Changeset b9e63ba in git

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:

• Singular/LIB/arr.lib (added)
• Singular/LIB/gradedModules.lib (modified) (25 diffs)
• Singular/LIB/grwalk.lib (modified) (10 diffs)
• Singular/LIB/modwalk.lib (modified) (22 diffs, 1 prop)
• Singular/LIB/normal.lib (modified) (2 diffs)
• Singular/LIB/polymake.lib (modified) (4 diffs)
• Singular/LIB/rwalk.lib (modified) (11 diffs, 1 prop)
• Singular/LIB/swalk.lib (modified) (1 prop)
• Singular/dyn_modules/gfanlib/Makefile.am (modified) (1 diff)
• Singular/dyn_modules/gfanlib/bbcone.cc (modified) (1 diff)
• Singular/dyn_modules/gfanlib/bbcone.h (modified) (1 diff)
• Singular/dyn_modules/gfanlib/groebnerComplex.cc (added)
• Singular/dyn_modules/gfanlib/groebnerComplex.h (added)
• Singular/dyn_modules/gfanlib/groebnerCone.cc (modified) (2 diffs)
• Singular/dyn_modules/gfanlib/groebnerFan.cc (added)
• Singular/dyn_modules/gfanlib/groebnerFan.h (added)
• Singular/dyn_modules/gfanlib/initial.cc (modified) (1 diff)
• Singular/dyn_modules/gfanlib/ppinitialReduction.cc (modified) (1 diff)
• Singular/dyn_modules/gfanlib/ppinitialReduction.h (modified) (1 diff)
• Singular/dyn_modules/gfanlib/startingCone.cc (modified) (2 diffs)
• Singular/dyn_modules/gfanlib/startingCone.h (modified) (1 diff)
• Singular/dyn_modules/gfanlib/tropical.cc (modified) (10 diffs)
• Singular/dyn_modules/gfanlib/tropical.h (modified) (1 diff)
• Singular/dyn_modules/gfanlib/tropicalCurves.cc (modified) (2 diffs)
• Singular/dyn_modules/gfanlib/tropicalStrategy.cc (modified) (3 diffs)
• Singular/dyn_modules/gfanlib/tropicalTraversal.cc (modified) (3 diffs)
• Singular/dyn_modules/gfanlib/tropicalTraversal.h (modified) (1 diff)
• Singular/dyn_modules/gfanlib/tropicalVariety.cc (modified) (5 diffs)
• Singular/extra.cc (modified) (11 diffs)
• Singular/iparith.cc (modified) (2 diffs)
• Singular/ipassign.cc (modified) (3 diffs)
• Singular/misc_ip.cc (modified) (1 diff)
• Singular/table.h (modified) (3 diffs)
• Singular/walk.cc (modified) (154 diffs, 1 prop)
• Singular/walk.h (modified) (1 diff, 1 prop)
• Tst/Short/arr.res.gz.uu (added)
• Tst/Short/arr.stat (added)
• Tst/Short/arr.tst (added)
• Tst/Short/ok_s.lst (modified) (1 diff)
• doc/NEWS.texi (modified) (1 diff)
• doc/gfanlib.doc (added)
• doc/polymake.doc (modified) (previous)
• doc/reference.doc (modified) (previous)
• doc/singular.doc (modified) (previous)
• libpolys/misc/options.c (modified) (1 diff)

Singular/LIB/gradedModules.lib

@@ -1 +1 @@
 ///////////////////////////////////////////////////////////////////////////
 version="version gradedModules.lib 4.0.1.1 Jan_2015 "; // $Id$
-category="General purpose?";
+category="Commutative Algebra";
 info="
 LIBRARY: gradedModules.lib     Operations with graded modules/matrices/resolutions
 AUTHORS:  Oleksandr Motsak <U@D>, where U=motsak, D=mathematik.uni-kl.de
-@*         Hanieh Keneshlou <hkeneshlou@yahoo.com>
+@*        Hanieh Keneshlou <hkeneshlou@yahoo.com>
 KEYWORDS: graded modules, graded homomorphisms, syzygies
 OVERVIEW:
-    The library contains several procedures for operations with graded modules/matrices/resolutions
-    TODO!
+    The library contains several procedures for constructing and manipulating graded modules/matrices/resolutions.
+NOTE:
+    set assumeLevel to positive integer value in order to auto-check all assumptions.
 REFERENCES:
 [MO]   Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related
-       structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010 TODO!?
+       structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010
 PROCEDURES:
     grzero()        presentation of basering(0)^1
@@ -36 +37 @@
 static proc pad(int m, string s, string c){ string r = s; while( size(r) < m ){ r = c + r; } return(r); }
 static proc mstring( int m, string c){ if( m < 0 ) { return (c); }; return (string(m)); }
-static proc zstring( int m, int b, string c){ if(b) { return (c); }; return (string(m)); }
 // view helper
-static proc draw ( intmat D, intvec zc, int d )
+static proc draw ( intmat D, int d )
 {
 //  print(D); return ();
@@ -50 +50 @@
   {
     head = head + pad(max, string(D[1 , c]), " ") + " ";
-    foot = foot + pad(max, zstring(D[nr, c], zc[c - d], "?"), " ") + " ";
+    foot = foot + pad(max, string(D[nr, c]), " ") + " ";
   }
   // last head/foot enties:
   head = head + pad(max, string(D[1 , c]), " ");
-  foot = foot + pad(max, zstring(D[nr, c], zc[c-d], "?"), " ");
+  foot = foot + pad(max, string(D[nr, c]), " ");
   // head/foot dash lines:
   string dash  = repeat( (max + 1) * (nc - 2*d) , "-");
@@ -74 +74 @@
 }
 
-proc grview(def N)
-"
-PURPOSE: print the degree/grading data about the GRADED matrix/module/ideal N
+proc grview(N)
+"USAGE:  grview(M), graded object M
+RETURN:  nothing
+PURPOSE: print the degree/grading data about the GRADED matrix/module/ideal/mapping object M             
+ASSUME:  M must be graded
+EXAMPLE: example grsum; shows an example
 "
 {
@@ -89 +92 @@
 //  typeof( N ) ;  attrib( N );  attrib(N, "isHomog");
 
-  ASSUME(0, /* input must be graded! */ typeof(attrib(N, "isHomog")) == "intvec" );
-
   // input should be graded:
-  intvec gr = attrib(N, "isHomog"); // grading weights?
-  ASSUME(0, /* input must be correctly graded! */ nrows(N) == size(gr) );
-
-//  intvec gr = attrib( N, "isHomog" ); //  module(N); "grading: ", gr;
-
+  ASSUME(1, grtest(N) );
+  
+  intvec G = grdeg(N); 
   matrix M = module(N);
+  
   int nc = ncols(M); int nr = nrows(M);
   int r,c;
@@ -103 +103 @@
   intmat D[nr+2*d][nc+2*d];
 
-  module L = module(N); L = lead(L); vector v;
-  int m = 1 + nvars(basering);
-  intvec zc = 0:nc;
   for( c = nc; c > 0; c-- )
   {
     D[1, c+d] = c; // top row indeces
-    v = L[c];
-    if( v != 0 )
-    {
-      D[nr+2*d, c+d] = deg(v) + gr[ leadexp(v)[m] ]; // bottom row with computed column induced degrees
-    } else
-    {
-//      D[nr+2*d, c+d] = 0; // TODO: 0/-1 is valid :(
-      zc[c] = 1;
-    }
-  }
+    D[nr+2*d, c+d] = G[c]; // deg(v) + gr[ leadexp(v)[m] ]; // bottom row with computed column induced degrees
+  }
+
+  intvec gr = attrib(N, "isHomog"); // grading weights?
 
   for( r = nr; r > 0; r-- )
@@ -129 +120 @@
     D[r+d, nc+2*d] = r; // right-most block with indeces
   }
-  draw(D, zc, d); // print it nicely!
+  draw(D, d); // print it nicely!
 }
 
@@ -200 +191 @@
 
 // Q@Wolfram: what should be done with zero gens!?
-proc grdeg( def M, list # )
-"graded degrees of gens(i.e. columns)"
-{
- // use initial grading if given
-  if( size(#) == 1 )
-  {
-    def w = #[1];
-    if( typeof(w) == "intvec" )
-    {
-      if( nrows(M) == size(w) )
-      {
-        attrib(M, "isHomog", w);
-      }
-    }
-    kill w;
-  }
-
+proc grdeg(M)
+"USAGE:  grdeg(M), graded object M
+RETURN:  intvec of degrees
+PURPOSE: graded degrees of columns (generators) of M
+ASSUME:  M must be a graded object (matrix/module/ideal/mapping)
+NOTE:    if M has zero cols it shoud have attrib(M,'degHomog') set.
+EXAMPLE: example grsum; shows an example
+"
+{           
   ASSUME(1, grtest(M) );
 
+  if ( typeof(attrib(M, "degHomog")) == "intvec" )
+  {    
+    intvec t = attrib(M, "degHomog"); // graded degrees
+    ASSUME(0, ncols(M) == size(t) );
+
+    return (t);
+  }
+  
+  ASSUME(0, ncols(M) == size(M) );
+  
   def w = attrib(M, "isHomog"); // grading weights?
 
