety;
    9495}
    9596
    96 groebnerCones tropicalTraversal(const groebnerCone startingCone)
     97
     98std::vector<bool> checkNecessaryGroebnerFlips(const groebnerCones &groebnerFan, const groebnerCones &workingList,
     99                                              const gfan::ZMatrix &interiorPoints)
    97100{
    98   groebnerCones tropicalVariety;
     101  int k = interiorPoints.getHeight();
     102  std::vector<bool> needToFlip(k,true);
     103
     104  for (groebnerCones::iterator sigma = groebnerFan.begin(); sigma!=groebnerFan.end(); sigma++)
     105  {
     106    for (int i=0; i<k; i++)
     107    {
     108      if (needToFlip[i] && sigma->contains(interiorPoints[i]))
     109        needToFlip[i] = false;
     110    }
     111  }
     112
     113  for (groebnerCones::iterator sigma = workingList.begin(); sigma!=workingList.end(); sigma++)
     114  {
     115    for (int i=0; i<k; i++)
     116    {
     117      if (needToFlip[i] && sigma->contains(interiorPoints[i]))
     118        needToFlip[i] = false;
     119    }
     120  }
     121
     122  return needToFlip;
     123}
     124
     125
     126groebnerCones groebnerTraversal(const groebnerCone startingCone)
     127{
     128  const tropicalStrategy* currentStrategy = startingCone.getTropicalStrategy();
     129
     130  groebnerCones groebnerFan;
    99131  groebnerCones workingList;
    100132  workingList.insert(startingCone);
    101   // std::cout << "starting traversal" << std::endl;
     133  std::set<gfan::ZVector> finishedInteriorPoints;
     134  bool onlyLowerHalfSpace = !currentStrategy->isValuationTrivial();
     135
    102136  while(!workingList.empty())
    103137  {
    104     const groebnerCone sigma=*(workingList.begin());
    105     const groebnerCones neighbours = sigma.tropicalNeighbours();
    106     for (groebnerCones::iterator tau = neighbours.begin(); tau!=neighbours.end(); tau++)
     138    /**
     139     * Pick a maximal Groebner cone from the working list
     140     * and compute interior points on its facets as well as outer facet normals
     141     */
     142    groebnerCone sigma=*(workingList.begin());
     143    workingList.erase(workingList.begin());
     144
     145    std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndOuterFacetNormals = interiorPointsAndNormalsOfFacets(sigma.getPolyhedralCone(), finishedInteriorPoints, onlyLowerHalfSpace);
     146    gfan::ZMatrix interiorPoints = interiorPointsAndOuterFacetNormals.first;
     147    gfan::ZMatrix outerFacetNormals = interiorPointsAndOuterFacetNormals.second;
     148    std::vector<bool> needToFlip = checkNecessaryGroebnerFlips(groebnerFan,workingList, interiorPoints);
     149
     150    for (int i=0; i<interiorPoints.getHeight(); i++)
    107151    {
    108       if (tropicalVariety.count(*tau)==0)
    109         workingList.insert(*tau);
     152      gfan::ZVector interiorPoint = interiorPoints[i];
     153
     154      if (needToFlip[i]==true)
     155      {
     156        groebnerCone neighbour = sigma.flipCone(interiorPoint,outerFacetNormals[i]);
     157        workingList.insert(neighbour);
     158      }
     159      finishedInteriorPoints.insert(interiorPoints[i]);
    110160    }
    111     tropicalVariety.insert(sigma);
    112     workingList.erase(sigma);
    113     // std::cout << "tropicalVariety.size():" << tropicalVariety.size() << std::endl;
    114     // std::cout << "workingList.size():" << workingList.size() << std::endl;
     161
     162    sigma.deletePolynomialData();
     163    groebnerFan.insert(sigma);
     164    if (printlevel > 0)
     165      Print("cones finished: %lu   cones in working list: %lu\n",
     166      (unsigned long)groebnerFan.size(), (unsigned long)workingList.size());
    115167  }
    116   return tropicalVariety;
     168  return groebnerFan;
    117169}
  • Singular/dyn_modules/gfanlib/tropicalTraversal.h

    r36f0e5 rb9e63ba  
    22#define TROPICAL_TRAVERSAL_H
    33
     4#include <groebnerCone.h>
     5
    46groebnerCones tropicalTraversalMinimizingFlips(const groebnerCone startingCone);
    57groebnerCones tropicalTraversal(const groebnerCone startingCone);
     8groebnerCones groebnerTraversal(const groebnerCone startingCone);
    69
    710#endif
  • Singular/dyn_modules/gfanlib/tropicalVariety.cc

    r36f0e5 rb9e63ba  
    1414BITSET bitsetSave1, bitsetSave2;
    1515
     16
    1617/***
    1718 * sets option(redSB)
     
    2223  si_opt_1|=Sy_bit(OPT_REDSB);
    2324}
     25
    2426
    2527/***
     
    4042}
    4143
     44
    4245BOOLEAN tropicalVariety(leftv res, leftv args)
    4346{
    4447  leftv u = args;
     48  if ((u!=NULL) && (u->Typ()==POLY_CMD))
     49  {
     50    poly g = (poly) u->Data();
     51    leftv v = u->next;
     52    if (v==NULL)
     53    {
     54      try
     55      {
     56        ideal I = idInit(1);
     57        I->m[0] = g;
     58        tropicalStrategy currentStrategy(I,currRing);
     59        std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
     60        res->rtyp = fanID;
     61        res->data = (char*) toZFan(maxCones);
     62        I->m[0] = NULL;
     63        id_Delete(&I,currRing);
     64        return FALSE;
     65      }
     66      catch (const std::exception& ex)
     67      {
     68        Werror("ERROR: %s",ex.what());
     69        return TRUE;
     70      }
     71    }
     72    if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
     73    {
     74      try
     75      {
     76        ideal I = idInit(1);
     77        I->m[0] = g;
     78        number p = (number) v->Data();
     79        tropicalStrategy currentStrategy(I,p,currRing);
     80        ideal startingIdeal = currentStrategy.getStartingIdeal();
     81        ring startingRing = currentStrategy.getStartingRing();
     82        poly gStart = startingIdeal->m[0];
     83        std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
     84        res->rtyp = fanID;
     85        res->data = (char*) toZFan(maxCones);
     86        I->m[0] = NULL;
     87        id_Delete(&I,currRing);
     88        return FALSE;
     89      }
     90      catch (const std::exception& ex)
     91      {
     92        Werror("ERROR: %s",ex.what());
     93        return TRUE;
     94      }
     95
     96    }
     97  }
    4598  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
    4699  {
     
    53106      if (v==NULL)
    54107      {
    55         tropicalStrategy currentStrategy(I,currRing);
    56         std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
    57         // gfan::ZFan* zf = toZFan(maxCones);
    58         // delete zf;
    59         // res->rtyp = NONE;
    60         // res->data = NULL;
    61         // while (1)
    62         // {
    63         //   omUpdateInfo();
    64         //   Print("usedBytesAfter=%ld\n",om_Info.UsedBytes);
    65         //   tropicalStrategy debugTest(I,currRing);
    66         //   maxCones = tropicalVariety(g,currRing,debugTest);
    67         //   gfan::ZFan* zf = toZFan(maxCones);
    68         //   delete zf;
    69         // }
    70         res->rtyp = fanID;
    71         res->data = (char*) toZFan(maxCones);
    72         return FALSE;
     108        try
     109        {
     110          tropicalStrategy currentStrategy(I,currRing);
     111          std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
     112          res->rtyp = fanID;
     113          res->data = (char*) toZFan(maxCones);
     114          return FALSE;
     115        }
     116        catch (const std::exception& ex)
     117        {
     118          Werror("ERROR: %s",ex.what());
     119          return TRUE;
     120        }
    73121      }
    74122      if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
    75123      {
    76         number p = (number) v->Data();
    77         tropicalStrategy currentStrategy(I,p,currRing);
    78         ideal startingIdeal = currentStrategy.getStartingIdeal();
    79         ring startingRing = currentStrategy.getStartingRing();
    80         poly gStart = startingIdeal->m[0];
    81         std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
    82         res->rtyp = fanID;
    83         res->data = (char*) toZFan(maxCones);
    84         return FALSE;
     124        try
     125        {
     126          number p = (number) v->Data();
     127          tropicalStrategy currentStrategy(I,p,currRing);
     128          ideal startingIdeal = currentStrategy.getStartingIdeal();
     129          ring startingRing = currentStrategy.getStartingRing();
     130          poly gStart = startingIdeal->m[0];
     131          std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
     132          res->rtyp = fanID;
     133          res->data = (char*) toZFan(maxCones);
     134          return FALSE;
     135        }
     136        catch (const std::exception& ex)
     137        {
     138          Werror("ERROR: %s",ex.what());
     139          return TRUE;
     140        }
    85141      }
    86142    }
     
    88144    if (v==NULL)
    89145    {
    90       setOptionRedSB();
    91       // ideal stdI;
    92       // if (!hasFlag(u,FLAG_STD))
    93       //   stdI = gfanlib_kStd_wrapper(I,currRing);
    94       // else
    95       //   stdI = id_Copy(I,currRing);
    96       tropicalStrategy currentStrategy(I,currRing);
    97       gfan::ZFan* tropI = tropicalVariety(currentStrategy);
    98       res->rtyp = fanID;
    99       res->data = (char*) tropI;
    100       undoSetOptionRedSB();
    101       // id_Delete(&stdI,currRing);
    102       return FALSE;
     146      try
     147      {
     148        setOptionRedSB();
     149        ideal stdI;
     150        if (!hasFlag(u,FLAG_STD))
     151          stdI = gfanlib_kStd_wrapper(I,currRing);
     152        else
     153          stdI = id_Copy(I,currRing);
     154        tropicalStrategy currentStrategy(stdI,currRing);
     155        gfan::ZFan* tropI = tropicalVariety(currentStrategy);
     156        res->rtyp = fanID;
     157        res->data = (char*) tropI;
     158        undoSetOptionRedSB();
     159        id_Delete(&stdI,currRing);
     160        return FALSE;
     161      }
     162      catch (const std::exception& ex)
     163      {
     164        Werror("ERROR: %s",ex.what());
     165        return TRUE;
     166      }
    103167    }
    104168    if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
    105169    {
    106       number p = (number) v->Data();
    107       // ideal stdI;
    108       // if (!hasFlag(u,FLAG_STD))
    109       //   stdI = gfanlib_kStd_wrapper(I,currRing);
    110       // else
    111       //   stdI = id_Copy(I,currRing);
    112       // tropicalStrategy currentStrategy(stdI,p,currRing);
    113       tropicalStrategy currentStrategy(I,p,currRing);
    114       gfan::ZFan* tropI = tropicalVariety(currentStrategy);
    115       res->rtyp = fanID;
    116       res->data = (char*) tropI;
    117       // id_Delete(&stdI,currRing);
    118       return FALSE;
     170      try
     171      {
     172        number p = (number) v->Data();
     173        ideal stdI;
     174        if (!hasFlag(u,FLAG_STD))
     175          stdI = gfanlib_kStd_wrapper(I,currRing);
     176        else
     177          stdI = id_Copy(I,currRing);
     178        tropicalStrategy currentStrategy(stdI,p,currRing);
     179        gfan::ZFan* tropI = tropicalVariety(currentStrategy);
     180        res->rtyp = fanID;
     181        res->data = (char*) tropI;
     182        id_Delete(&stdI,currRing);
     183        return FALSE;
     184      }
     185      catch (const std::exception& ex)
     186      {
     187        Werror("ERROR: %s",ex.what());
     188        return TRUE;
     189      }
    119190    }
    120191    return FALSE;
  • Singular/extra.cc

    rf38979 rb9e63ba  
    18641864    if (strcmp(sys_cmd, "Mwalk") == 0)
    18651865    {
    1866       const short t[]={4,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,RING_CMD};
     1866      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,RING_CMD,INT_CMD,INT_CMD};
    18671867      if (!iiCheckTypes(h,t,1)) return TRUE;
    18681868      if (((intvec*) h->next->Data())->length() != currRing->N &&
     