@@ -230 +223 @@
   intvec c = leadexp(L[1..m])[n]; // their module-components
 
-  w = intvec(-6665, w); // 0?????
-  intvec gr = w[1+c]; // weights
+//   w = intvec(-6665), w; // 0?????
+  intvec gr = w[c]; //  + 1]; // weights?????
 
   gr = gr + d; // finally we compute their graded degrees
 
-  return (gr); // do we need g or w[c] ?
+  return (gr); 
 }
 
@@ -257 +250 @@
   ASSUME(1, issorted(gr[pivot], s));
 
-  module N = grobj(module(M[pivot]), w);  // reorder the starting ideal/module
+  module N = grobj(module(M[pivot]), w, intvec(gr[pivot]));  // reorder the starting ideal/module
 
 //  "reorder: "; grview(N);
@@ -264 +257 @@
 }
 
+static proc gtranspose(M)
+"??????"
+{   
+  ASSUME(1, grtest(M) );
+  return (  grobj(transpose(M), -grdeg(M), -attrib(M, "isHomog"))  );
+}
+
+
 proc grtranspose(def M)
-"
-transpose graded module/map or a chain complex?...
+"USAGE:  grtranspose(M), graded object or list M
+RETURN:  same as input
+PURPOSE: graded transpose of graded object or chain complex M
+ASSUME:  M must be a graded object or a list of graded objects
+EXAMPLE: example TestGRRes; shows an example
 "
 {
@@ -293 +297 @@
     {
 //      grview(M[i]);
-      L[j] = grtranspose(M[i]);
+      L[j] = grtranspose( grobj( M[i], attrib(M[i], "isHomog")) );
 //      grview(L[j]);
 
@@ -311 +315 @@
   ASSUME(1, grtest(M) );
 
-  // TODO: something is wrong here:
-
  intvec d; module N;
 
  (N,d) = reorder(M, -1);
 
- kill M; module M = grobj(transpose(N), -d);
+ kill M; module M = grobj(transpose(N), -d, -attrib(N, "isHomog"));
 
 // "b";  grview(M);
@@ -334 +336 @@
 }
 
-
-
 proc grorder(def M)
-"
-reorder graded module/map or a chain complex?...
+"USAGE:  grorder(M), graded object or list M
+RETURN:  same as input
+PURPOSE: reorder/transform graded object or chain complex M into block form
+ASSUME:  M must be a graded object or a list of graded objects
+EXAMPLE: example TestGRRes; shows an example
 "
 {
@@ -361 +364 @@
     {
 //      "i: ", i;      "A"; grview(M[i]);
-      L[i] = grorder(M[i]);
+      L[i] = grorder( grobj( M[i], attrib(M[i], "isHomog")) );
 //      "B"; grview(L[i]);
       if( i < j )
@@ -382 +385 @@
   (N,d) = reorder(M, 1); kill M;
 
-  module M = grobj(transpose(N), -d); kill N,d;
+  module M = grobj(transpose(N), -d, -attrib(N, "isHomog")); kill N,d;
 
 // "b";  grview(M);
@@ -390 +393 @@
   (N,d) = reorder(M, -1); kill M;
 
-  module M = grobj(transpose(N), -d);
+  module M = grobj(transpose(N), -d, -attrib(N, "isHomog"));
 
 // "c";  grview(M);
@@ -400 +403 @@
 }
 
-proc TestGRRes(string Name, int version, ideal I )
-"
-test/output reordering res(I) & gr-traspose of res
+proc TestGRRes(Name, J)
+"USAGE:  TestGRRes(name, I), string name, ideal I
+RETURN:  nothing
+PURPOSE: compute/test/output/order/transpose a graded resolution of I
+EXAMPLE: example TestGRRes; shows an example
 "
 {
@@ -410 +415 @@
   " = Ring: ", string(basering);
 
-  I = groebner(I); attrib(I, "isHomog", intvec(0));
+  def I = grobj( groebner(J), intvec(0) ); // ASSUME: no zero entries in I!
   ASSUME(0, grtest(I));
 //  " = Input degrees: "; grview(I);
@@ -440 +445 @@
   assumeLevel = 5;
 
-  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;  "";
-
-  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;  "";
-
-  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;  "";
-
-  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;  "";
-
-  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; "";
-
-  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;  "";
-
-  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; "";
-
-  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; "";
-
-  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; "";
-
-  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; "";
+  // note: data from random generation 2
+  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;  "";
+
+  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;  "";
+
+  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;  "";
+
+  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;  "";
+
+  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; "";
+
+  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;  "";
+
+  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; "";
+
+  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; "";
+
+  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; "";
+
+  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; "";
 
   if( defined(assumeLevel0) ){ assumeLevel = assumeLevel0; } else { kill assumeLevel; } // restore the state of aL
@@ -467 +473 @@
 // Q@Woflram?
 proc grzero()
-"presentation of S(0)^1
-TODO: can we return this as an undefined value?????
-"
-{
- return ( grobj(module([0]), intvec(0)) );
+"USAGE:  grzero() 
+RETURN:  graded object representing S(0)^1
+PURPOSE: compute presentation of S(0)^1
+EXAMPLE: example grsum; shows an example
+"
+{
+ return ( grobj(module([0]), intvec(0), intvec(0)) );
 }
 
 proc grpower(def A, int p)
-"
-compute A \oplus ... \opuls A (p-times)
+"USAGE:  grpower(A, p), graded object A, int p > 0
+RETURN:  graded direct power A^p
+PURPOSE: compute the graded direct power A^p
+NOTE:    the power p must be positive
+EXAMPLE: example grsum; shows an example
 "
 {
@@ -499 +510 @@
 
 
-proc grsum(def A,def B)
-"
-direct sum of graded modules
+proc grsum(A,B)
+"USAGE:  grsum(A, B), graded objects A and B 
+RETURN:  graded direct sum of input objects
+PURPOSE: compute the graded direct sum of A and B
+EXAMPLE: example grsum; shows an example
 "
 {
@@ -515 +528 @@
   module S = module(A), T;
 
-  return(grobj(S, c));
+  intvec da = grdeg(A);
+  intvec db = grdeg(B);
+  intvec dc = da, db;
+
+  return(grobj(S, c, dc));
 }
 example
@@ -576 +593 @@
 
 proc grshift( def M, int d)
-"
-shift graded module M by delta so that 1 is in M_d
-"
-{
+"USAGE:  grshift(A, d), graded objects A, int d
+RETURN:  shifted graded object
+PURPOSE: shift the grading on A by d: A_i -> A_{i+/-d}?
+EXAMPLE: example grsum; shows an example
+"
+{
+  ASSUME(1, grtest(M) );
+  
   intvec a = attrib(M, "isHomog");
-  return (grobj(M, intvec( a - intvec(d:size(a))) ));
-}
-
+  a = a - intvec(d:size(a));
+  
+  intvec t = attrib(M, "degHomog");
+  t = t - intvec(d:size(t));
+  
+  return (grobj(M, a, t));
+}
+
+
+static proc grisequal (def A, def B)
+"USAGE:  grisequal(A, B), graded objects A and B 
+RETURN:  1 if A == B as graded objects, 0 otherwise
+PURPOSE: test the equality of two graded object
+NOTE: A and B should be literarly the same at the moment. TODO?
+EXAMPLE: example grsum; shows an example
+"
+{
+  ASSUME(1, grtest(A) );
+  ASSUME(1, grtest(B) );
+
+  int ra = nrows(A);
+  int rb = nrows(B);
+
+  intvec wa = attrib(A, "isHomog");
+  intvec wb = attrib(B, "isHomog");
+
+  if( (ra != rb) || (ncols(A) != ncols(B)) ){ return (0); } // TODO: ???
+
+  intvec da = grdeg(A);
+  intvec db = grdeg(B);
+  
+  return ( (da == db) && (wa == wb) &&
+           (size(module(matrix(A) - matrix(B))) == 0)    ); // TODO: ???
+}
+
+proc grtwist(int a, int d)
+"USAGE:  grtwist(a,d), int a, d 
+RETURN:  graded object representing S(d)^a
+PURPOSE: compute presentation of S(d)^a
+EXAMPLE: example grsum; shows an example
+"
+{
+  ASSUME(0, a > 0);
+  
+  module Z; Z[a] = [0];
+  intvec w = -intvec(d:a);
+  Z = grobj(Z, w, w); // will set the rank as well
+  ASSUME(2, grisequal(Z, grpower( grshift(grzero(), d), a ) )); // optional check
+  return(Z);
+}
+
+proc grobj(def A, intvec w, list #)
+"USAGE:  grobj(M, w[, d]), matrix/ideal/module M, intvec w, d 
+RETURN:  graded object with matrix presentation M, row weighting w [and total graded degrees d of columns]
+PURPOSE: create a valid graded object with a given matrix presentation, weighting [and total graded degrees (in case of zero columns)]
+EXAMPLE: example grsum; shows an example
+"
+{
+  module M = module(A);
+  ASSUME(0, size(w) >= nrows(M) );
+  
+  attrib(M, "rank", size(w));
+  attrib(M, "isHomog", w);
+
+  if( size(#) > 0 )
+  {
+    ASSUME(0, typeof(#[1]) == "intvec" );
+    ASSUME(0, size(#[1]) == ncols(M) ); 
+    attrib(M, "degHomog", #[1]);
+  }
+  else
+  {
+    ASSUME(0, /* no zero cols please! */ size(M) == ncols(M) ); 
+    attrib(M, "degHomog", grdeg(M));
+  }    
+
+  ASSUME(0, grtest(M) );
+  return (M);
+}
 
 proc grtest(def N)
-"test if N is a matrix/module with matching isHomog attribute (intvec)"
+"USAGE:  grtest(M), anyting M 
+RETURN:  1 if M is a valid graded object, 0 otherwise
+PURPOSE: validate a graded object
+NOTE: M should be an ideal or module or matrix, with weighting attribute
+   'isHomog' and optionally total graded degrees attribute 'degHomog'. 
+   Attributes should be compatible with the presentation matrix.
+EXAMPLE: example grsum; shows an example
+"
 {
   string t = typeof(N);
@@ -595 +699 @@
 
   intvec gr = attrib(N, "isHomog"); // grading weights...
-  if ( nrows(N) > size(gr) ) { return (0); };  // wrong number of rows?
+  if ( nrows(N) != size(gr) ) { return (0); };  // wrong number of rows?
 