    18751875      ideal arg1 = (ideal) h->Data();
    18761876      intvec* arg2 = (intvec*) h->next->Data();
    1877       intvec* arg3   =  (intvec*) h->next->next->Data();
    1878       ring arg4   =  (ring) h->next->next->next->Data();
    1879       ideal result = (ideal) Mwalk(arg1, arg2, arg3,arg4);
     1877      intvec* arg3 = (intvec*) h->next->next->Data();
     1878      ring arg4 = (ring) h->next->next->next->Data();
     1879      int arg5 = (int) (long) h->next->next->next->next->Data();
     1880      int arg6 = (int) (long) h->next->next->next->next->next->Data();
     1881      ideal result = (ideal) Mwalk(arg1, arg2, arg3, arg4, arg5, arg6);
    18801882      res->rtyp = IDEAL_CMD;
    18811883      res->data =  result;
     
    19131915    if (strcmp(sys_cmd, "Mpwalk") == 0)
    19141916    {
    1915       const short t[]={6,IDEAL_CMD,INT_CMD,INT_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD};
     1917      const short t[]={8,IDEAL_CMD,INT_CMD,INT_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD};
    19161918      if (!iiCheckTypes(h,t,1)) return TRUE;
    19171919      if(((intvec*) h->next->next->next->Data())->length() != currRing->N &&
     
    19271929      intvec* arg5 = (intvec*) h->next->next->next->next->Data();
    19281930      int arg6 = (int) (long) h->next->next->next->next->next->Data();
    1929       ideal result = (ideal) Mpwalk(arg1, arg2, arg3, arg4, arg5,arg6);
     1931      int arg7 = (int) (long) h->next->next->next->next->next->next->Data();
     1932      int arg8 = (int) (long) h->next->next->next->next->next->next->next->Data();
     1933      ideal result = (ideal) Mpwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8);
    19301934      res->rtyp = IDEAL_CMD;
    19311935      res->data =  result;
     
    19391943    if (strcmp(sys_cmd, "Mrwalk") == 0)
    19401944    {
    1941       const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,RING_CMD};
     1945      const short t[]={7,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD};
    19421946      if (!iiCheckTypes(h,t,1)) return TRUE;
    1943       if((((intvec*) h->next->Data())->length() != currRing->N &&
    1944          ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
    1945          (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
    1946          ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
     1947      if(((intvec*) h->next->Data())->length() != currRing->N &&
     1948         ((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
     1949         ((intvec*) h->next->next->Data())->length() != currRing->N &&
     1950         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) )
    19471951      {
    19481952        Werror("system(\"Mrwalk\" ...) intvecs not of length %d or %d\n",
     
    19551959      int arg4 = (int)(long) h->next->next->next->Data();
    19561960      int arg5 = (int)(long) h->next->next->next->next->Data();
    1957       ring arg6 = (ring) h->next->next->next->next->next->Data();
    1958       ideal result = (ideal) Mrwalk(arg1, arg2, arg3, arg4, arg5, arg6);
     1961      int arg6 = (int)(long) h->next->next->next->next->next->Data();
     1962      int arg7 = (int)(long) h->next->next->next->next->next->next->Data();
     1963      ideal result = (ideal) Mrwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7);
    19591964      res->rtyp = IDEAL_CMD;
    19601965      res->data =  result;
     
    20182023    if (strcmp(sys_cmd, "Mfwalk") == 0)
    20192024    {
    2020       const short t[]={3,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD};
     2025      const short t[]={5,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD};
    20212026      if (!iiCheckTypes(h,t,1)) return TRUE;
    20222027      if (((intvec*) h->next->Data())->length() != currRing->N &&
     
    20252030        Werror("system(\"Mfwalk\" ...) intvecs not of length %d\n",
    20262031                 currRing->N);
    2027         return TRUE;
    2028       }
    2029       ideal arg1 = (ideal) h->Data();
    2030       intvec* arg2 = (intvec*) h->next->Data();
    2031       intvec* arg3   =  (intvec*) h->next->next->Data();
    2032       ideal result = (ideal) Mfwalk(arg1, arg2, arg3);
    2033       res->rtyp = IDEAL_CMD;
    2034       res->data =  result;
    2035       return FALSE;
    2036     }
    2037     else
    2038   #endif
    2039   /*==================== Mfrwalk =================*/
    2040   #ifdef HAVE_WALK
    2041     if (strcmp(sys_cmd, "Mfrwalk") == 0)
    2042     {
    2043       const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,RING_CMD};
    2044       if (!iiCheckTypes(h,t,1)) return TRUE;
    2045       if (((intvec*) h->next->Data())->length() != currRing->N &&
    2046           ((intvec*) h->next->next->Data())->length() != currRing->N)
    2047       {
    2048         Werror("system(\"Mfrwalk\" ...) intvecs not of length %d\n",currRing->N);
    20492032        return TRUE;
    20502033      }
     
    20532036      intvec* arg3 = (intvec*) h->next->next->Data();
    20542037      int arg4 = (int)(long) h->next->next->next->Data();
    2055       ideal result = (ideal) Mfrwalk(arg1, arg2, arg3, arg4);
     2038      int arg5 = (int)(long) h->next->next->next->next->Data();
     2039      ideal result = (ideal) Mfwalk(arg1, arg2, arg3, arg4, arg5);
    20562040      res->rtyp = IDEAL_CMD;
    20572041      res->data =  result;
     
    20592043    }
    20602044    else
     2045  #endif
     2046  /*==================== Mfrwalk =================*/
     2047  #ifdef HAVE_WALK
     2048    if (strcmp(sys_cmd, "Mfrwalk") == 0)
     2049    {
     2050      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD};
     2051      if (!iiCheckTypes(h,t,1)) return TRUE;
     2052/*
     2053      if (((intvec*) h->next->Data())->length() != currRing->N &&
     2054          ((intvec*) h->next->next->Data())->length() != currRing->N)
     2055      {
     2056        Werror("system(\"Mfrwalk\" ...) intvecs not of length %d\n",currRing->N);
     2057        return TRUE;
     2058      }
     2059*/
     2060      if((((intvec*) h->next->Data())->length() != currRing->N &&
     2061         ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
     2062         (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
     2063         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
     2064      {
     2065        Werror("system(\"Mfrwalk\" ...) intvecs not of length %d or %d\n",
     2066               currRing->N,(currRing->N)*(currRing->N));
     2067        return TRUE;
     2068      }
     2069
     2070      ideal arg1 = (ideal) h->Data();
     2071      intvec* arg2 = (intvec*) h->next->Data();
     2072      intvec* arg3 = (intvec*) h->next->next->Data();
     2073      int arg4 = (int)(long) h->next->next->next->Data();
     2074      int arg5 = (int)(long) h->next->next->next->next->Data();
     2075      int arg6 = (int)(long) h->next->next->next->next->next->Data();
     2076      ideal result = (ideal) Mfrwalk(arg1, arg2, arg3, arg4, arg5, arg6);
     2077      res->rtyp = IDEAL_CMD;
     2078      res->data =  result;
     2079      return FALSE;
     2080    }
     2081    else
    20612082  /*==================== Mprwalk =================*/
    20622083    if (strcmp(sys_cmd, "Mprwalk") == 0)
    20632084    {
    2064       const short t[]={7,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,RING_CMD};
     2085      const short t[]={9,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD};
    20652086      if (!iiCheckTypes(h,t,1)) return TRUE;
    2066       if (((intvec*) h->next->Data())->length() != currRing->N &&
    2067           ((intvec*) h->next->next->Data())->length() != currRing->N )
    2068       {
    2069         Werror("system(\"Mrwalk\" ...) intvecs not of length %d\n",
    2070                currRing->N);
     2087      if((((intvec*) h->next->Data())->length() != currRing->N &&
     2088         ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
     2089         (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
     2090         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
     2091      {
     2092        Werror("system(\"Mrwalk\" ...) intvecs not of length %d or %d\n",
     2093               currRing->N,(currRing->N)*(currRing->N));
    20712094        return TRUE;
    20722095      }
     
    20772100      int arg5 = (int)(long) h->next->next->next->next->Data();
    20782101      int arg6 = (int)(long) h->next->next->next->next->next->Data();
    2079       ring arg7 = (ring) h->next->next->next->next->next->next->Data();
    2080       ideal result = (ideal) Mprwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7);
     2102      int arg7 = (int)(long) h->next->next->next->next->next->next->Data();
     2103      int arg8 = (int)(long) h->next->next->next->next->next->next->next->Data();
     2104      int arg9 = (int)(long) h->next->next->next->next->next->next->next->next->Data();
     2105      ideal result = (ideal) Mprwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9);
    20812106      res->rtyp = IDEAL_CMD;
    20822107      res->data =  result;
  • Singular/iparith.cc

    r36f0e5 rb9e63ba  
    61546154    return TRUE;
    61556155  }
     6156  res->rtyp=IDEAL_CMD;
    61566157  if ((mk < 1) || (mk > m->rows()) || (mk > m->cols()))
    61576158  {
    6158     Werror("invalid size of minors: %d (matrix is (%d x %d))", mk,
    6159            m->rows(), m->cols());
    6160     return TRUE;
     6159    ideal I=idInit(1,1);
     6160    if (mk<1) I->m[0]=p_One(currRing);
     6161    //Werror("invalid size of minors: %d (matrix is (%d x %d))", mk,
     6162    //       m->rows(), m->cols());
     6163    res->data=(void*)I;
     6164    return FALSE;
    61616165  }
    61626166  if ((!noAlgorithm) && (strcmp(algorithm, "Cache") == 0)
     
    61796183                              (noIdeal ? 0 : IasSB), false);
    61806184  if (v_typ!=MATRIX_CMD) idDelete((ideal *)&m);
    6181   res->rtyp = IDEAL_CMD;
    61826185  return FALSE;
    61836186}
  • Singular/ipassign.cc

    r36f0e5 rb9e63ba  
    974974  }
    975975
    976   int i=0;
    977976  if (lt==DEF_CMD)
    978977  {
     
    10281027    return (bb==NULL) || bb->blackbox_Assign(l,r);
    10291028  }
    1030   while (((dAssign[i].res!=lt)
    1031       || (dAssign[i].arg!=rt))
    1032     && (dAssign[i].res!=0)) i++;
    1033   if (dAssign[i].res!=0)
     1029  int start=0;
     1030  while ((dAssign[start].res!=lt)
     1031      && (dAssign[start].res!=0)) start++;
     1032  int i=start;
     1033  while ((dAssign[i].res==lt)
     1034      && (dAssign[i].arg!=rt)) i++;
     1035  if (dAssign[i].res==lt)
    10341036  {
    10351037    if (traceit&TRACE_ASSIGN) Print("assign %s=%s\n",Tok2Cmdname(lt),Tok2Cmdname(rt));
     