 //  if( attrib(N, "rank") != size(gr) ){ return (0); } // wrong rank :(
 
-
+  if ( typeof(attrib(N, "degHomog")) == "intvec" )
+  {
+    intvec T = attrib(N, "degHomog"); // graded degrees
+    if ( ncols(N) != size(T) ) { return (0); };  // wrong number of cols?
+
+    int k = nvars(basering) + 1; // index of mod. column in the leadexp
+
+    module L = lead(module(N)); vector v;
+
+    // checking T for non-zero N[i]
+    int i = size(T);
+    
+    for (; i > 0; i-- )
+    {
+      v = L[i];
+      if( v != 0 )
+      {
+        if( (deg(v) + gr[ leadexp(v)[k] ]) != T[i] ) { return (0); };  // wrong T[i]        
+      }
+    }
+
+    // TODO: check t on nonzero cols...
+  } else
+  {
+    if( ncols(N) != size(N) ) { return (0); };
+  }
+  
 //  if( !homog(N) ) { return (0); };  // N should be homogenous
 
-
   return (1);
 }
-
-proc grisequal (def A, def B)
-"TODO"
-{
-  ASSUME(1, grtest(A) );
-  ASSUME(1, grtest(B) );
-
-  int ra = nrows(A);
-  int rb = nrows(B);
-
-  intvec wa = attrib(A, "isHomog");
-  intvec wb = attrib(B, "isHomog");
-
-  if( (ra != rb) || (ncols(A) != ncols(B)) ){ return (0); } // TODO: ???
-  return ( (wa == wb) &&
-           (size(module(matrix(A) - matrix(B))) == 0)    ); // TODO: ???
-}
-
-proc grtwist(int a, int d)
-"
-matrix presentation for twisted polynomial ring S(d)^a
-"
-{
-  module Z; Z[a] = [0];
-  Z = grobj(Z, -intvec(d:a)); // will set the rank as well
-
-  ASSUME(2, grisequal(Z, grpower( grshift(grzero(), d), a ) )); // optional check
-  return(Z);
-}
-
-proc grobj(def A, intvec w)
-""
-{
-  module M = module(A);
-  ASSUME(0, size(w) >= nrows(M) );
-  attrib(M, "rank", size(w));
-  attrib(M, "isHomog", w);
-  ASSUME(1, grtest(M) );
-  return (M);
-}
-
+   
 
 static proc align( def A, int d)

Singular/LIB/grwalk.lib

@@ -255 +255 @@
 }
 
-proc gwalk(ideal Go, list #)
-"SYNTAX: gwalk(ideal i);
-         gwalk(ideal i, intvec v, intvec w);
+proc gwalk(ideal Go, int reduction,int printout, list #)
+"SYNTAX: gwalk(ideal i, int reduction, int printout);
+         gwalk(ideal i, int reduction, int printout, intvec v, intvec w);
 TYPE:    ideal
 PURPOSE: compute the standard basis of the ideal, calculated via
@@ -274 +274 @@
    string ord_str =   OSCTW[2];
    intvec curr_weight   =   OSCTW[3]; /* original weight vector */
-   intvec target_weight =   OSCTW[4]; /* terget weight vector */
+   intvec target_weight =   OSCTW[4]; /* target weight vector */
    kill OSCTW;
    option(redSB);
@@ -284 +284 @@
    //print("//** help ring = " + string(basering));
    ideal G = fetch(xR, Go);
-   G = system("Mwalk", G, curr_weight, target_weight,basering);
+   G = system("Mwalk", G, curr_weight, target_weight,basering,reduction,printout);
 
    setring xR;
@@ -299 +299 @@
   //** compute a Groebner basis of I w.r.t. lp.
   ring r = 32003,(z,y,x), lp;
-  ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
-  gwalk(I);
+  ideal I = zy2+yx2+yx+3,
+            z3x+y3+zyx-yx2-yx-3,
+            z2yx3-y5+z2yx2+y3x2+y2x3+y3x+y2x2+3z2x+3y2+3yx,
+            zyx5+y6-y4x2-y3x3+2zyx4-y4x-y3x2+zyx3-3z2yx+3zx3-3y3-3y2x+3zx2,
+            yx7-y7+y5x2+y4x3+3yx6+y5x+y4x2+3yx5-6zyx3+yx4+3x5+3y4+3y3x-6zyx2+6x4+3x3-9zx;
+  gwalk(I,0,1);
 }
 
@@ -346 +350 @@
 }
 
-proc fwalk(ideal Go, list #)
-"SYNTAX: fwalk(ideal i);
-         fwalk(ideal i, intvec v, intvec w);
+proc fwalk(ideal Go, int reduction, int printout, list #)
+"SYNTAX: fwalk(ideal i,int reductioin);
+         fwalk(ideal i, int reduction intvec v, intvec w);
 TYPE:    ideal
 PURPOSE: compute the standard basis of the ideal w.r.t. the
@@ -372 +376 @@
 
    ideal G = fetch(xR, Go);
-   G = system("Mfwalk", G, curr_weight, target_weight);
+   G = system("Mfwalk", G, curr_weight, target_weight, reduction, printout);
 
    setring xR;
@@ -387 +391 @@
     ring r = 32003,(z,y,x), lp;
     ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
-    fwalk(I);
+    int reduction = 1;
+    int printout = 1;
+    fwalk(I,reduction,printout);
 }
 
@@ -437 +443 @@
 }
 
-proc pwalk(ideal Go, int n1, int n2, list #)
-"SYNTAX: pwalk(int d, ideal i, int n1, int n2);
-         pwalk(int d, ideal i, int n1, int n2, intvec v, intvec w);
+proc pwalk(ideal Go, int n1, int n2, int reduction, int printout, list #)
+"SYNTAX: pwalk(int d, ideal i, int n1, int n2, int reduction, int printout);
+         pwalk(int d, ideal i, int n1, int n2, int reduction, int printout, intvec v, intvec w);
 TYPE:    ideal
 PURPOSE: compute the standard basis of the ideal, calculated via
@@ -477 +483 @@
   ideal G = fetch(xR, Go);
 
-  G = system("Mpwalk", G, n1, n2, curr_weight, target_weight,nP);
-
+  G = system("Mpwalk",G,n1,n2,curr_weight,target_weight,nP,reduction,printout);
+ 
   setring xR;
-  //kill Go;
+  //kill Go; //unused
 
   keepring basering;
@@ -492 +498 @@
     ring r = 32003,(z,y,x), lp;
     ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
-    //I = std(I);
-    //ring rr = 32003,(z,y,x),lp;
-    //ideal I = fetch(r,I);
-    pwalk(I,2,2);
+    int reduction = 1;
+    int printout = 2;
+    pwalk(I,2,2,reduction,printout);
 }
 

Singular/LIB/modwalk.lib

@@ -16 +16 @@
 
 PROCEDURES:
+modpWalk(ideal,int,int,int[,int,int,int,int])    standard basis conversion of I in prime characteristic
 modWalk(ideal,int,int[,int,int,int,int]);        standard basis conversion of I using modular methods (chinese remainder)
 ";
@@ -29 +30 @@
 ////////////////////////////////////////////////////////////////////////////////
 
-static proc modpWalk(def II, int p, int variant, list #)
+proc modpWalk(def II, int p, int variant, int reduction, list #)
 "USAGE:  modpWalk(I,p,#); I ideal, p integer, variant integer
 ASSUME:  If size(#) > 0, then
@@ -80 +81 @@
     }
   }
+<<<<<<< HEAD
+=======
 
 //-------------------------  make i homogeneous  -----------------------------
@@ -106 +109 @@
   }
 
+>>>>>>> f533f6f7667328bccb271b19b2f603aaebe41596
 //-------------------------  compute a standard basis mod p  -----------------------------
-
   if(variant == 1)
   {
     if(size(#)>0)
     {
-      i = rwalk(i,radius,pert_deg,#);
-     // rwalk(i,radius,pert_deg,#); std(i);
+      i = rwalk(i,radius,pert_deg,reduction,#);
     }
     else
     {
-      i = rwalk(i,radius,pert_deg);
+      i = rwalk(i,radius,pert_deg,reduction);
     }
   }
@@ -124 +126 @@
     if(size(#) == 2)
     {
-      i = gwalk(i,#);
+      i = gwalk(i,reduction,#);
     }
     else
     {
-      i = gwalk(i);
+      i = gwalk(i,reduction);
     }
   }
@@ -135 +137 @@
     if(size(#) == 2)
     {
-      i = frandwalk(i,radius,#);
+      i = frandwalk(i,radius,reduction,#);
     }
     else
     {
-      i = frandwalk(i,radius);
+      i = frandwalk(i,radius,reduction);
     }
   }
@@ -157 +159 @@
     if(size(#) == 2)
     {
-     i=prwalk(i,radius,pert_deg,pert_deg,#);
+     i=prwalk(i,radius,pert_deg,pert_deg,reduction,#);
     }
     else
     {
-      i=prwalk(i,radius,pert_deg,pert_deg);
+      i=prwalk(i,radius,pert_deg,pert_deg,reduction);
     }
   }
@@ -168 +170 @@
     if(size(#) == 2)
     {
-      i=pwalk(i,pert_deg,pert_deg,#);
+      i=pwalk(i,pert_deg,pert_deg,reduction,#);
     }
     else
     {
+<<<<<<< HEAD
+      i=pwalk(i,pert_deg,pert_deg,reduction);
+=======
       i=pwalk(i,pert_deg,pert_deg);
     }
@@ -189 +194 @@
         kill HomR;
       }
-    }
-  }
+>>>>>>> f533f6f7667328bccb271b19b2f603aaebe41596
+    }
+  }
+
   setring R0;
   return(list(fetch(@r,i),p));
@@ -204 +211 @@
   ring ra = 0,x(1..4),(a(a),lp);
   ideal I = std(cyclic(4));
+  int reduction = 1;
   ring rb = 0,x(1..4),(a(b),lp);
   ideal I = imap(ra,I);
-  modpWalk(I,p,1,a,b);
+  modpWalk(I,p,1,reduction,a,b);
   std(I);
 }
@@ -212 +220 @@
 ////////////////////////////////////////////////////////////////////////////////
 