    10441046  }
    10451047  // implicite type conversion ----------------------------------------------
    1046   if (dAssign[i].res==0)
     1048  if (dAssign[i].res!=lt)
    10471049  {
    10481050    int ri;
    10491051    leftv rn = (leftv)omAlloc0Bin(sleftv_bin);
    10501052    BOOLEAN failed=FALSE;
    1051     i=0;
    1052     while ((dAssign[i].res!=lt)
    1053       && (dAssign[i].res!=0)) i++;
     1053    i=start;
     1054    //while ((dAssign[i].res!=lt)
     1055    //  && (dAssign[i].res!=0)) i++;
    10541056    while (dAssign[i].res==lt)
    10551057    {
  • Singular/misc_ip.cc

    r36f0e5 rb9e63ba  
    12161216    omInitInfo();
    12171217
     1218// options ---------------------------------------------------------------
     1219  si_opt_1=0;
    12181220// interpreter tables etc.: -----------------------------------------------
    12191221  memset(&sLastPrinted,0,sizeof(sleftv));
  • Singular/table.h

    r36f0e5 rb9e63ba  
    11851185struct sValAssign dAssign[]=
    11861186{
     1187// same res types must be grouped together
    11871188// proc         res             arg
    11881189 {D(jiA_IDEAL),    IDEAL_CMD,      IDEAL_CMD }
     
    11981199,{D(jiA_POLY),     POLY_CMD,       POLY_CMD }
    11991200,{D(jiA_1x1MATRIX),POLY_CMD,       MATRIX_CMD }
     1201,{D(jiA_RING),     RING_CMD,       RING_CMD }
    12001202,{D(jiA_QRING),    QRING_CMD,      IDEAL_CMD }
    1201 ,{D(jiA_RING),     RING_CMD,       RING_CMD }
    12021203,{D(jiA_RING),     QRING_CMD,      QRING_CMD }
    12031204,{D(jiA_RING),     QRING_CMD,      RING_CMD }
     
    12081209,{D(jiA_INTVEC),   INTVEC_CMD,     INTVEC_CMD }
    12091210,{D(jiA_INTVEC),   INTMAT_CMD,     INTMAT_CMD }
    1210 //,{D(jiA_INTVEC),   INTMAT_CMD,     INTVEC_CMD }
    12111211,{D(jiA_BIGINTMAT),BIGINTMAT_CMD,  BIGINTMAT_CMD}
    12121212,{D(jiA_NUMBER),   NUMBER_CMD,     NUMBER_CMD }
  • Singular/walk.cc

    • Property mode changed from 100644 to 100755
    rf38979 rb9e63ba  
    2727
    2828#define FIRST_STEP_FRACTAL // to define the first step of the fractal
    29 //#define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if
     29#define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if
    3030//                          tau doesn't stay in the correct cone
    3131
     
    4242#include <Singular/ipshell.h>
    4343#include <Singular/ipconv.h>
     44#include <coeffs/ffields.h>
    4445#include <coeffs/coeffs.h>
    4546#include <Singular/subexpr.h>
     47#include <polys/templates/p_Procs.h>
    4648
    4749#include <polys/monomials/maps.h>
     
    429431#endif
    430432
    431 #ifdef CHECK_IDEAL_MWALK
     433//#ifdef CHECK_IDEAL_MWALK
    432434static void idString(ideal L, const char* st)
    433435{
     
    441443  Print(" %s;", pString(L->m[nL-1]));
    442444}
    443 #endif
     445//#endif
    444446
    445447#if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS)
     
    558560  }
    559561  return p0;
     562}
     563
     564/*****************************************************************************
     565 * compute the gcd of the entries of the vectors curr_weight and diff_weight *
     566 *****************************************************************************/
     567static int simplify_gcd(intvec* curr_weight, intvec* diff_weight)
     568{
     569  int j;
     570  int nRing = currRing->N;
     571  int gcd_tmp = (*curr_weight)[0];
     572  for (j=1; j<nRing; j++)
     573  {
     574    gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]);
     575    if(gcd_tmp == 1)
     576    {
     577      break;
     578    }
     579  }
     580  if(gcd_tmp != 1)
     581  {
     582    for (j=0; j<nRing; j++)
     583    {
     584    gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]);
     585    if(gcd_tmp == 1)
     586      {
     587        break;
     588      }
     589    }
     590  }
     591  return gcd_tmp;
    560592}
    561593
     
    953985}
    954986
    955 /*****************************************************************************
    956 * create a weight matrix order as intvec of an extra weight vector (a(iv),lp)*
    957 ******************************************************************************/
     987/*********************************************************************************
     988* create a weight matrix order as intvec of an extra weight vector (a(iv),M(iw)) *
     989**********************************************************************************/
    958990intvec* MivMatrixOrderRefine(intvec* iv, intvec* iw)
    959991{
    960   assume(iv->length() == iw->length());
    961   int i, nR = iv->length();
    962 
     992  assume((iv->length())*(iv->length()) == iw->length());
     993  int i,j, nR = iv->length();
     994 
    963995  intvec* ivm = new intvec(nR*nR);
    964996
     
    966998  {
    967999    (*ivm)[i] = (*iv)[i];
    968     (*ivm)[i+nR] = (*iw)[i];
    969   }
    970   for(i=2; i<nR; i++)
    971   {
    972     (*ivm)[i*nR+i-2] = 1;
     1000  }
     1001  for(i=1; i<nR; i++)
     1002  {
     1003    for(j=0; j<nR; j++)
     1004    {
     1005      (*ivm)[j+i*nR] = (*iw)[j+i*nR];
     1006    }
    9731007  }
    9741008  return ivm;
     
    18591893}
    18601894
     1895
     1896/**************************************************************
     1897 * Look for the position of the smallest absolut value in vec *
     1898 **************************************************************/
     1899static int MivAbsMaxArg(intvec* vec)
     1900{
     1901  int k = MivAbsMax(vec);
     1902  int i=0;
     1903  while(1)
     1904  {
     1905    if((*vec)[i] == k || (*vec)[i] == -k)
     1906    {
     1907      break;
     1908    }
     1909    i++;
     1910  }
     1911  return i;
     1912}
     1913
     1914
    18611915/**********************************************************************
    18621916 * Compute a next weight vector between curr_weight and target_weight *
     
    18731927
    18741928  int nRing = currRing->N;
    1875   int checkRed, j, kkk, nG = IDELEMS(G);
     1929  int checkRed, j, nG = IDELEMS(G);
    18761930  intvec* ivtemp;
    18771931
     
    19111965  mpz_init(dcw);
    19121966
    1913   //int tn0, tn1, tz1, ncmp, gcd_tmp, ntmp;
    19141967  int gcd_tmp;
    19151968  intvec* diff_weight = MivSub(target_weight, curr_weight);
     
    19171970  intvec* diff_weight1 = MivSub(target_weight, curr_weight);
    19181971  poly g;
    1919   //poly g, gw;
     1972
    19201973  for (j=0; j<nG; j++)
    19211974  {
     
    19792032    }
    19802033  }
    1981 //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t));
     2034  //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t));
    19822035  mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t));
    19832036
    19842037
    1985   // there is no 0<t<1 and define the next weight vector that is equal to the current weight vector
     2038  // there is no 0<t<1 and define the next weight vector that is equal
     2039  // to the current weight vector
    19862040  if(mpz_cmp(t_nenner, t_null) == 0)
    19872041  {
     
    20542108#endif
    20552109
    2056   //  BOOLEAN isdwpos;
    2057 
    2058   // construct a new weight vector
     2110// construct a new weight vector and check whether vec[j] is overflow,
     2111// i.e. vec[j] > 2^31.
     2112// If vec[j] doesn't overflow, define a weight vector. Otherwise,
     2113// report that overflow appears. In the second case, test whether the
     2114// the correctness of the new vector plays an important role
     2115
    20592116  for (j=0; j<nRing; j++)
    20602117  {
     
    21002157    }
    21012158  }
    2102 
     2159  // reduce the vector with the gcd
     2160  if(mpz_cmp_si(ggt,1) != 0)
     2161  {
     2162    for (j=0; j<nRing; j++)
     2163    {
     2164      mpz_divexact(vec[j], vec[j], ggt);
     2165    }
     2166  }
    21032167#ifdef  NEXT_VECTORS_CC
    21042168  PrintS("\n// gcd of elements of the vector: ");
     
    21062170#endif
    21072171
    2108 /**********************************************************************
    2109 * construct a new weight vector and check whether vec[j] is overflow, *
    2110 * i.e. vec[j] > 2^31.                                                 *
    2111 * If vec[j] doesn't overflow, define a weight vector. Otherwise,      *
    2112 * report that overflow appears. In the second case, test whether the  *
    2113 * the correctness of the new vector plays an important role           *
    2114 **********************************************************************/
    2115   kkk=0;
    21162172  for(j=0; j<nRing; j++)
    21172173    {
     
    21292185
    21302186  REDUCTION:
     2187  checkRed = 1;
    21312188  for (j=0; j<nRing; j++)
    21322189  {
    2133     (*diff_weight)[j] = mpz_get_si(vec[j]);
    2134   }
    2135   while(MivAbsMax(diff_weight) >= 5)
    2136   {
    2137     for (j=0; j<nRing; j++)
    2138     {
    2139       if(mpz_cmp_si(ggt,1)==0)
    2140       {
    2141         (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
    2142         // Print("\n//  vector[%d] = %d \n",j+1, (*diff_weight1)[j]);
    2143       }
    2144       else
    2145       {
    2146         mpz_divexact(vec[j], vec[j], ggt);
    2147         (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
    2148         // Print("\n//  vector[%d] = %d \n",j+1, (*diff_weight1)[j]);
    2149       }
    2150 /*
    2151       if((*diff_weight1)[j] == 0)
    2152       {
    2153         kkk = kkk + 1;
    2154       }
    2155 */
    2156     }
    2157 
    2158 
    2159 /*
    2160     if(kkk > nRing - 1)
    2161     {
    2162       // diff_weight was reduced to zero
    2163       // Print("\n // MwalkNextWeightCC: geaenderter Vector gleich Null! \n");
    2164       goto TEST_OVERFLOW;
    2165     }
    2166 */
    2167 
    2168     if(test_w_in_ConeCC(G,diff_weight1) != 0)
    2169     {
    2170       Print("\n// MwalkNextWeightCC: geaenderter vector liegt in Groebnerkegel! \n");
    2171       for (j=0; j<nRing; j++)
    2172       {
    2173         (*diff_weight)[j] = (*diff_weight1)[j];
    2174       }
    2175       if(MivAbsMax(diff_weight) < 5)
    2176       {
    2177         checkRed = 1;
    2178         goto SIMPLIFY_GCD;
    2179       }
    2180     }
    2181     else
    2182     {
    2183       // Print("\n// MwalkNextWeightCC: geaenderter vector liegt nicht in Groebnerkegel! \n");
    2184       break;
    2185     }
     2190    (*diff_weight1)[j] = mpz_get_si(vec[j]);
     2191  }
     2192  while(test_w_in_ConeCC(G,diff_weight1))
     2193  {
     2194    for(j=0; j<nRing; j++)
     2195    {
     2196      (*diff_weight)[j] = (*diff_weight1)[j];
     2197      mpz_set_si(vec[j], (*diff_weight)[j]);     
     2198    }
     2199    for(j=0; j<nRing; j++)
     2200    {
     2201      (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
     2202    }
     2203  }
     2204  if(MivAbsMax(diff_weight)>10000)
     2205  {
     2206    for(j=0; j<nRing; j++)
     2207    {
     2208      (*diff_weight1)[j] = (*diff_weight)[j];
     2209    }
     2210    j = 0;
     2211    while(test_w_in_ConeCC(G,diff_weight1))
     2212    {
     2213      (*diff_weight)[j] = (*diff_weight1)[j];
     2214      mpz_set_si(vec[j], (*diff_weight)[j]);
     2215      j = MivAbsMaxArg(diff_weight1);
     2216      (*diff_weight1)[j] = floor(0.1*(*diff_weight1)[j] + 0.5);
     2217    }
     2218    goto SIMPLIFY_GCD;
    21862219  }
    21872220
     
    22222255   mpz_clear(t_null);
    22232256
    2224 
    2225 
    22262257  if(Overflow_Error == FALSE)
    22272258  {
    22282259    Overflow_Error = nError;
    22292260  }
    2230  rComplete(currRing);
    2231   for(kkk=0; kkk<IDELEMS(G);kkk++)
    2232   {
    2233     poly p=G->m[kkk];
     2261  rComplete(currRing);
     2262  for(j=0; j<IDELEMS(G); j++)
     2263  {
     2264    poly p=G->m[j];
    22342265    while(p!=NULL)
    22352266    {
     
    22712302}
    22722303
    2273 /**************************************************************
     2304/********************************************************************
    22742305 * define and execute a new ring which order is (a(vb),a(va),lp,C)  *
    2275  * ************************************************************/
     2306 * ******************************************************************/
    22762307static void VMrHomogeneous(intvec* va, intvec* vb)
    22772308{
     
    24262457}
    24272458
    2428 static ring VMrDefault1(intvec* va)
    2429 {
    2430 
    2431   if ((currRing->ppNoether)!=NULL)
    2432   {
    2433     pDelete(&(currRing->ppNoether));
    2434   }
    2435   if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) ||
    2436       ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data))))
    2437   {
    2438     sLastPrinted.CleanUp();
    2439   }
    2440 
    2441   ring r = (ring) omAlloc0Bin(sip_sring_bin);
    2442   int i, nv = currRing->N;
    2443 
    2444   r->cf  = currRing->cf;
    2445   r->N   = currRing->N;
    2446 
    2447   int nb = 4;
    2448 
    2449   //names
    2450   char* Q; // In order to avoid the corrupted memory, do not change.
    2451   r->names = (char **) omAlloc0(nv * sizeof(char_ptr));
    2452   for(i=0; i<nv; i++)
    2453   {
    2454     Q = currRing->names[i];
    2455     r->names[i]  = omStrDup(Q);
    2456   }
    2457 
    2458   /*weights: entries for 3 blocks: NULL Made:???*/
    2459   r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
    2460   r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
    2461   for(i=0; i<nv; i++)
    2462     r->wvhdl[0][i] = (*va)[i];
    2463 
    2464   /* order: a,lp,C,0 */
    2465   r->order = (int *) omAlloc(nb * sizeof(int *));
    2466   r->block0 = (int *)omAlloc0(nb * sizeof(int *));
    2467   r->block1 = (int *)omAlloc0(nb * sizeof(int *));
    2468 
    2469   // ringorder a for the first block: var 1..nv
    2470   r->order[0]  = ringorder_a;
    2471   r->block0[0] = 1;
    2472   r->block1[0] = nv;
    2473 
    2474   // ringorder lp for the second block: var 1..nv
    2475   r->order[1]  = ringorder_lp;
    2476   r->block0[1] = 1;
    2477   r->block1[1] = nv;
    2478 
    2479   // ringorder C for the third block
    2480   // it is very important within "idLift",
    2481   // especially, by ring syz_ring=rCurrRingAssure_SyzComp();
    2482   // therefore, nb  must be (nBlocks(currRing)  + 1)
    2483   r->order[2]  = ringorder_C;
    2484 
    2485   // the last block: everything is 0
    2486   r->order[3]  = 0;
    2487 
    2488   // polynomial ring
    2489   r->OrdSgn    = 1;
    2490 
    2491   // complete ring intializations
    2492 
    2493   rComplete(r);
    2494 
    2495   //rChangeCurrRing(r);
    2496   return r;
    2497 }
    2498 
    24992459/****************************************************************
    25002460 * define and execute a new ring with ordering (a(va),Wp(vb),C) *
    25012461 * **************************************************************/
    2502 
    25032462static ring VMrRefine(intvec* va, intvec* vb)
    25042463{
     
    25742533
    25752534  // complete ring intializations
    2576 
     2535 
    25772536  rComplete(r);
    25782537
     
    28042763}
    28052764
    2806 
    2807 /* define a ring with parameters und change to it */
    2808 /* DefRingPar and DefRingParlp corrupt still memory */
     2765/***************************************************
     2766* define a ring with parameters und change to it   *
     2767* DefRingPar and DefRingParlp corrupt still memory *
     2768****************************************************/
    28092769static void DefRingPar(intvec* va)
    28102770{
     
    29542914}
    29552915
    2956 //unused
    2957 /**************************************************************
    2958  * check wheather one or more components of a vector are zero *
    2959  **************************************************************/
    2960 //#if 0
     2916/*************************************************************
     2917 * check whether one or more components of a vector are zero *
     2918 *************************************************************/
    29612919static int isNolVector(intvec* hilb)
    29622920{
     
    29712929  return 0;
    29722930}
    2973 //#endif
     2931
     2932/*************************************************************
     2933 * check whether one or more components of a vector are <= 0 *
     2934 *************************************************************/
     2935static int isNegNolVector(intvec* hilb)
     2936{
     2937  int i;
     2938  for(i=hilb->length()-1; i>=0; i--)
     2939  {
     2940    if((* hilb)[i]<=0)
     2941    {
     2942      return 1;
     2943    }
     2944  }
     2945  return 0;
     2946}
     2947
     2948/**************************************************************************
     2949* Gomega is the initial ideal of G w. r. t. the current weight vector     *
     2950* curr_weight. Check whether curr_weight lies on a border of the Groebner *
     2951* cone, i. e. check whether a monomial is divisible by a leading monomial *
     2952***************************************************************************/
     2953static ideal middleOfCone(ideal G, ideal Gomega)
     2954{
     2955  BOOLEAN middle = FALSE;
     2956  int i,j,N = IDELEMS(Gomega);
     2957  poly p,lm,factor1,factor2;
     2958  PrintS("\n//** idCopy\n");
     2959  ideal Go = idCopy(G);
     2960 
     2961  PrintS("\n//** jetzt for-Loop!\n");
     2962  for(i=0; i<N; i++)
     2963  {
     2964    for(j=0; j<N; j++)
     2965    {
     2966      if(i!=j)
     2967      {
     2968        p = pCopy(Gomega->m[i]);
     2969        lm = pCopy(Gomega->m[j]);
     2970        pIter(p);
     2971        while(p!=NULL)
     2972        {
     2973          if(pDivisibleBy(lm,p))
     2974          {
     2975            if(middle == FALSE)
     2976            {
     2977              middle = TRUE;
     2978            }
     2979            factor1 = singclap_pdivide(pHead(p),lm,currRing);
     2980            factor2 = pMult(pCopy(factor1),pCopy(Go->m[j]));
     2981            pDelete(&factor1);
     2982            Go->m[i] = pAdd((Go->m[i]),pNeg(pCopy(factor2)));
     2983            pDelete(&factor2);
     2984          }
     2985          pIter(p);
     2986        }
     2987        pDelete(&lm);
     2988        pDelete(&p);
     2989      }
     2990    }
     2991  }
     2992 
     2993  //PrintS("\n//** jetzt Delete!\n");
     2994  //pDelete(&p);
     2995  //pDelete(&factor);
     2996  //pDelete(&lm);
     2997  if(middle == TRUE)
     2998  {
     2999    PrintS("\n//** middle TRUE!\n");
     3000    return Go;
     3001  }
     3002  PrintS("\n//** middle FALSE!\n");
     3003  idDelete(&Go);
     3004  return NULL;
     3005}
    29743006
    29753007/******************************  Februar 2002  ****************************
     
    31263158    else
    31273159    {
    3128       rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung
     3160      rChangeCurrRing(VMrDefault(curr_weight));
    31293161    }
    31303162    newRing = currRing;
     
    32783310  }
    32793311  return 0;
     3312}
     3313
     3314/*****************************************
     3315 * return maximal polynomial length of G *
     3316 *****************************************/
     3317static int maxlengthpoly(ideal G)
     3318{
     3319  int i,k,length=0;
     3320  for(i=IDELEMS(G)-1; i>=0; i--)
     3321  {
     3322    k = pLength(G->m[i]);
     3323    if(k>length)
     3324    {
     3325      length = k;
     3326    }
     3327  }
     3328  return length;
    32803329}
    32813330
     
    38823931    else
    38833932    {
    3884       rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung
     3933      rChangeCurrRing(VMrDefault(curr_weight));
    38853934    }
    38863935    newRing = currRing;
     
    41434192    else
    41444193    {
    4145       rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
     4194      rChangeCurrRing(VMrDefault(curr_weight));
    41464195    }
    41474196    newRing = currRing;
     
    42854334intvec* Xivlp;
    42864335
    4287 #if 0
     4336
    42884337/********************************
    42894338 * compute a next weight vector *
    42904339 ********************************/
    4291 static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg)
    4292 {
    4293   int i, weight_norm;
    4294   int nV = currRing->N;
    4295   intvec* next_weight2;
    4296   intvec* next_weight22 = new intvec(nV);
    4297   intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight, G);
    4298   if(MivComp(next_weight, target_weight) == 1)
    4299   {
    4300     return(next_weight);
    4301   }
    4302   else
    4303   {
    4304     //compute a perturbed next weight vector "next_weight1"
    4305     intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G, MivMatrixOrder(curr_weight), pert_deg), target_weight, G);
    4306     //Print("\n // size of next_weight1 = %d", sizeof((*next_weight1)));
    4307 
    4308     //compute a random next weight vector "next_weight2"
    4309     while(1)
    4310     {
    4311       weight_norm = 0;
    4312       while(weight_norm == 0)
    4313       {
    4314         for(i=0; i<nV; i++)
    4315         {
    4316           //Print("\n//  next_weight[%d]  = %d", i, (*next_weight)[i]);
    4317           (*next_weight22)[i] = rand() % 60000 - 30000;
    4318           weight_norm = weight_norm + (*next_weight22)[i]*(*next_weight22)[i];
    4319         }
    4320         weight_norm = 1 + floor(sqrt(weight_norm));
    4321       }
    4322 
    4323       for(i=nV-1; i>=0; i--)
    4324       {
    4325         if((*next_weight22)[i] < 0)
    4326         {
    4327           (*next_weight22)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm);
    4328         }
    4329         else
    4330         {
    4331           (*next_weight22)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm);
    4332         }
    4333       //Print("\n//  next_weight22[%d]  = %d", i, (*next_weight22)[i]);
    4334       }
    4335 
    4336       if(test_w_in_ConeCC(G, next_weight22) == 1)
    4337       {
    4338         //Print("\n//MWalkRandomNextWeight: next_weight2 im Kegel\n");
    4339         next_weight2 = MkInterRedNextWeight(next_weight22, target_weight, G);
    4340         delete next_weight22;
    4341         break;
    4342       }
    4343     }
    4344     intvec* result = new intvec(nV);
    4345     ideal G_test = MwalkInitialForm(G, next_weight);
    4346     ideal G_test1 = MwalkInitialForm(G, next_weight1);
    4347     ideal G_test2 = MwalkInitialForm(G, next_weight2);
    4348 
    4349     // compare next_weights
    4350     if(IDELEMS(G_test1) < IDELEMS(G_test))
    4351     {
    4352       if(IDELEMS(G_test2) <= IDELEMS(G_test1)) // |G_test2| <= |G_test1| < |G_test|
    4353       {
    4354         for(i=0; i<nV; i++)
    4355         {
    4356           (*result)[i] = (*next_weight2)[i];
    4357         }
    4358       }
    4359       else // |G_test1| < |G_test|, |G_test1| < |G_test2|
    4360       {
    4361         for(i=0; i<nV; i++)
    4362         {
    4363           (*result)[i] = (*next_weight1)[i];
    4364         }
    4365       }
    4366     }
    4367     else
    4368     {
    4369       if(IDELEMS(G_test2) <= IDELEMS(G_test)) // |G_test2| <= |G_test| <= |G_test1|
    4370       {
    4371         for(i=0; i<nV; i++)
    4372         {
    4373           (*result)[i] = (*next_weight2)[i];
    4374         }
    4375       }
    4376       else // |G_test| <= |G_test1|, |G_test| < |G_test2|
    4377       {
    4378         for(i=0; i<nV; i++)
    4379         {
    4380           (*result)[i] = (*next_weight)[i];
    4381         }
    4382       }
    4383     }
    4384     delete next_weight;
    4385     delete next_weight1;
    4386     idDelete(&G_test);
    4387     idDelete(&G_test1);
    4388     idDelete(&G_test2);
    4389     if(test_w_in_ConeCC(G, result) == 1)
    4390     {
    4391       delete next_weight2;
    4392       return result;
    4393     }
    4394     else
    4395     {
    4396       delete result;
    4397       return next_weight2;
    4398     }
    4399   }
    4400 }
    4401 #endif
    4402 
    4403 /********************************
    4404  * compute a next weight vector *
    4405  ********************************/
    4406 static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg)
    4407 {
    4408   int i, weight_norm;
    4409   //int randCount=0;
    4410   int nV = currRing->N;
     4340static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight,
     4341               intvec* target_weight, int weight_rad, int pert_deg)
     4342{
     4343  assume(currRing != NULL && curr_weight != NULL &&
     4344         target_weight != NULL && G->m[0] != NULL);
     4345
     4346  int i,weight_norm,nV = currRing->N;
    44114347  intvec* next_weight2;
    44124348  intvec* next_weight22 = new intvec(nV);
    44134349  intvec* result = new intvec(nV);
    44144350
    4415   //compute a perturbed next weight vector "next_weight1"
    4416   //intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G,MivMatrixOrderRefine(curr_weight,target_weight),pert_deg),target_weight,G);
    44174351  intvec* next_weight1 =MkInterRedNextWeight(curr_weight,target_weight,G);
    44184352  //compute a random next weight vector "next_weight2"
     