-proc modWalk(def II, int variant, list #)
+proc modWalk(def II, int variant, int reduction, list #)
 "USAGE:  modWalk(II); II ideal or list(ideal,int)
 ASSUME:  If variant =
@@ -487 +495 @@
   if(n2 > 4)
   {
-  //  L[5] = prime(random(an,en));
+    L[5] = prime(random(an,en));
   }
   if(printlevel >= 10)
@@ -504 +512 @@
     for(i=1; i<=size(L); i++)
     {
-      Arguments[i] = list(II,L[i],variant,list(curr_weight,target_weight));
+      Arguments[i] = list(II,L[i],variant,reduction,list(curr_weight,target_weight));
     }
   }
@@ -511 +519 @@
     for(i=1; i<=size(L); i++)
     {
-      Arguments[i] = list(II,L[i],variant);
+      Arguments[i] = list(II,L[i],variant,reduction);
     }
   }
@@ -528 +536 @@
 //-------------------  Now all leading ideals are the same  --------------------
 //-------------------  Lift results to basering via farey  ---------------------
-
     tt = timer; rt = rtimer;
     N = T2[1];
@@ -545 +552 @@
 
 //----------------  Test if we already have a standard basis of I --------------
-
     tt = timer; rt = rtimer;
-    pTest = pTestSB(I,J,L,variant);
-    //pTest = primeTestSB(I,J,L,variant);
+    pTest = primeTest(J, prime(random(1000000000,2134567879)));
     if(printlevel >= 10)
     {
@@ -596 +601 @@
     }
 //--------------  We do not already have a standard basis of I, therefore do the main computation for more primes  --------------
-
     T1 = H;
     T2 = N;
@@ -613 +617 @@
       for(i=j; i<=size(L); i++)
       {
-        //Arguments[i-j+1] = list(II,L[i],variant,list(curr_weight,target_weight));
-        Arguments[size(Arguments)+1] = list(II,L[i],variant,list(curr_weight,target_weight));
+        Arguments[size(Arguments)+1] = list(II,L[i],variant,reduction,list(curr_weight,target_weight));
       }
     }
@@ -621 +624 @@
       for(i=j; i<=size(L); i++)
       {
-        //Arguments[i-j+1] = list(II,L[i],variant);
-        Arguments[size(Arguments)+1] = list(II,L[i],variant);
+        Arguments[size(Arguments)+1] = list(II,L[i],variant,reduction);
       }
     }
@@ -632 +634 @@
     for(i=1; i<=size(PP); i++)
     {
-      //P[size(P) + 1] = PP[i];
       T1[size(T1) + 1] = PP[i][1];
       T2[size(T2) + 1] = bigint(PP[i][2]);
@@ -649 +650 @@
   echo = 2;
   ring R=0,(x,y,z),lp;
-  ideal I=-x+y2z-z,xz+1,x2+y2-1;
-  // I is a standard basis in dp
-  ideal J = modWalk(I,1);
+  ideal I= y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
+  int reduction = 0;
+  ideal J = modWalk(I,1,1);
   J;
 }
@@ -772 +773 @@
   return(J);
 }
-//////////////////////////////////////////////////////////////////////////////////
-static proc primeTestSB(def II, ideal J, list L, int variant, list #)
-"USAGE:  primeTestSB(I,J,L,variant,#); I,J ideals, L intvec of primes, variant int
-RETURN:  1 (resp. 0) if for a randomly chosen prime p that is not in L
-         J mod p is (resp. is not) a standard basis of I mod p
-EXAMPLE: example primeTestSB; shows an example
-"
-{
-if(typeof(II) == "ideal")
-  {
-  ideal I = II;
-  int radius = 2;
-  }
-if(typeof(II) == "list")
-  {
-  ideal I = II[1];
-  int radius = II[2];
-  }
-
-int i,j,k,p;
-def R = basering;
-list r = ringlist(R);
-
-while(!j)
-  {
-  j = 1;
-  p = prime(random(1000000000,2134567879));
-  for(i = 1; i <= size(L); i++)
-    {
-    if(p == L[i])
-      {
-      j = 0;
-      break;
-      }
-    }
-  if(j)
-    {
-    for(i = 1; i <= ncols(I); i++)
-      {
-      for(k = 2; k <= size(I[i]); k++)
-        {
-        if((denominator(leadcoef(I[i][k])) mod p) == 0)
-          {
-          j = 0;
-          break;
-          }
-        }
-      if(!j)
-        {
-        break;
-        }
-      }
-    }
-  if(j)
-    {
-    if(!primeTest(I,p))
-      {
-      j = 0;
-      }
-    }
-  }
-r[1] = p;
-def @R = ring(r);
-setring @R;
-ideal I = imap(R,I);
-ideal J = imap(R,J);
-attrib(J,"isSB",1);
-
-int t = timer;
-j = 1;
-if(isIncluded(I,J) == 0)
-  {
-  j = 0;
-  }
-if(printlevel >= 11)
-  {
-  "isIncluded(I,J) takes "+string(timer - t)+" seconds";
-  "j = "+string(j);
-  }
-t = timer;
-if(j)
-  {
-  if(size(#) > 0)
-    {
-    ideal K = modpWalk(I,p,variant,#)[1];
-    }
-  else
-    {
-    ideal K = modpWalk(I,p,variant)[1];
-    }
-  t = timer;
-  if(isIncluded(J,K) == 0)
-    {
-    j = 0;
-    }
-  if(printlevel >= 11)
-    {
-    "isIncluded(K,J) takes "+string(timer - t)+" seconds";
-    "j = "+string(j);
-    }
-  }
-setring R;
-
-return(j);
-}
-example
-{ "EXAMPLE:"; echo = 2;
-   intvec L = 2,3,5;
-   ring r = 0,(x,y,z),lp;
-   ideal I = x+1,x+y+1;
-   ideal J = x+1,y;
-   primeTestSB(I,I,L,1);
-   primeTestSB(I,J,L,1);
-}
-
-////////////////////////////////////////////////////////////////////////////////
-static proc pTestSB(ideal I, ideal J, list L, int variant, list #)
-"USAGE:  pTestSB(I,J,L,variant,#); I,J ideals, L intvec of primes, variant int
-RETURN:  1 (resp. 0) if for a randomly chosen prime p that is not in L
-         J mod p is (resp. is not) a standard basis of I mod p
-EXAMPLE: example pTestSB; shows an example
-"
-{
-   int i,j,k,p;
-   def R = basering;
-   list r = ringlist(R);
-
-   while(!j)
-   {
-      j = 1;
-      p = prime(random(1000000000,2134567879));
-      for(i = 1; i <= size(L); i++)
-      {
-         if(p == L[i]) { j = 0; break; }
-      }
-      if(j)
-      {
-         for(i = 1; i <= ncols(I); i++)
-         {
-            for(k = 2; k <= size(I[i]); k++)
-            {
-               if((denominator(leadcoef(I[i][k])) mod p) == 0) { j = 0; break; }
-            }
-            if(!j){ break; }
-         }
-      }
-      if(j)
-      {
-         if(!primeTest(I,p)) { j = 0; }
-      }
-   }
-   r[1] = p;
-   def @R = ring(r);
-   setring @R;
-   ideal I = imap(R,I);
-   ideal J = imap(R,J);
-   attrib(J,"isSB",1);
-
-   int t = timer;
-   j = 1;
-   if(isIncluded(I,J) == 0) { j = 0; }
-
-   if(printlevel >= 11)
-   {
-      "isIncluded(I,J) takes "+string(timer - t)+" seconds";
-      "j = "+string(j);
-   }
-
-   t = timer;
-   if(j)
-   {
-      if(size(#) > 0)
-      {
-         ideal K = modpStd(I,p,variant,#[1])[1];
-      }
-      else
-      {
-         ideal K = groebner(I);
-      }
-      t = timer;
-      if(isIncluded(J,K) == 0) { j = 0; }
-
-      if(printlevel >= 11)
-      {
-         "isIncluded(J,K) takes "+string(timer - t)+" seconds";
-         "j = "+string(j);
-      }
-   }
-   setring R;
-   return(j);
-}
-example
-{ "EXAMPLE:"; echo = 2;
-   intvec L = 2,3,5;
-   ring r = 0,(x,y,z),dp;
-   ideal I = x+1,x+y+1;
-   ideal J = x+1,y;
-   pTestSB(I,I,L,2);
-   pTestSB(I,J,L,2);
-}
+
 ////////////////////////////////////////////////////////////////////////////////
 static proc mixedTest()

Singular/LIB/normal.lib

@@ -3670 +3670 @@
    }
 
+   // check for 0-ideal
+   if (size(id)==0)
+   {
+     list result=list(ideal(1)),list(intvec(0),int(0));
+     // delta invariant,total delta invariant
+     if (wring)
+     {
+       result[3]=result[2]; // pair(delta invariants , total delta invariant)
+       result[2]=result[1];
+       def BR = basering;
+       list rl = ringlist(basering);
+       def rng = ring(rl);
+       setring rng;
+       ideal norid = 0;
+       ideal normap = maxideal(1);
+       export(norid);
+       export(normap);
+       setring BR;
+       result[1] = list(rng);
+     }
+     return (result);
+   }
+
    kill #;
    list #;
@@ -3856 +3879 @@
 
    ideal J = mstdid[1];         //J is the SB of I
+   if (J[1]==1) { return(ideal(0));}
    ideal I = mstdid[2];
    int h = n-dim(J);            //codimension of V(I), I is a prime ideal

Singular/LIB/polymake.lib

@@ -42 +42 @@
   newtonPolytopeLP()  computes the lattice points of the Newton polytope
   normalFanL()         computes the normal fan of a polytope
-  groebnerFan()       computes the Groebner fan of a polynomial
+  groebnerFanP()       computes the Groebner fan of a polynomial
 