    44224356    while(weight_norm == 0)
    44234357    {
     4358
    44244359      for(i=0; i<nV; i++)
    44254360      {
     
    44294364      weight_norm = 1 + floor(sqrt(weight_norm));
    44304365    }
     4366
    44314367    for(i=0; i<nV; i++)
    44324368    {
     
    44404376      }
    44414377    }
     4378
    44424379    if(test_w_in_ConeCC(G, next_weight22) == 1)
    44434380    {
    44444381      next_weight2 = MkInterRedNextWeight(next_weight22,target_weight,G);
     4382      if(MivAbsMax(next_weight2)>1147483647)
     4383      {
     4384        for(i=0; i<nV; i++)
     4385        {
     4386          (*next_weight22)[i] = (*next_weight2)[i];
     4387        }
     4388        i = 0;
     4389        /* reduce the size of the maximal entry of the vector*/
     4390        while(test_w_in_ConeCC(G,next_weight22))
     4391        {
     4392          (*next_weight2)[i] = (*next_weight22)[i];
     4393          i = MivAbsMaxArg(next_weight22);
     4394          (*next_weight22)[i] = floor(0.1*(*next_weight22)[i] + 0.5);
     4395        }
     4396      }
    44454397      delete next_weight22;
    44464398      break;
    44474399    }
    44484400  }
     4401 
    44494402  // compute "usual" next weight vector
    44504403  intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight, G);
     
    44564409  {
    44574410    ideal G_test1 = MwalkInitialForm(G, next_weight1);
    4458     if(IDELEMS(G_test1) < IDELEMS(G_test))
    4459     {
    4460       if(IDELEMS(G_test2) < IDELEMS(G_test1))
     4411    if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test))//if(IDELEMS(G_test1) < IDELEMS(G_test))
     4412    {
     4413      if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test1)) //if(IDELEMS(G_test2) < IDELEMS(G_test1))
    44614414      {
    44624415        // |G_test2| < |G_test1| < |G_test|
     
    44734426          (*result)[i] = (*next_weight1)[i];
    44744427        }
    4475       }
     4428      }   
    44764429    }
    44774430    else
    44784431    {
    4479       if(IDELEMS(G_test2) < IDELEMS(G_test)) // |G_test2| < |G_test| <= |G_test1|
     4432      if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test))//if(IDELEMS(G_test2) < IDELEMS(G_test)) // |G_test2| < |G_test| <= |G_test1|
    44804433      {
    44814434        for(i=0; i<nV; i++)
     
    44984451  {
    44994452    Overflow_Error = FALSE;
    4500     if(IDELEMS(G_test2) < IDELEMS(G_test))
     4453    if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test))//if(IDELEMS(G_test2) < IDELEMS(G_test))
    45014454    {
    45024455      for(i=1; i<nV; i++)
     
    45134466    }
    45144467  }
     4468  PrintS("\n MWalkRandomNextWeight: Ende ok!\n");
    45154469  idDelete(&G_test);
    45164470  idDelete(&G_test2);
     
    45734527    else
    45744528    {
    4575       rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
     4529      rChangeCurrRing(VMrDefault(orig_target_weight));
    45764530    }
    45774531    TargetRing = currRing;
     
    46444598    else
    46454599    {
    4646       rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
     4600      rChangeCurrRing(VMrDefault(curr_weight));
    46474601    }
    46484602    newRing = currRing;
     
    47534707    else
    47544708    {
    4755       rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
     4709      rChangeCurrRing(VMrDefault(orig_target_weight));
    47564710    }
    47574711    F1 = idrMoveR(G, newRing,currRing);
     
    47844738      else
    47854739      {
    4786         rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
     4740        rChangeCurrRing(VMrDefault(orig_target_weight));
    47874741      }
    47884742    KSTD_Finish:
     
    48824836      tim = clock();
    48834837      /*
    4884         Print("\n// **** Grï¿œbnerwalk took %d steps and ", nwalk);
     4838        Print("\n// **** Groebnerwalk took %d steps and ", nwalk);
    48854839        PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:");
    48864840        idElements(Gomega, "G_omega");
     
    49124866      oldRing = currRing;
    49134867
    4914       /* create a new ring newRing */
     4868      // create a new ring newRing
    49154869       if (rParameter(currRing) != NULL)
    49164870       {
     
    49194873       else
    49204874       {
    4921          rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
     4875         rChangeCurrRing(VMrDefault(curr_weight));
    49224876       }
    49234877      newRing = currRing;
     
    49454899      else
    49464900      {
    4947         rChangeCurrRing(VMrDefault(curr_weight));  //Aenderung
     4901        rChangeCurrRing(VMrDefault(curr_weight));
    49484902      }
    49494903      newRing = currRing;
     
    49574911      M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    49584912      delete hilb_func;
    4959 #endif // BUCHBERGER_ALG
     4913#endif
    49604914      tstd = tstd + clock() - to;
    49614915
     
    49664920
    49674921      to = clock();
    4968       // compute a representation of the generators of submod (M) with respect to those of mod (Gomega). Gomega is a reduced Groebner basis w.r.t. the current ring.
     4922      // compute a representation of the generators of submod (M) with respect
     4923      // to those of mod (Gomega).
     4924      // Gomega is a reduced Groebner basis w.r.t. the current ring.
    49694925      F = MLifttwoIdeal(Gomega2, M1, G);
    49704926      tlift = tlift + clock() - to;
     
    50164972      else
    50174973      {
    5018         rChangeCurrRing(VMrDefault(target_weight)); // Aenderung
     4974        rChangeCurrRing(VMrDefault(target_weight));
    50194975      }
    50204976      F1 = idrMoveR(G, newRing,currRing);
     
    50635019 * THE GROEBNER WALK ALGORITHM *
    50645020 *******************************/
    5065 ideal Mwalk(ideal Go, intvec* orig_M, intvec* target_M, ring baseRing)
    5066 {
    5067   BITSET save1 = si_opt_1; // save current options
    5068   //si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    5069   //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
    5070   //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
     5021ideal Mwalk(ideal Go, intvec* orig_M, intvec* target_M,
     5022            ring baseRing, int reduction, int printout)
     5023{
     5024  // save current options
     5025  BITSET save1 = si_opt_1;
     5026  if(reduction == 0)
     5027  {
     5028    // no reduced Groebner basis
     5029    si_opt_1 &= (~Sy_bit(OPT_REDSB));
     5030    // not tail reductions
     5031    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL));
     5032  }
    50715033  Set_Error(FALSE);
    50725034  Overflow_Error = FALSE;
     
    50815043  int nV = baseRing->N;
    50825044
    5083   ideal Gomega, M, F, Gomega1, Gomega2, M1; //, F1;
     5045  ideal Gomega, M, F, FF, Gomega1, Gomega2, M1; //, F1;
    50845046  ring newRing;
    50855047  ring XXRing = baseRing;
     
    51095071#endif
    51105072  rComplete(currRing);
    5111 #ifdef CHECK_IDEAL_MWALK
    5112     idString(Go,"Go");
    5113 #endif
     5073//#ifdef CHECK_IDEAL_MWALK
     5074  if(printout > 2)
     5075  {
     5076    idString(Go,"//** Mwalk: Go");
     5077  }
     5078//#endif
    51145079#ifdef TIME_TEST
    51155080  to = clock();
    51165081#endif
    5117      if(orig_M->length() == nV)
    5118       {
    5119         newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
    5120       }
    5121       else
    5122       {
    5123         newRing = VMatrDefault(orig_M);
    5124       }
     5082  if(orig_M->length() == nV)
     5083  {
     5084    // define a new ring with ordering "(a(curr_weight),lp)
     5085    newRing = VMrDefault(curr_weight);
     5086  }
     5087  else
     5088  {
     5089    newRing = VMatrDefault(orig_M);
     5090  }
    51255091  rChangeCurrRing(newRing);
    5126   ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
     5092  //ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
     5093  ideal G = idrMoveR(Go,baseRing,currRing);
    51275094  baseRing = currRing;
    51285095#ifdef TIME_TEST
     
    51385105    to = clock();
    51395106#endif
    5140 #ifdef CHECK_IDEAL_MWALK
    5141     idString(G,"G");
    5142 #endif
    5143     Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
     5107//#ifdef CHECK_IDEAL_MWALK
     5108    if(printout > 2)
     5109    {
     5110      idString(G,"//** Mwalk: G");
     5111    }
     5112//#endif
     5113    // compute an initial form ideal of <G> w.r.t. "curr_vector"
     5114    Gomega = MwalkInitialForm(G, curr_weight);
    51445115#ifdef TIME_TEST
    5145     tif = tif + clock()-to; //time for computing initial form ideal
    5146 #endif
    5147 #ifdef CHECK_IDEAL_MWALK
    5148     idString(Gomega,"Gomega");
    5149 #endif
     5116    //time for computing initial form ideal
     5117    tif = tif + clock()-to;
     5118#endif
     5119//#ifdef CHECK_IDEAL_MWALK
     5120    if(printout > 1)
     5121    {
     5122      idString(Gomega,"//** Mwalk: Gomega");
     5123    }
     5124//#endif
     5125
     5126
     5127    if(reduction == 0)
     5128    {
     5129      PrintS("\n//** Mwalk: test middle of cone!\n");
     5130      FF = middleOfCone(G,Gomega);
     5131      PrintS("\n//** Mwalk: Test F!\n");
     5132      if( FF != NULL)
     5133      {
     5134        idDelete(&G);
     5135        G = idCopy(FF);
     5136        idDelete(&FF);
     5137        PrintS("\n//** Mwalk: FF nicht NULL! Compue next vector.\n");
     5138        goto NEXT_VECTOR;
     5139      }
     5140    }
     5141
    51505142#ifndef  BUCHBERGER_ALG
    51515143    if(isNolVector(curr_weight) == 0)
    51525144    {
    51535145      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    5154     }
     5146    }   
    51555147    else
    51565148    {
     