 PROCEDURES USING TOPCOM:
@@ -436 +436 @@
 /////////////////////////////////////////////////////////////////////////////
 
-proc groebnerFan (poly f)
-"USAGE:  groebnerFan(f);  f poly
+proc groebnerFanP (poly f)
+"USAGE:  groebnerFanP(f);  f poly
 RETURN:  list, the ith entry of L[1] contains information about the ith cone
                in the Groebner fan dual to the ith vertex in the Newton
@@ -460 +460 @@
         TU Berlin and Michael Joswig, so it only works if polymake is installed;
         see http://www.math.tu-berlin.de/polymake/
-EXAMPLE: example groebnerFan;   shows an example"
+EXAMPLE: example groebnerFanP;   shows an example"
 {
   int i,j;
@@ -497 +497 @@
    poly f=y3+x2+xy+2xz+yz+z2+1;
    // the Newton polytope of f is
-   list gf=groebnerFan(f);
+   list gf=groebnerFanP(f);
    // the exponent vectors of f are ordered as follows
    gf[4];

Singular/LIB/rwalk.lib

@@ -10 +10 @@
 rwalk(ideal,int,int[,intvec,intvec]);   standard basis of ideal via Random Walk algorithm
 rwalk(ideal,int[,intvec,intvec]);       standard basis of ideal via Random Perturbation Walk algorithm
-frwalk(ideal,int[,intvec,intvec]);      standard basis of ideal via Random Fractal Walk algorithm
+frandwalk(ideal,int[,intvec,intvec]);      standard basis of ideal via Random Fractal Walk algorithm
 ";
 
@@ -141 +141 @@
  * Random Walk  *
  ****************/
-proc rwalk(ideal Go, int radius, int pert_deg, list #)
+proc rwalk(ideal Go, int radius, int pert_deg, int reduction, int printout, list #)
 "SYNTAX: rwalk(ideal i, int radius);
          if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
+         intermediate Groebner bases are not reduced if reduction = 0
 TYPE:    ideal
 PURPOSE: compute the standard basis of the ideal, calculated via
@@ -178 +179 @@
 
 ideal G = fetch(xR, Go);
-G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg, basering);
+G = system("Mrwalk", G, curr_weight, target_weight, radius, pert_deg, reduction, printout);
 
 setring xR;
@@ -196 +197 @@
   int radius = 1;
   int perturb_deg = 2;
-  rwalk(I,radius,perturb_deg);
+  int reduction = 0;
+  int printout = 1;
+  rwalk(I,radius,perturb_deg,reduction,printout);
 }
 
@@ -202 +205 @@
  * Perturbation Walk with random element *
  *****************************************/
-proc prwalk(ideal Go, int radius, int o_pert_deg, int t_pert_deg, list #)
+proc prwalk(ideal Go, int radius, int o_pert_deg, int t_pert_deg, int reduction, int printout, list #)
 "SYNTAX: rwalk(ideal i, int radius);
          if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
@@ -227 +230 @@
   OSCTW= OrderStringalp_NP("al", #);
   }
+int nP = OSCTW[1];
 string ord_str = OSCTW[2];
 intvec curr_weight = OSCTW[3]; // original weight vector
@@ -238 +242 @@
 
 ideal G = fetch(xR, Go);
-G = system("Mprwalk", G, curr_weight, target_weight, radius, o_pert_deg, t_pert_deg, basering);
+G = system("Mprwalk", G, curr_weight, target_weight, radius, o_pert_deg, t_pert_deg,
+           nP, reduction, printout);
 
 setring xR;
@@ -257 +262 @@
   int o_perturb_deg = 2;
   int t_perturb_deg = 2;
-  prwalk(I,radius,o_perturb_deg,t_perturb_deg);
+  int reduction = 0;
+  int printout = 2;
+  prwalk(I,radius,o_perturb_deg,t_perturb_deg,reduction,printout);
 }
 
@@ -263 +270 @@
  * Fractal Walk with random element *
  ************************************/
-proc frandwalk(ideal Go, int radius, list #)
-"SYNTAX: frwalk(ideal i, int radius);
-         frwalk(ideal i, int radius, intvec v, intvec w);
+proc frandwalk(ideal Go, int radius, int reduction, int printout, list #)
+"SYNTAX: frwalk(ideal i, int radius, int reduction, int printout);
+         frwalk(ideal i, int radius, int reduction, int printout, intvec v, intvec w);
 TYPE:    ideal
 PURPOSE: compute the standard basis of the ideal, calculated via
@@ -299 +306 @@
    ideal G = fetch(xR, Go);
    int pert_deg = 2;
-   G = system("Mfrwalk", G, curr_weight, target_weight, radius);
+
+   G = system("Mfrwalk", G, curr_weight, target_weight, radius, reduction, printout);
 
    setring xR;
@@ -314 +322 @@
     ring r = 0,(z,y,x), lp;
     ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
-    frandwalk(I,2);
-}
+    int reduction = 0;
+    frandwalk(I,2,0,1);
+}

Singular/dyn_modules/gfanlib/Makefile.am

@@ -1 +1 @@
 ACLOCAL_AMFLAGS = -I ../../m4
 
-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
+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 groebnerFan.cc groebnerFan.h groebnerComplex.cc groebnerComplex.h tropical.cc tropical.h gfanlib.cc
 
 MY_CPPFLAGS = -I${srcdir} -I${top_srcdir} -I${top_builddir} \

Singular/dyn_modules/gfanlib/bbcone.cc

@@ -1666 +1666 @@
 
   return relativeInteriorPoints;
+}
+
+
+/***
+ * Computes a relative interior point and an outer normal vector for each facet of zc
+ **/
+std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc, const std::set<gfan::ZVector> &exceptThesePoints, const bool onlyLowerHalfSpace)
+{
+  gfan::ZMatrix inequalities = zc.getFacets();
+  gfan::ZMatrix equations = zc.getImpliedEquations();
+  int r = inequalities.getHeight();
+  int c = inequalities.getWidth();
+
+  /* our cone has r facets, if r==0 return empty matrices */
+  gfan::ZMatrix relativeInteriorPoints = gfan::ZMatrix(0,c);
+  gfan::ZMatrix outerFacetNormals = gfan::ZMatrix(0,c);
+  if (r==0)
+    return std::make_pair(relativeInteriorPoints,outerFacetNormals);
+
+  /* next we iterate over each of the r facets,
+   * build the respective cone and add it to the list
+   * this is the i=0 case */
+  gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c);
+  gfan::ZMatrix newEquations = equations;
+  newEquations.appendRow(inequalities[0]);
+  gfan::ZCone facet = gfan::ZCone(newInequalities,newEquations);
+  gfan::ZVector interiorPoint = facet.getRelativeInteriorPoint();
+  if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
+  {
+    if (exceptThesePoints.count(interiorPoint)==0)
+    {
+      relativeInteriorPoints.appendRow(interiorPoint);
+      outerFacetNormals.appendRow(-inequalities[0]);
+    }
+  }
+
+  /* these are the cases i=1,...,r-2 */
+  for (int i=1; i<r-1; i++)
+  {
+    newInequalities = inequalities.submatrix(0,0,i,c);
+    newInequalities.append(inequalities.submatrix(i+1,0,r,c));
+    newEquations = equations;
+    newEquations.appendRow(inequalities[i]);
+    facet = gfan::ZCone(newInequalities,newEquations);
+    interiorPoint = facet.getRelativeInteriorPoint();
+    if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
+    {
+      if (exceptThesePoints.count(interiorPoint)==0)
+      {
+        relativeInteriorPoints.appendRow(interiorPoint);
+        outerFacetNormals.appendRow(-inequalities[i]);
+      }
+    }
+  }
+
+  /* this is the i=r-1 case */
+  newInequalities = inequalities.submatrix(0,0,r-1,c);
+  newEquations = equations;
+  newEquations.appendRow(inequalities[r-1]);
+  facet = gfan::ZCone(newInequalities,newEquations);
+  interiorPoint = facet.getRelativeInteriorPoint();
+  if (onlyLowerHalfSpace==false || interiorPoint[0].sign()<0)
+  {
+    if (exceptThesePoints.count(interiorPoint)==0)
+    {
+      relativeInteriorPoints.appendRow(interiorPoint);
+      outerFacetNormals.appendRow(-inequalities[r-1]);
+    }
+  }
+
+  return std::make_pair(relativeInteriorPoints,outerFacetNormals);
 }
 

Singular/dyn_modules/gfanlib/bbcone.h

@@ -21 +21 @@
 gfan::ZCone liftUp(const gfan::ZCone &zc);
 gfan::ZMatrix interiorPointsOfFacets(const gfan::ZCone &zc, const std::set<gfan::ZVector> &exceptThese=std::set<gfan::ZVector>());
+std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc, const std::set<gfan::ZVector> &exceptThesePoints=std::set<gfan::ZVector>(), const bool onlyLowerHalfSpace=false);
 
 #endif

Singular/dyn_modules/gfanlib/groebnerCone.cc

@@ -444 +444 @@
 
 /***
- * Computes a relative interior point and an outer normal vector for each facet of zc
- **/
-static std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndNormalsOfFacets(const gfan::ZCone zc)
-{
-  gfan::ZMatrix inequalities = zc.getFacets();
-  gfan::ZMatrix equations = zc.getImpliedEquations();
-  int r = inequalities.getHeight();
-  int c = inequalities.getWidth();
-
-  /* our cone has r facets, if r==0 return empty matrices */
-  gfan::ZMatrix relativeInteriorPoints = gfan::ZMatrix(0,c);
-  gfan::ZMatrix outerFacetNormals = gfan::ZMatrix(0,c);
-  if (r==0)
-    return std::make_pair(relativeInteriorPoints,outerFacetNormals);
-
-  /* next we iterate over each of the r facets,
-   * build the respective cone and add it to the list
-   * this is the i=0 case */
-  gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c);
-  gfan::ZMatrix newEquations = equations;
-  newEquations.appendRow(inequalities[0]);
-  gfan::ZCone facet = gfan::ZCone(newInequalities,newEquations);
-  relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
-  assume(zc.contains(relativeInteriorPoints[0]) && !zc.containsRelatively(relativeInteriorPoints[0]));
-  outerFacetNormals.appendRow(-inequalities[0]);
-
-  /* these are the cases i=1,...,r-2 */
-  for (int i=1; i<r-1; i++)
-  {
-    newInequalities = inequalities.submatrix(0,0,i,c);
-    newInequalities.append(inequalities.submatrix(i+1,0,r,c));
-    newEquations = equations;
-    newEquations.appendRow(inequalities[i]);
-    facet = gfan::ZCone(newInequalities,newEquations);
-    relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
-    assume(zc.contains(relativeInteriorPoints[i]) && !zc.containsRelatively(relativeInteriorPoints[i]));
-    outerFacetNormals.appendRow(-inequalities[i]);
-  }
-
-  /* this is the i=r-1 case */
-  newInequalities = inequalities.submatrix(0,0,r-1,c);
-  newEquations = equations;
-  newEquations.appendRow(inequalities[r-1]);
-  facet = gfan::ZCone(newInequalities,newEquations);
-  relativeInteriorPoints.appendRow(facet.getRelativeInteriorPoint());
-  assume(zc.contains(relativeInteriorPoints[r-1]) && !zc.containsRelatively(relativeInteriorPoints[r-1]));
-  outerFacetNormals.appendRow(-inequalities[r-1]);
-
-  return std::make_pair(relativeInteriorPoints,outerFacetNormals);
-}
-
-
-/***
  * Returns a complete list of neighboring Groebner cones.
  **/
@@ -565 +512 @@
     {
       gfan::ZCone zc = sigma->getPolyhedralCone();
-      assume(isCompatible(zf,&zc));
+      // assume(isCompatible(zf,&zc));
       zf->insert(zc);
     }

Singular/dyn_modules/gfanlib/initial.cc

@@ -12 +12 @@
   {
     if (!w[i].fitsInInt())
+    {
+      WerrorS("wDeg: overflow in weight vector");
       throw 0; // weightOverflow;
+    }
     d += p_GetExp(p,i+1,r)*w[i].toInt();
   }

Singular/dyn_modules/gfanlib/ppinitialReduction.cc

@@ -121 +121 @@
 }
 
+bool p_xLeadmonomDivisibleBy(const poly g, const poly f, const ring r)
+{
+  poly gx = p_Head(g,r);
+  poly fx = p_Head(f,r);
+  p_SetExp(gx,1,0,r);
+  p_SetExp(fx,1,0,r);
+  p_Setm(gx,r);
+  p_Setm(fx,r);
+  bool b = p_LeadmonomDivisibleBy(gx,fx,r);
+  p_Delete(&gx,r);
+  p_Delete(&fx,r);
+  return b;
+}
+
+void pReduceInhomogeneous(poly &g, const number p, const ring r)
+{
+  if (g==NULL)
+    return;
+  p_Test(g,r);
+
+  poly toBeChecked = pNext(g);
+  pNext(g) = NULL; poly gEnd = g;
+  poly gCache;
+
+  number coeff, pPower; int power; poly subst;
+  while(toBeChecked)
+  {
+    for (gCache = g; gCache; pIter(gCache))
+      if (p_xLeadmonomDivisibleBy(gCache,toBeChecked,r)) break;
+    if (gCache)
+    {
+      n_Power(p,p_GetExp(toBeChecked,1,r)-p_GetExp(gCache,1,r),&pPower,r->cf);
+      coeff = n_Mult(p_GetCoeff(toBeChecked,r),pPower,r->cf);
+      p_SetCoeff(gCache,n_Add(p_GetCoeff(gCache,r),coeff,r->cf),r);
+      n_Delete(&pPower,r->cf); n_Delete(&coeff,r->cf);
+      toBeChecked=p_LmDeleteAndNext(toBeChecked,r);
+    }
+    else
+    {
+      if (n_DivBy(p_GetCoeff(toBeChecked,r),p,r->cf))
+      {
+        power=1;
+        coeff=n_Div(p_GetCoeff(toBeChecked,r),p,r->cf);
+        while (n_DivBy(coeff,p,r->cf))
+        {
+          power++;
+          number coeff0 = n_Div(coeff,p,r->cf);
+          n_Delete(&coeff,r->cf);
+          coeff = coeff0;
+          coeff0 = NULL;
+          if (power<1)
+          {
+            WerrorS("pReduce: overflow in exponent");
+            throw 0;
+          }
+        }
+        subst=p_LmInit(toBeChecked,r);
+        p_AddExp(subst,1,power,r);
+        p_SetCoeff(subst,coeff,r);
+        p_Setm(subst,r); p_Test(subst,r);
+        toBeChecked=p_LmDeleteAndNext(toBeChecked,r);
+        toBeChecked=p_Add_q(toBeChecked,subst,r);
+        p_Test(toBeChecked,r);
+      }
+      else
+      {
+        pNext(gEnd)=toBeChecked;
+        pIter(gEnd); pIter(toBeChecked);
+        pNext(gEnd)=NULL;
+        p_Test(g,r);
+      }
+    }
+  }
+  p_Test(g,r);
+  divideByCommonGcd(g,r);
+  return;
+}
+
 void ptNormalize(poly* gStar, const number p, const ring r)
 {

Singular/dyn_modules/gfanlib/ppinitialReduction.h

@@ -10 +10 @@
 bool isOrderingLocalInT(const ring r);
 void pReduce(ideal &I, const number p, const ring r);
+void pReduceInhomogeneous(poly &g, const number p, const ring r);
 bool ppreduceInitially(ideal I, const ring r, const number p);
 /* BOOLEAN ppreduceInitially(leftv res, leftv args); */

Singular/dyn_modules/gfanlib/startingCone.cc

@@ -5 +5 @@
 #include <lift.h>
 #include <groebnerCone.h>
-// #include <neighbours.h>
 #include <tropicalStrategy.h>
 #include <tropicalCurves.h>
@@ -14 +13 @@
 
 
-/***
- * checks whether sigma is contained in the tropical variety
- * by testing whether the initial Ideal with respect to the interior point
- * is monomial free.
- **/
-// static bool checkContainmentInTropicalVariety(const groebnerCone sigma)
-// {
-//   ideal I = sigma.getPolynomialIdeal();
-//   ring r = sigma.getPolynomialRing();
-//   const tropicalStrategy* currentStrategy = sigma.getTropicalStrategy();
-
-//   gfan::ZCone zc = sigma.getPolyhedralCone();
-//   gfan::ZMatrix zm = zc.extremeRays();
-//   for (int i=0; i<zm.getHeight(); i++)
-//   {
-//     gfan::ZVector w = zm[i];
-//     if (currentStrategy->isValuationNonTrivial() && w[0].sign()==0)
-//       continue;
-//     poly s = currentStrategy->checkInitialIdealForMonomial(I,r,w);
-//     if (s)
-//     {
-//       p_Delete(&s,r);
-//       return false;
-//     }
-//   }
-
-//   zm = zc.generatorsOfLinealitySpace();
-//   for (int i=0; i<zm.getHeight(); i++)
-//   {
-//     gfan::ZVector w = zm[i];
-//     if (currentStrategy->isValuationNonTrivial() && w[0].sign()==0)
-//       continue;
-//     poly s = currentStrategy->checkInitialIdealForMonomial(I,r,w);
-//     if (s)
-//     {
-//       p_Delete(&s,r);
-//       return false;
-//     }
-//   }
-
-//   return true;
-// }
-
-
-// static bool checkOneCodimensionalLinealitySpace(const groebnerCone sigma)
-// {
-//   gfan::ZCone zc = sigma.getPolyhedralCone();
-//   int linDim = zc.dimensionOfLinealitySpace();
-//   int dim = zc.dimension();
-//   return (linDim+1)==dim;
-// }
+groebnerCone groebnerStartingCone(const tropicalStrategy& currentStrategy)
+{
+  groebnerCone sigma(currentStrategy.getStartingIdeal(), currentStrategy.getStartingRing(), currentStrategy);
+  return sigma;
+}
 
 

Singular/dyn_modules/gfanlib/startingCone.h

@@ -5 +5 @@
 #include <tropicalStrategy.h>
 
+groebnerCone groebnerStartingCone(const tropicalStrategy& currentStrategy);
 groebnerCone tropicalStartingCone(const tropicalStrategy& currentCase);
 

Singular/dyn_modules/gfanlib/tropical.cc

@@ -5 +5 @@
 #include <bbcone.h>
 #include <ppinitialReduction.h>
-// #include <ttinitialReduction.h>
 #include <containsMonomial.h>
 #include <initial.h>
 #include <witness.h>
 #include <tropicalCurves.h>
-// #include <neighbours.h>
 #include <tropicalStrategy.h>
 #include <startingCone.h>
+#include <groebnerFan.h>
+#include <groebnerComplex.h>
 #include <tropicalVariety.h>
 