    51625154      if(orig_M->length() == nV)
    51635155      {
    5164         newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
     5156        // define a new ring with ordering "(a(curr_weight),lp)
     5157        newRing = VMrDefault(curr_weight);
    51655158      }
    51665159      else
     
    51735166     if(target_M->length() == nV)
    51745167     {
    5175        newRing = VMrRefine(curr_weight,target_weight); //define a new ring with ordering "(a(curr_weight),Wp(target_weight))"
     5168       //define a new ring with ordering "(a(curr_weight),Wp(target_weight))"
     5169       newRing = VMrRefine(curr_weight,target_weight);
    51765170     }
    51775171     else
    51785172     {
     5173       //define a new ring with matrix ordering
    51795174       newRing = VMatrRefine(target_M,curr_weight);
    51805175     }
     
    51975192#endif
    51985193    idSkipZeroes(M);
    5199 #ifdef CHECK_IDEAL_MWALK
    5200     PrintS("\n//** Mwalk: computed M.\n");
    5201     idString(M, "M");
    5202 #endif
     5194//#ifdef CHECK_IDEAL_MWALK
     5195    if(printout > 2)
     5196    {
     5197      idString(M, "//** Mwalk: M");
     5198    }
     5199//#endif
    52035200    //change the ring to baseRing
    52045201    rChangeCurrRing(baseRing);
     
    52105207    to = clock();
    52115208#endif
    5212     // compute a representation of the generators of submod (M) with respect to those of mod (Gomega), where Gomega is a reduced Groebner basis w.r.t. the current ring
     5209    // compute a representation of the generators of submod (M) with respect to those of mod (Gomega),
     5210    // where Gomega is a reduced Groebner basis w.r.t. the current ring
    52135211    F = MLifttwoIdeal(Gomega2, M1, G);
    52145212#ifdef TIME_TEST
    52155213    tlift = tlift + clock() - to;
    52165214#endif
    5217 #ifdef CHECK_IDEAL_MWALK
    5218     idString(F, "F");
    5219 #endif
     5215//#ifdef CHECK_IDEAL_MWALK
     5216    if(printout > 2)
     5217    {
     5218      idString(F, "//** Mwalk: F");
     5219    }
     5220//#endif
    52205221    idDelete(&Gomega2);
    52215222    idDelete(&M1);
     
    52275228    to = clock();
    52285229#endif
    5229     //G = kStd(F1,NULL,testHomog,NULL,NULL,0,0,NULL);
     5230
    52305231#ifdef TIME_TEST
    52315232    tstd = tstd + clock() - to;
    52325233#endif
    52335234    idSkipZeroes(G);
    5234 #ifdef CHECK_IDEAL_MWALK
    5235     idString(G, "G");
    5236 #endif
     5235//#ifdef CHECK_IDEAL_MWALK
     5236    if(printout > 2)
     5237    {
     5238      idString(G, "//** Mwalk: G");
     5239    }
     5240//#endif
    52375241#ifdef TIME_TEST
    52385242    to = clock();
    52395243#endif
     5244    NEXT_VECTOR:
     5245    PrintS("\n//** Mwalk: NEXT_VECTOR!\n");
    52405246    intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
    52415247#ifdef TIME_TEST
    52425248    tnw = tnw + clock() - to;
    52435249#endif
    5244 #ifdef PRINT_VECTORS
    5245     MivString(curr_weight, target_weight, next_weight);
    5246 #endif
    5247     if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1)// || test_w_in_ConeCC(G, target_weight) == 1 || MivComp(next_weight,curr_weight) == 1)
    5248     {
    5249 #ifdef CHECK_IDEAL_MWALK
    5250       PrintS("\n//** Mwalk: entering last cone.\n");
    5251 #endif
     5250//#ifdef PRINT_VECTORS
     5251    if(printout > 0)
     5252    {
     5253      MivString(curr_weight, target_weight, next_weight);
     5254    }
     5255//#endif
     5256    if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1 || test_w_in_ConeCC(G, target_weight) == 1)
     5257    {
     5258//#ifdef CHECK_IDEAL_MWALK
     5259      if(printout > 0)
     5260      {
     5261        PrintS("\n//** Mwalk: entering last cone.\n");
     5262      }
     5263//#endif
    52525264      Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
    52535265      if(target_M->length() == nV)
     
    52625274      Gomega1 = idrMoveR(Gomega, baseRing,currRing);
    52635275      idDelete(&Gomega);
    5264 #ifdef CHECK_IDEAL_MWALK
    5265       idString(Gomega1, "Gomega");
    5266 #endif
     5276//#ifdef CHECK_IDEAL_MWALK
     5277      if(printout > 1)
     5278      {
     5279        idString(Gomega1, "//** Mwalk: Gomega");
     5280      }
     5281      PrintS("\n //** Mwalk: kStd(Gomega)");
     5282//#endif
    52675283      M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
    5268 #ifdef CHECK_IDEAL_MWALK
    5269       idString(M,"M");
    5270 #endif
     5284//#ifdef CHECK_IDEAL_MWALK
     5285      if(printout > 1)
     5286      {
     5287        idString(M,"//** Mwalk: M");
     5288      }
     5289//#endif
    52715290      rChangeCurrRing(baseRing);
    52725291      M1 =  idrMoveR(M, newRing,currRing);
     
    52745293      Gomega2 = idrMoveR(Gomega1, newRing,currRing);
    52755294      idDelete(&Gomega1);
     5295      PrintS("\n //** Mwalk: MLifttwoIdeal");
    52765296      F = MLifttwoIdeal(Gomega2, M1, G);
    5277 #ifdef CHECK_IDEAL_MWALK
    5278       idString(F,"F");
    5279 #endif
     5297//#ifdef CHECK_IDEAL_MWALK
     5298    if(printout > 2)
     5299    {
     5300      idString(F,"//** Mwalk: F");
     5301    }
     5302//#endif
    52805303      idDelete(&Gomega2);
    52815304      idDelete(&M1);
     
    52895312      to = clock();
    52905313#endif
    5291  //     if(si_opt_1 == (Sy_bit(OPT_REDSB)))
    5292   //    {
    5293         G = kInterRedCC(G,NULL); //reduce the Groebner basis <G> w.r.t. currRing, if option(redSB) is set
    5294   //    }
     5314      //PrintS("\n //**Mwalk: Interreduce");
     5315      //interreduce the Groebner basis <G> w.r.t. currRing
     5316      //G = kInterRedCC(G,NULL);
    52955317#ifdef TIME_TEST
    52965318      tred = tred + clock() - to;
     
    52995321      delete next_weight;
    53005322      break;
    5301 #ifdef CHECK_IDEAL_MWALK
    5302       PrintS("\n//** Mwalk: last cone.\n");
    5303 #endif
    5304     }
    5305 #ifdef CHECK_IDEAL_MWALK
    5306     PrintS("\n//** Mwalk: update weight vectors.\n");
    5307 #endif
     5323    }
    53085324    for(i=nV-1; i>=0; i--)
    53095325    {
     
    53165332  ideal result = idrMoveR(G,baseRing,currRing);
    53175333  idDelete(&G);
    5318 /*#ifdef CHECK_IDEAL_MWALK
    5319   pDelete(&p);
    5320 #endif*/
    53215334  delete tmp_weight;
    53225335  delete ivNull;
     
    53265339#endif
    53275340#ifdef TIME_TEST
    5328   Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
    53295341  TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
    5330   Print("\n//** Mwalk: Ergebnis.\n");
    53315342  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
    53325343  //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
    53335344#endif
     5345  Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
    53345346  return(result);
    53355347}
    53365348
    5337 // 07.11.2012
    5338 // THE RANDOM WALK ALGORITHM  ideal Go, intvec* orig_M, intvec* target_M, ring baseRing
    5339 ideal Mrwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, int pert_deg, ring baseRing)
     5349// THE RANDOM WALK ALGORITHM
     5350ideal Mrwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, int pert_deg,
     5351             int reduction, int printout)
    53405352{
    53415353  BITSET save1 = si_opt_1; // save current options
    5342   //si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    5343   //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
    5344   //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
     5354  if(reduction == 0)
     5355  {
     5356    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
     5357    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
     5358    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
     5359  }
    53455360  Set_Error(FALSE);
    53465361  Overflow_Error = FALSE;
     
    53525367#endif
    53535368  nstep=0;
    5354   int i,nwalk,endwalks = 0;
    5355   int nV = baseRing->N;
     5369  int i,polylength,nwalk,endwalks = 0;
     5370  int nV = currRing->N;
    53565371
    53575372  ideal Gomega, M, F, Gomega1, Gomega2, M1; //, F1;
    53585373  ring newRing;
    5359   ring XXRing = baseRing;
     5374  ring baseRing = currRing;
     5375  ring XXRing = currRing;
    53605376  intvec* ivNull = new intvec(nV);
    53615377  intvec* curr_weight = new intvec(nV);
     
    53635379  intvec* exivlp = Mivlp(nV);
    53645380  intvec* tmp_weight = new intvec(nV);
     5381  intvec* next_weight= new intvec(nV);
    53655382  for(i=0; i<nV; i++)
    53665383  {
     
    53835400#endif
    53845401  rComplete(currRing);
    5385 #ifdef CHECK_IDEAL_MWALK
    5386     idString(Go,"Go");
    5387 #endif
    53885402#ifdef TIME_TEST
    53895403  to = clock();
    53905404#endif
    5391      if(orig_M->length() == nV)
    5392       {
    5393         newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
    5394       }
    5395       else
    5396       {
    5397         newRing = VMatrDefault(orig_M);
    5398       }
     5405  if(orig_M->length() == nV)
     5406  {
     5407    newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
     5408  }
     5409  else
     5410  {
     5411    newRing = VMatrDefault(orig_M);
     5412  }
    53995413  rChangeCurrRing(newRing);
    5400   ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
     5414  //ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
     5415  ideal G = idrMoveR(Go,baseRing,currRing);
    54015416  baseRing = currRing;
    54025417#ifdef TIME_TEST
     
    54125427    to = clock();
    54135428#endif
    5414 #ifdef CHECK_IDEAL_MWALK
    5415     idString(G,"G");
    5416 #endif
     5429//#ifdef CHECK_IDEAL_MWALK
     5430    if(printout > 2)
     5431    {
     5432      idString(G,"//** Mrwalk: G");
     5433    }
     5434//#endif
    54175435    Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
     5436    //polylength = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise
     5437    polylength = lengthpoly(Gomega);
    54185438#ifdef TIME_TEST
    54195439    tif = tif + clock()-to; //time for computing initial form ideal
    54205440#endif
    5421 #ifdef CHECK_IDEAL_MWALK
    5422     idString(Gomega,"Gomega");
    5423 #endif
     5441//#ifdef CHECK_IDEAL_MWALK
     5442    if(printout > 1)
     5443    {
     5444      idString(Gomega,"//** Mrwalk: Gomega");
     5445    }
     5446//#endif
    54245447#ifndef  BUCHBERGER_ALG
    54255448    if(isNolVector(curr_weight) == 0)
    54265449    {
    54275450      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    5428     }
     5451    }   
    54295452    else
    54305453    {
     