+int tropicalVerboseLevel = 0;
 
 gfan::ZCone homogeneitySpace(ideal I, ring r)
@@ -51 +52 @@
 {
   leftv u = args;
+  if ((u != NULL) && (u->Typ() == POLY_CMD))
+  {
+    leftv v = u->next;
+    if (v == NULL)
+    {
+      poly g = (poly) u->Data();
+      ideal I = idInit(1);
+      I->m[0] = g;
+      res->rtyp = coneID;
+      res->data = (void*) new gfan::ZCone(homogeneitySpace(I,currRing));
+      I->m[0] = NULL;
+      id_Delete(&I,currRing);
+      return FALSE;
+    }
+  }
   if ((u != NULL) && (u->Typ() == IDEAL_CMD))
   {
@@ -107 +123 @@
 {
   leftv u = args;
+  if ((u != NULL) && (u->Typ() == POLY_CMD))
+  {
+    leftv v = u->next;
+    if (v == NULL)
+    {
+      poly g = (poly) u->Data();
+      ideal I = idInit(1);
+      I->m[0] = g;
+      res->rtyp = coneID;
+      res->data = (void*) new gfan::ZCone(lowerHomogeneitySpace(I,currRing));
+      I->m[0] = NULL;
+      id_Delete(&I,currRing);
+      return FALSE;
+    }
+  }
   if ((u != NULL) && (u->Typ() == IDEAL_CMD))
   {
@@ -181 +212 @@
 {
   leftv u = args;
+  if ((u != NULL) && (u->Typ() == POLY_CMD))
+  {
+    leftv v = u->next;
+    if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
+    {
+      try
+      {
+        poly g = (poly) u->Data();
+        ideal I = idInit(1);
+        I->m[0] = g;
+        gfan::ZVector* weightVector;
+        if (v->Typ() == INTVEC_CMD)
+        {
+          intvec* w0 = (intvec*) v->Data();
+          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
+          w1->inpTranspose();
+          weightVector = bigintmatToZVector(*w1);
+          delete w1;
+        }
+        else
+        {
+          bigintmat* w1 = (bigintmat*) v->Data();
+          weightVector = bigintmatToZVector(*w1);
+        }
+        res->rtyp = coneID;
+        res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
+        delete weightVector;
+        I->m[0] = NULL;
+        id_Delete(&I,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
+    }
+  }
   if ((u != NULL) && (u->Typ() == IDEAL_CMD))
   {
@@ -186 +255 @@
     if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
     {
-      ideal I = (ideal) u->Data();
-      gfan::ZVector* weightVector;
-      if (v->Typ() == INTVEC_CMD)
-      {
-        intvec* w0 = (intvec*) v->Data();
-        bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
-        w1->inpTranspose();
-        weightVector = bigintmatToZVector(*w1);
-        delete w1;
-      }
-      else
-      {
-        bigintmat* w1 = (bigintmat*) v->Data();
-        weightVector = bigintmatToZVector(*w1);
-      }
-      res->rtyp = coneID;
-      res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
-      delete weightVector;
-      return FALSE;
+      try
+      {
+        ideal I = (ideal) u->Data();
+        gfan::ZVector* weightVector;
+        if (v->Typ() == INTVEC_CMD)
+        {
+          intvec* w0 = (intvec*) v->Data();
+          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
+          w1->inpTranspose();
+          weightVector = bigintmatToZVector(*w1);
+          delete w1;
+        }
+        else
+        {
+          bigintmat* w1 = (bigintmat*) v->Data();
+          weightVector = bigintmatToZVector(*w1);
+        }
+        res->rtyp = coneID;
+        res->data = (void*) new gfan::ZCone(groebnerCone(I,currRing,*weightVector));
+        delete weightVector;
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
     }
   }
@@ -243 +320 @@
 {
   leftv u = args;
+  if ((u != NULL) && (u->Typ() == POLY_CMD))
+  {
+    leftv v = u->next;
+    if (v == NULL)
+    {
+      try
+      {
+        poly g = (poly) u->Data();
+        ideal I = idInit(1);
+        I->m[0] = g;
+        res->rtyp = coneID;
+        res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
+        I->m[0] = NULL;
+        id_Delete(&I,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
+    }
+  }
   if ((u != NULL) && (u->Typ() == IDEAL_CMD))
   {
@@ -248 +348 @@
     if (v == NULL)
     {
-      ideal I = (ideal) u->Data();
-      res->rtyp = coneID;
-      res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
-      return FALSE;
+      try
+      {
+        ideal I = (ideal) u->Data();
+        res->rtyp = coneID;
+        res->data = (void*) new gfan::ZCone(maximalGroebnerCone(I,currRing));
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
     }
   }
@@ -293 +401 @@
     if ((v !=NULL) && ((v->Typ() == BIGINTMAT_CMD) || (v->Typ() == INTVEC_CMD)))
     {
-      ideal I = (ideal) u->Data();
-      gfan::ZVector* weightVector;
-      if (v->Typ() == INTVEC_CMD)
-      {
-        intvec* w0 = (intvec*) v->Data();
-        bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
-        w1->inpTranspose();
-        weightVector = bigintmatToZVector(*w1);
-        delete w1;
-      }
-      else
-      {
-        bigintmat* w1 = (bigintmat*) v->Data();
-        weightVector = bigintmatToZVector(*w1);
-      }
-      res->rtyp = IDEAL_CMD;
-      res->data = (void*) initial(I, currRing, *weightVector);
-      delete weightVector;
-      return FALSE;
+      try
+      {
+        ideal I = (ideal) u->Data();
+        gfan::ZVector* weightVector;
+        if (v->Typ() == INTVEC_CMD)
+        {
+          intvec* w0 = (intvec*) v->Data();
+          bigintmat* w1 = iv2bim(w0,coeffs_BIGINT);
+          w1->inpTranspose();
+          weightVector = bigintmatToZVector(*w1);
+          delete w1;
+        }
+        else
+        {
+          bigintmat* w1 = (bigintmat*) v->Data();
+          weightVector = bigintmatToZVector(*w1);
+        }
+        res->rtyp = IDEAL_CMD;
+        res->data = (void*) initial(I, currRing, *weightVector);
+        delete weightVector;
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
     }
   }
@@ -326 +442 @@
   p->iiAddCproc("","lowerHomogeneitySpace",FALSE,lowerHomogeneitySpace);
   p->iiAddCproc("","initial",FALSE,initial);
+  p->iiAddCproc("","tropicalVariety",FALSE,tropicalVariety);
+  p->iiAddCproc("","groebnerFan",FALSE,groebnerFan);
+  p->iiAddCproc("","groebnerComplex",FALSE,groebnerComplex);
+#ifndef NDEBUG
   // p->iiAddCproc("","tropicalNeighbours",FALSE,tropicalNeighbours);
-#ifndef NDEBUG
   // p->iiAddCproc("","initial0",FALSE,initial0);
   p->iiAddCproc("","pReduceDebug",FALSE,pReduceDebug);
@@ -362 +481 @@
   p->iiAddCproc("","nonPositiveTropicalStartingPoint",FALSE,nonPositiveTropicalStartingPoint);
   p->iiAddCproc("","tropicalStartingCone",FALSE,tropicalStartingCone);
-  p->iiAddCproc("","tropicalVariety",FALSE,tropicalVariety);
 #endif //NDEBUG
   // p->iiAddCproc("","ppreduceInitially",FALSE,ppreduceInitially);

Singular/dyn_modules/gfanlib/tropical.h

@@ -4 +4 @@
 #include "Singular/ipid.h"
 
+
+extern int tropicalVerboseLevel;
+
+
 gfan::ZCone homogeneitySpace(ideal I, ring r);
 void tropical_setup(SModulFunctions* p);

Singular/dyn_modules/gfanlib/tropicalCurves.cc

@@ -70 +70 @@
 
   /* construct a new ordering as describe above */
-  bool overflow;
+  bool overflow = false;
   s->order[0] = ringorder_a;
   s->block0[0] = 1;
@@ -97 +97 @@
 
   if (overflow)
-    throw 0; //todo: use a proper custom exception
+  {
+    WerrorS("genericlyWeightedOrdering: overflow in weight vector");
+    throw 0; // weightOverflow;
+  }
 
   /* complete the ring and return it */

Singular/dyn_modules/gfanlib/tropicalStrategy.cc

@@ -134 +134 @@
   extraReductionAlgorithm(noExtraReduction)
 {
-  assume(rField_is_Q(r) || rField_is_Zp(r));
+  assume(rField_is_Q(r) || rField_is_Zp(r) || rField_is_Ring_Z(r));
   if (!completelyHomogeneous)
   {
@@ -225 +225 @@
   omFreeSize(shiftByOne,(n+1)*sizeof(int));
 
-  // ring origin = currRing;
-  // rChangeCurrRing(startingRing);
-  // ideal startingIdeal = kNF(pt,startingRing->qideal,J);
-  // rChangeCurrRing(origin);
-  ideal startingIdeal = J; J = NULL;
+  ring origin = currRing;
+  rChangeCurrRing(startingRing);
+  ideal startingIdeal = kNF(pt,startingRing->qideal,J); // mathematically redundant,
+  rChangeCurrRing(origin);                              // but helps with upcoming std computation
+  // ideal startingIdeal = J; J = NULL;
   assume(startingIdeal->m[k]==NULL);
   startingIdeal->m[k] = pt->m[0];
@@ -271 +271 @@
   /* map the input ideal into the new polynomial ring */
   startingIdeal = constructStartingIdeal(J,s,uniformizingParameter,startingRing);
+  reduce(startingIdeal,startingRing);
 
   linealitySpace = homogeneitySpace(startingIdeal,startingRing);

Singular/dyn_modules/gfanlib/tropicalTraversal.cc

@@ -3 +3 @@
 #include <tropicalCurves.h>
 
-std::vector<bool> checkNecessaryFlips(const groebnerCones &tropicalVariety, const groebnerCones &workingList,
-                                      const gfan::ZVector &interiorPoint, const gfan::ZMatrix &normalVectors)
+std::vector<bool> checkNecessaryTropicalFlips(const groebnerCones &tropicalVariety, const groebnerCones &workingList,
+                                              const gfan::ZVector &interiorPoint, const gfan::ZMatrix &normalVectors)
 {
   int k = normalVectors.getHeight();
@@ -72 +72 @@
         id_Delete(&inI,sigma.getPolynomialRing());
 