    54715494#endif
    54725495    idSkipZeroes(M);
    5473 #ifdef CHECK_IDEAL_MWALK
    5474     PrintS("\n//** Mwalk: computed M.\n");
    5475     idString(M, "M");
    5476 #endif
     5496//#ifdef CHECK_IDEAL_MWALK
     5497    if(printout > 2)
     5498    {
     5499      idString(M, "//** Mrwalk: M");
     5500    }
     5501//#endif
    54775502    //change the ring to baseRing
    54785503    rChangeCurrRing(baseRing);
     
    54845509    to = clock();
    54855510#endif
    5486     // compute a representation of the generators of submod (M) with respect to those of mod (Gomega), where Gomega is a reduced Groebner basis w.r.t. the current ring
     5511    // compute a representation of the generators of submod (M) with respect to those of mod (Gomega),
     5512    // where Gomega is a reduced Groebner basis w.r.t. the current ring
    54875513    F = MLifttwoIdeal(Gomega2, M1, G);
    54885514#ifdef TIME_TEST
    54895515    tlift = tlift + clock() - to;
    54905516#endif
    5491 #ifdef CHECK_IDEAL_MWALK
    5492     idString(F, "F");
    5493 #endif
     5517//#ifdef CHECK_IDEAL_MWALK
     5518    if(printout > 2)
     5519    {
     5520      idString(F, "//** Mrwalk: F");
     5521    }
     5522//#endif
    54945523    idDelete(&Gomega2);
    54955524    idDelete(&M1);
     
    55005529#ifdef TIME_TEST
    55015530    to = clock();
    5502 #endif
    5503     //G = kStd(F1,NULL,testHomog,NULL,NULL,0,0,NULL);
    5504 #ifdef TIME_TEST
    55055531    tstd = tstd + clock() - to;
    55065532#endif
    55075533    idSkipZeroes(G);
    5508 #ifdef CHECK_IDEAL_MWALK
    5509     idString(G, "G");
    5510 #endif
     5534//#ifdef CHECK_IDEAL_MWALK
     5535    if(printout > 2)
     5536    {
     5537      idString(G, "//** Mrwalk: G");
     5538    }
     5539//#endif
    55115540#ifdef TIME_TEST
    55125541    to = clock();
    55135542#endif
    5514     intvec* next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg);//next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
     5543    next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
     5544    if(polylength > 0)
     5545    {
     5546      //there is a polynomial in Gomega with at least 3 monomials,
     5547      //low-dimensional facet of the cone
     5548      delete next_weight;
     5549      next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg);
     5550    }
    55155551#ifdef TIME_TEST
    55165552    tnw = tnw + clock() - to;
    55175553#endif
    5518 #ifdef PRINT_VECTORS
    5519     MivString(curr_weight, target_weight, next_weight);
    5520 #endif
    5521     if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1)// || test_w_in_ConeCC(G, target_weight) == 1 || MivComp(next_weight,curr_weight) == 1)
     5554//#ifdef PRINT_VECTORS
     5555    if(printout > 0)
     5556    {
     5557      MivString(curr_weight, target_weight, next_weight);
     5558    }
     5559//#endif
     5560    if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1 || test_w_in_ConeCC(G, target_weight) == 1) // || MivComp(next_weight,curr_weight) == 1)
    55225561    {
    55235562#ifdef CHECK_IDEAL_MWALK
     
    55255564#endif
    55265565      Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
     5566//#ifdef CHECK_IDEAL_MWALK
     5567      if(printout > 1)
     5568      {
     5569        idString(Gomega, "//** Mrwalk: Gomega");
     5570      }
     5571//#endif
    55275572      if(target_M->length() == nV)
    55285573      {
     
    55365581      Gomega1 = idrMoveR(Gomega, baseRing,currRing);
    55375582      idDelete(&Gomega);
    5538 #ifdef CHECK_IDEAL_MWALK
    5539       idString(Gomega1, "Gomega");
    5540 #endif
    55415583      M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
    5542 #ifdef CHECK_IDEAL_MWALK
    5543       idString(M,"M");
    5544 #endif
     5584//#ifdef CHECK_IDEAL_MWALK
     5585      if(printout > 2)
     5586      {
     5587        idString(M,"//** Mrwalk: M");
     5588      }
     5589//#endif
    55455590      rChangeCurrRing(baseRing);
    55465591      M1 =  idrMoveR(M, newRing,currRing);
     
    55495594      idDelete(&Gomega1);
    55505595      F = MLifttwoIdeal(Gomega2, M1, G);
    5551 #ifdef CHECK_IDEAL_MWALK
    5552       idString(F,"F");
    5553 #endif
    55545596      idDelete(&Gomega2);
    55555597      idDelete(&M1);
     
    55585600      idDelete(&F);
    55595601      baseRing = currRing;
    5560       si_opt_1 = save1; //set original options, e. g. option(RedSB)
    55615602      idSkipZeroes(G);
    55625603#ifdef TIME_TEST
    55635604      to = clock();
    55645605#endif
    5565  //     if(si_opt_1 == (Sy_bit(OPT_REDSB)))
    5566   //    {
    5567         //G = kInterRedCC(G,NULL); //reduce the Groebner basis <G> w.r.t. currRing, if option(redSB) is set
    5568   //    }
     5606//#ifdef CHECK_IDEAL_MWALK
     5607      if(printout > 2)
     5608      {
     5609        idString(G,"//** Mrwalk: G");
     5610      }
     5611///#endif
     5612      if(si_opt_1 == (Sy_bit(OPT_REDSB)))
     5613      {
     5614        //G = kInterRedCC(G,NULL); //interreduce the Groebner basis <G> w.r.t. currRing
     5615      }
    55695616#ifdef TIME_TEST
    55705617      tred = tred + clock() - to;
     
    55735620      delete next_weight;
    55745621      break;
    5575 #ifdef CHECK_IDEAL_MWALK
    5576       PrintS("\n//** Mwalk: last cone.\n");
    5577 #endif
    5578     }
    5579 #ifdef CHECK_IDEAL_MWALK
    5580     PrintS("\n//** Mwalk: update weight vectors.\n");
    5581 #endif
     5622    }
    55825623    for(i=nV-1; i>=0; i--)
    55835624    {
     
    55875628    delete next_weight;
    55885629  }
     5630  baseRing = currRing;
    55895631  rChangeCurrRing(XXRing);
    55905632  ideal result = idrMoveR(G,baseRing,currRing);
    55915633  idDelete(&G);
    5592 /*#ifdef CHECK_IDEAL_MWALK
    5593   pDelete(&p);
    5594 #endif*/
     5634  si_opt_1 = save1; //set original options, e. g. option(RedSB)
    55955635  delete tmp_weight;
    55965636  delete ivNull;
     
    55995639  delete last_omega;
    56005640#endif
     5641  Print("\n//** Mrwalk: Groebner Walk took %d steps.\n", nstep);
    56015642#ifdef TIME_TEST
    5602   Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
    56035643  TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
    5604   Print("\n//** Mwalk: Ergebnis.\n");
    56055644  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
    56065645  //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
     
    57495788// use kStd, if nP = 0, else call LastGB
    57505789ideal Mpwalk(ideal Go, int op_deg, int tp_deg,intvec* curr_weight,
    5751              intvec* target_weight, int nP)
    5752 {
     5790             intvec* target_weight, int nP, int reduction, int printout)
     5791{
     5792  BITSET save1 = si_opt_1; // save current options
     5793  if(reduction == 0)
     5794  {
     5795    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
     5796    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
     5797    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
     5798  }
    57535799  Set_Error(FALSE  );
    57545800  Overflow_Error = FALSE;
     
    57885834  ring XXRing = currRing;
    57895835
    5790 
    57915836  to = clock();
    5792   /* perturbs the original vector */
     5837  // perturbs the original vector
    57935838  if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
    57945839  {
     
    58075852      DefRingPar(curr_weight);
    58085853    else
    5809       rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung 1
     5854      rChangeCurrRing(VMrDefault(curr_weight));
    58105855
    58115856    G = idrMoveR(Go, XXRing,currRing);
     
    58225867  ring HelpRing = currRing;
    58235868
    5824   /* perturbs the target weight vector */
     5869  // perturbs the target weight vector
    58255870  if(tp_deg > 1 && tp_deg <= nV)
    58265871  {
     
    58285873      DefRingPar(target_weight);
    58295874    else
    5830       rChangeCurrRing(VMrDefault(target_weight)); // Aenderung 2
     5875      rChangeCurrRing(VMrDefault(target_weight));
    58315876
    58325877    TargetRing = currRing;
     
    58505895    G = idrMoveR(ssG, TargetRing,currRing);
    58515896  }
    5852   /*
    5853     Print("\n// Perturbationwalkalg. vom Gradpaar (%d,%d):",op_deg,tp_deg);
    5854     ivString(curr_weight, "new sigma");
    5855     ivString(target_weight, "new tau");
    5856   */
     5897    if(printout > 0)
     5898    {
     5899      Print("\n//** Mpwalk: Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
     5900      ivString(curr_weight, "//** Mpwalk: new current weight");
     5901      ivString(target_weight, "//** Mpwalk: new target weight");
     5902    }
    58575903  while(1)
    58585904  {
    58595905    nstep ++;
    58605906    to = clock();
    5861     /* compute an initial form ideal of <G> w.r.t. the weight vector
    5862        "curr_weight" */
     5907    // compute an initial form ideal of <G> w.r.t. the weight vector
     5908    // "curr_weight"
    58635909    Gomega = MwalkInitialForm(G, curr_weight);
    5864 
     5910//#ifdef CHECK_IDEAL_MWALK
     5911    if(printout > 1)
     5912    {
     5913      idString(Gomega,"//** Mpwalk: Gomega");
     5914    }
     5915//#endif
    58655916
    58665917#ifdef ENDWALKS
    5867     if(endwalks == 1){
     5918    if(endwalks == 1)
     5919    {
    58685920      Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
    58695921      idElements(G, "G");
    5870       // idElements(Gomega, "Gw");
    58715922      headidString(G, "G");
    5872       //headidString(Gomega, "Gw");
    58735923    }
    58745924#endif
     
    58895939      DefRingPar(curr_weight);
    58905940    else
    5891       rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung 3
     5941      rChangeCurrRing(VMrDefault(curr_weight));
    58925942
    58935943    newRing = currRing;
     
    59105960    tim = clock();
    59115961    to = clock();
    5912     /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */
     5962    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
    59135963#ifdef  BUCHBERGER_ALG
    59145964    M = MstdhomCC(Gomega1);
     
    59165966    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    59175967    delete hilb_func;
    5918 #endif // BUCHBERGER_ALG
     5968#endif
     5969//#ifdef CHECK_IDEAL_MWALK
     5970      if(printout > 2)
     5971      {
     5972        idString(M,"//** Mpwalk: M");
     5973      }
     5974//#endif
    59195975
    59205976    if(endwalks == 1){
     
    59285984      tstd=tstd+clock()-to;
    59295985
    5930     /* change the ring to oldRing */
     5986    // change the ring to oldRing
    59315987    rChangeCurrRing(oldRing);
    59325988    M1 =  idrMoveR(M, newRing,currRing);
    59335989    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
    5934 
    5935     //if(endwalks==1)  PrintS("\n// Lifting is working:..");
    59365990
    59375991    to=clock();
     
    59455999      xtlift=clock()-to;
    59466000
     6001//#ifdef CHECK_IDEAL_MWALK
     6002    if(printout > 2)
     6003    {
     6004      idString(F,"//** Mpwalk: F");
     6005    }
     6006//#endif
     6007
    59476008    idDelete(&M1);
    59486009    idDelete(&Gomega2);
    59496010    idDelete(&G);
    59506011
    5951     /* change the ring to newRing */
     6012    // change the ring to newRing
    59526013    rChangeCurrRing(newRing);
    59536014    F1 = idrMoveR(F, oldRing,currRing);
    5954 
    5955     //if(endwalks==1)PrintS("\n// InterRed is working now:");
    5956 
     6015    //G = idrMoveR(F,oldRing,currRing);
    59576016    to=clock();
    5958     /* reduce the Groebner basis <G> w.r.t. new ring */
     6017    PrintS("\n //** Mpwalk: reduce the Groebner basis.\n");
    59596018    G = kInterRedCC(F1, NULL);
    59606019    if(endwalks != 1)
     
    59696028
    59706029    to=clock();
    5971     /* compute a next weight vector */
     6030    // compute a next weight vector
    59726031    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
    59736032    tnw=tnw+clock()-to;
    5974 #ifdef PRINT_VECTORS
    5975     MivString(curr_weight, target_weight, next_weight);
    5976 #endif
     6033//#ifdef PRINT_VECTORS
     6034    if(printout > 0)
     6035    {
     6036      MivString(curr_weight, target_weight, next_weight);
     6037    }
     6038//#endif
    59776039
    59786040    if(Overflow_Error == TRUE)
     
    59986060
    59996061    delete next_weight;
    6000   }//while
     6062  }//end of while-loop
    60016063
    60026064  if(tp_deg != 1)
     
    60126074        DefRingPar(orig_target);
    60136075      else
    6014         rChangeCurrRing(VMrDefault(orig_target)); //Aenderung
     6076        rChangeCurrRing(VMrDefault(orig_target));
    60156077
    60166078    TargetRing=currRing;
     
    60666128    Eresult = idrMoveR(G, newRing,currRing);
    60676129  }
     6130  si_opt_1 = save1; //set original options, e. g. option(RedSB)
    60686131  delete ivNull;
    60696132  if(tp_deg != 1)
     
    60806143             tnw+xtnw);
    60816144
    6082   Print("\n// pSetm_Error = (%d)", ErrorCheck());
    6083   Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
    6084 #endif
     6145  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
     6146  //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
     6147#endif
     6148  Print("\n//** Mpwalk: Perturbation Walk took %d steps.\n", nstep);
     6149  return(Eresult);
     6150}
     6151
     6152/*******************************************************
     6153 * THE PERTURBATION WALK ALGORITHM WITH RANDOM ELEMENT *
     6154 *******************************************************/
     6155ideal Mprwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad,
     6156              int op_deg, int tp_deg, int nP, int reduction, int printout)
     6157{
     6158  BITSET save1 = si_opt_1; // save current options
     6159  if(reduction == 0)
     6160  {
     6161    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
     6162    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
     6163    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
     6164  }
     6165  Set_Error(FALSE);
     6166  Overflow_Error = FALSE;
     6167  //Print("// pSetm_Error = (%d)", ErrorCheck());
     6168
     6169  clock_t  tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
     6170  xtextra=0;
     6171  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
     6172  tinput = clock();
     6173
     6174  clock_t tim;
     6175
     6176  nstep = 0;
     6177  int i, ntwC=1, ntestw=1, polylength, nV = currRing->N;
     6178  int endwalks=0;
     6179
     6180  ideal Gomega, M, F, G, Gomega1, Gomega2, M1,F1,Eresult,ssG;
     6181  ring newRing, oldRing, TargetRing;
     6182  intvec* iv_M_dp;
     6183  intvec* iv_M_lp;
     6184  intvec* exivlp = Mivlp(nV);
     6185  intvec* curr_weight = new intvec(nV);
     6186  intvec* target_weight = new intvec(nV);
     6187  for(i=0; i<nV; i++)
     6188  {
     6189    (*curr_weight)[i] = (*orig_M)[i];
     6190    (*target_weight)[i] = (*target_M)[i];
     6191  }
     6192  intvec* orig_target = target_weight;
     6193  intvec* pert_target_vector = target_weight;
     6194  intvec* ivNull = new intvec(nV);
     6195  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
     6196#ifndef BUCHBERGER_ALG
     6197  intvec* hilb_func;
     6198#endif
     6199  intvec* next_weight;
     6200
     6201  // to avoid (1,0,...,0) as the target vector
     6202  intvec* last_omega = new intvec(nV);
     6203  for(i=nV-1; i>0; i--)
     6204    (*last_omega)[i] = 1;
     6205  (*last_omega)[0] = 10000;
     6206
     6207  ring XXRing = currRing;
     6208
     6209  to = clock();
     6210  // perturbs the original vector
     6211  if(orig_M->length() == nV)
     6212  {
     6213    if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
     6214    {
     6215      G = MstdCC(Go);
     6216      tostd = clock()-to;
     6217      if(op_deg != 1)
     6218      {
     6219        iv_M_dp = MivMatrixOrderdp(nV);
     6220        //ivString(iv_M_dp, "iv_M_dp");
     6221        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
     6222      }
     6223    }
     6224    else
     6225    {
     6226      //define ring order := (a(curr_weight),lp);
     6227      if (rParameter(currRing) != NULL)
     6228        DefRingPar(curr_weight);
     6229      else
     6230        rChangeCurrRing(VMrDefault(curr_weight));
     6231
     6232      G = idrMoveR(Go, XXRing,currRing);
     6233      G = MstdCC(G);
     6234      tostd = clock()-to;
     6235      if(op_deg != 1)
     6236      {
     6237        iv_M_dp = MivMatrixOrder(curr_weight);
     6238        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
     6239      }
     6240    }
     6241  }
     6242  else
     6243  {
     6244    rChangeCurrRing(VMatrDefault(orig_M));
     6245    G = idrMoveR(Go, XXRing,currRing);
     6246    G = MstdCC(G);
     6247    tostd = clock()-to;
     6248    if(op_deg != 1)
     6249    {
     6250      curr_weight = MPertVectors(G, orig_M, op_deg);
     6251    }
     6252  }
     6253
     6254  delete iv_dp;
     6255  if(op_deg != 1) delete iv_M_dp;
     6256
     6257  ring HelpRing = currRing;
     6258
     6259  // perturbs the target weight vector
     6260  if(target_M->length() == nV)
     6261  {
     6262    if(tp_deg > 1 && tp_deg <= nV)
     6263    {
     6264      if (rParameter(currRing) != NULL)
     6265        DefRingPar(target_weight);
     6266      else
     6267        rChangeCurrRing(VMrDefault(target_weight));
     6268
     6269      TargetRing = currRing;
     6270      ssG = idrMoveR(G,HelpRing,currRing);
     6271      if(MivSame(target_weight, exivlp) == 1)
     6272      {
     6273        iv_M_lp = MivMatrixOrderlp(nV);
     6274        //ivString(iv_M_lp, "iv_M_lp");
     6275        //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg);
     6276        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
     6277      }
     6278      else
     6279      {
     6280        iv_M_lp = MivMatrixOrder(target_weight);
     6281        //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg);
     6282        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
     6283      }
     6284      delete iv_M_lp;
     6285      pert_target_vector = target_weight;
     6286      rChangeCurrRing(HelpRing);
     6287      G = idrMoveR(ssG, TargetRing,currRing);
     6288    }
     6289  }
     6290  else
     6291  {
     6292    if(tp_deg > 1 && tp_deg <= nV)
     6293    {
     6294      rChangeCurrRing(VMatrDefault(target_M));
     6295      TargetRing = currRing;
     6296      ssG = idrMoveR(G,HelpRing,currRing);
     6297      target_weight = MPertVectors(ssG, target_M, tp_deg);
     6298    }
     6299  }
     6300  if(printout > 0)
     6301  {
     6302    Print("\n//** Mprwalk: Random Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
     6303    ivString(curr_weight, "//** Mprwalk: new current weight");
     6304    ivString(target_weight, "//** Mprwalk: new target weight");
     6305  }
     6306  while(1)
     6307  {
     6308    nstep ++;
     6309    to = clock();
     6310    // compute an initial form ideal of <G> w.r.t. the weight vector
     6311    // "curr_weight"
     6312    Gomega = MwalkInitialForm(G, curr_weight);
     6313//#ifdef CHECK_IDEAL_MWALK
     6314    if(printout > 0)
     6315    {
     6316      idString(Gomega,"//** Mprwalk: Gomega");
     6317    }
     6318//#endif
     6319    polylength = lengthpoly(Gomega);
     6320#ifdef ENDWALKS
     6321    if(endwalks == 1)
     6322    {
     6323      Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
     6324      idElements(G, "G");
     6325      headidString(G, "G");
     6326    }
     6327#endif
     6328
     6329    tif = tif + clock()-to;
     6330
     6331#ifndef  BUCHBERGER_ALG
     6332    if(isNolVector(curr_weight) == 0)
     6333      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
     6334    else
     6335      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
     6336#endif // BUCHBERGER_ALG
     6337
     6338    oldRing = currRing;
     6339
     6340    if(target_M->length() == nV)
     6341    {
     6342      // define a new ring with ordering "(a(curr_weight),lp)
     6343      if (rParameter(currRing) != NULL)
     6344        DefRingPar(curr_weight);
     6345      else
     6346        rChangeCurrRing(VMrDefault(curr_weight));
     6347    }
     6348    else
     6349    {
     6350      rChangeCurrRing(VMatrRefine(target_M,curr_weight));
     6351    }
     6352    newRing = currRing;
     6353    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
     6354    PrintS("\n //** Mprwalk: Changed ring.\n");
     6355#ifdef ENDWALKS
     6356    if(endwalks==1)
     6357    {
     6358      Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
     6359      idElements(Gomega1, "Gw");
     6360      headidString(Gomega1, "headGw");
     6361      PrintS("\n// compute a rGB of Gw:\n");
     6362
     6363#ifndef  BUCHBERGER_ALG
     6364      ivString(hilb_func, "w");
     6365#endif
     6366    }
     6367#endif
     6368
     6369    tim = clock();
     6370    to = clock();
     6371    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
     6372#ifdef  BUCHBERGER_ALG
     6373    M = MstdhomCC(Gomega1);
     6374#else
     6375    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
     6376    delete hilb_func;
     6377#endif
     6378//#ifdef CHECK_IDEAL_MWALK
     6379    Print("\n //** Mprwalk: M");
     6380    if(printout > 2)
     6381    {
     6382      idString(M,"//** Mprwalk: M");
     6383    }
     6384//#endif
     6385
     6386    if(endwalks == 1)
     6387    {
     6388      xtstd = xtstd+clock()-to;
     6389#ifdef ENDWALKS
     6390      Print("\n// time for the last std(Gw)  = %.2f sec\n",
     6391            ((double) clock())/1000000 -((double)tim) /1000000);
     6392#endif
     6393    }
     6394    else
     6395      tstd=tstd+clock()-to;
     6396
     6397    /* change the ring to oldRing */
     6398    rChangeCurrRing(oldRing);
     6399    M1 =  idrMoveR(M, newRing,currRing);
     6400    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
     6401
     6402    to=clock();
     6403    /* compute a representation of the generators of submod (M)
     6404       with respect to those of mod (Gomega).
     6405       Gomega is a reduced Groebner basis w.r.t. the current ring */
     6406    F = MLifttwoIdeal(Gomega2, M1, G);
     6407    if(endwalks != 1)
     6408      tlift = tlift+clock()-to;
     6409    else
     6410      xtlift=clock()-to;
     6411    Print("\n //** Mprwalk: F.\n");
     6412//#ifdef CHECK_IDEAL_MWALK
     6413    if(printout > 2)