-        std::vector<bool> needToFlip = checkNecessaryFlips(tropicalVariety,workingList,interiorPoint,normalVectors);
+        std::vector<bool> needToFlip = checkNecessaryTropicalFlips(tropicalVariety,workingList,interiorPoint,normalVectors);
         for (int j=0; j<normalVectors.getHeight(); j++)
         {
@@ -88 +88 @@
     workingList.erase(sigma);
     tropicalVariety.insert(sigma);
-    // std::cout << "tropicalVariety.size():" << tropicalVariety.size() << std::endl;
-    // std::cout << "workingList.size():" << workingList.size() << std::endl;
+    if (printlevel > 0)
+      Print("cones finished: %lu   cones in working list: %lu\n",
+      (unsigned long)tropicalVariety.size(), (unsigned long)workingList.size());
   }
   return tropicalVariety;
 }
 
-groebnerCones tropicalTraversal(const groebnerCone startingCone)
+
+std::vector<bool> checkNecessaryGroebnerFlips(const groebnerCones &groebnerFan, const groebnerCones &workingList,
+                                              const gfan::ZMatrix &interiorPoints)
 {
-  groebnerCones tropicalVariety;
+  int k = interiorPoints.getHeight();
+  std::vector<bool> needToFlip(k,true);
+
+  for (groebnerCones::iterator sigma = groebnerFan.begin(); sigma!=groebnerFan.end(); sigma++)
+  {
+    for (int i=0; i<k; i++)
+    {
+      if (needToFlip[i] && sigma->contains(interiorPoints[i]))
+        needToFlip[i] = false;
+    }
+  }
+
+  for (groebnerCones::iterator sigma = workingList.begin(); sigma!=workingList.end(); sigma++)
+  {
+    for (int i=0; i<k; i++)
+    {
+      if (needToFlip[i] && sigma->contains(interiorPoints[i]))
+        needToFlip[i] = false;
+    }
+  }
+
+  return needToFlip;
+}
+
+
+groebnerCones groebnerTraversal(const groebnerCone startingCone)
+{
+  const tropicalStrategy* currentStrategy = startingCone.getTropicalStrategy();
+
+  groebnerCones groebnerFan;
   groebnerCones workingList;
   workingList.insert(startingCone);
-  // std::cout << "starting traversal" << std::endl;
+  std::set<gfan::ZVector> finishedInteriorPoints;
+  bool onlyLowerHalfSpace = !currentStrategy->isValuationTrivial();
+
   while(!workingList.empty())
   {
-    const groebnerCone sigma=*(workingList.begin());
-    const groebnerCones neighbours = sigma.tropicalNeighbours();
-    for (groebnerCones::iterator tau = neighbours.begin(); tau!=neighbours.end(); tau++)
+    /**
+     * Pick a maximal Groebner cone from the working list
+     * and compute interior points on its facets as well as outer facet normals
+     */
+    groebnerCone sigma=*(workingList.begin());
+    workingList.erase(workingList.begin());
+
+    std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndOuterFacetNormals = interiorPointsAndNormalsOfFacets(sigma.getPolyhedralCone(), finishedInteriorPoints, onlyLowerHalfSpace);
+    gfan::ZMatrix interiorPoints = interiorPointsAndOuterFacetNormals.first;
+    gfan::ZMatrix outerFacetNormals = interiorPointsAndOuterFacetNormals.second;
+    std::vector<bool> needToFlip = checkNecessaryGroebnerFlips(groebnerFan,workingList, interiorPoints);
+
+    for (int i=0; i<interiorPoints.getHeight(); i++)
     {
-      if (tropicalVariety.count(*tau)==0)
-        workingList.insert(*tau);
+      gfan::ZVector interiorPoint = interiorPoints[i];
+
+      if (needToFlip[i]==true)
+      {
+        groebnerCone neighbour = sigma.flipCone(interiorPoint,outerFacetNormals[i]);
+        workingList.insert(neighbour);
+      }
+      finishedInteriorPoints.insert(interiorPoints[i]);
     }
-    tropicalVariety.insert(sigma);
-    workingList.erase(sigma);
-    // std::cout << "tropicalVariety.size():" << tropicalVariety.size() << std::endl;
-    // std::cout << "workingList.size():" << workingList.size() << std::endl;
+
+    sigma.deletePolynomialData();
+    groebnerFan.insert(sigma);
+    if (printlevel > 0)
+      Print("cones finished: %lu   cones in working list: %lu\n",
+      (unsigned long)groebnerFan.size(), (unsigned long)workingList.size());
   }
-  return tropicalVariety;
+  return groebnerFan;
 }

Singular/dyn_modules/gfanlib/tropicalTraversal.h

@@ -2 +2 @@
 #define TROPICAL_TRAVERSAL_H
 
+#include <groebnerCone.h>
+
 groebnerCones tropicalTraversalMinimizingFlips(const groebnerCone startingCone);
 groebnerCones tropicalTraversal(const groebnerCone startingCone);
+groebnerCones groebnerTraversal(const groebnerCone startingCone);
 
 #endif

Singular/dyn_modules/gfanlib/tropicalVariety.cc

@@ -14 +14 @@
 BITSET bitsetSave1, bitsetSave2;
 
+
 /***
  * sets option(redSB)
@@ -22 +23 @@
   si_opt_1|=Sy_bit(OPT_REDSB);
 }
+
 
 /***
@@ -40 +42 @@
 }
 
+
 BOOLEAN tropicalVariety(leftv res, leftv args)
 {
   leftv u = args;
+  if ((u!=NULL) && (u->Typ()==POLY_CMD))
+  {
+    poly g = (poly) u->Data();
+    leftv v = u->next;
+    if (v==NULL)
+    {
+      try
+      {
+        ideal I = idInit(1);
+        I->m[0] = g;
+        tropicalStrategy currentStrategy(I,currRing);
+        std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
+        res->rtyp = fanID;
+        res->data = (char*) toZFan(maxCones);
+        I->m[0] = NULL;
+        id_Delete(&I,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
+    }
+    if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
+    {
+      try
+      {
+        ideal I = idInit(1);
+        I->m[0] = g;
+        number p = (number) v->Data();
+        tropicalStrategy currentStrategy(I,p,currRing);
+        ideal startingIdeal = currentStrategy.getStartingIdeal();
+        ring startingRing = currentStrategy.getStartingRing();
+        poly gStart = startingIdeal->m[0];
+        std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
+        res->rtyp = fanID;
+        res->data = (char*) toZFan(maxCones);
+        I->m[0] = NULL;
+        id_Delete(&I,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
+
+    }
+  }
   if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
   {
@@ -53 +106 @@
       if (v==NULL)
       {
-        tropicalStrategy currentStrategy(I,currRing);
-        std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
-        // gfan::ZFan* zf = toZFan(maxCones);
-        // delete zf;
-        // res->rtyp = NONE;
-        // res->data = NULL;
-        // while (1)
-        // {
-        //   omUpdateInfo();
-        //   Print("usedBytesAfter=%ld\n",om_Info.UsedBytes);
-        //   tropicalStrategy debugTest(I,currRing);
-        //   maxCones = tropicalVariety(g,currRing,debugTest);
-        //   gfan::ZFan* zf = toZFan(maxCones);
-        //   delete zf;
-        // }
-        res->rtyp = fanID;
-        res->data = (char*) toZFan(maxCones);
-        return FALSE;
+        try
+        {
+          tropicalStrategy currentStrategy(I,currRing);
+          std::set<gfan::ZCone> maxCones = tropicalVariety(g,currRing,&currentStrategy);
+          res->rtyp = fanID;
+          res->data = (char*) toZFan(maxCones);
+          return FALSE;
+        }
+        catch (const std::exception& ex)
+        {
+          Werror("ERROR: %s",ex.what());
+          return TRUE;
+        }
       }
       if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
       {
-        number p = (number) v->Data();
-        tropicalStrategy currentStrategy(I,p,currRing);
-        ideal startingIdeal = currentStrategy.getStartingIdeal();
-        ring startingRing = currentStrategy.getStartingRing();
-        poly gStart = startingIdeal->m[0];
-        std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
-        res->rtyp = fanID;
-        res->data = (char*) toZFan(maxCones);
-        return FALSE;
+        try
+        {
+          number p = (number) v->Data();
+          tropicalStrategy currentStrategy(I,p,currRing);
+          ideal startingIdeal = currentStrategy.getStartingIdeal();
+          ring startingRing = currentStrategy.getStartingRing();
+          poly gStart = startingIdeal->m[0];
+          std::set<gfan::ZCone> maxCones = tropicalVariety(gStart,startingRing,&currentStrategy);
+          res->rtyp = fanID;
+          res->data = (char*) toZFan(maxCones);
+          return FALSE;
+        }
+        catch (const std::exception& ex)
+        {
+          Werror("ERROR: %s",ex.what());
+          return TRUE;
+        }
       }
     }
@@ -88 +144 @@
     if (v==NULL)
     {
-      setOptionRedSB();
-      // ideal stdI;
-      // if (!hasFlag(u,FLAG_STD))
-      //   stdI = gfanlib_kStd_wrapper(I,currRing);
-      // else
-      //   stdI = id_Copy(I,currRing);
-      tropicalStrategy currentStrategy(I,currRing);
-      gfan::ZFan* tropI = tropicalVariety(currentStrategy);
-      res->rtyp = fanID;
-      res->data = (char*) tropI;
-      undoSetOptionRedSB();
-      // id_Delete(&stdI,currRing);
-      return FALSE;
+      try
+      {
+        setOptionRedSB();
+        ideal stdI;
+        if (!hasFlag(u,FLAG_STD))
+          stdI = gfanlib_kStd_wrapper(I,currRing);
+        else
+          stdI = id_Copy(I,currRing);
+        tropicalStrategy currentStrategy(stdI,currRing);
+        gfan::ZFan* tropI = tropicalVariety(currentStrategy);
+        res->rtyp = fanID;
+        res->data = (char*) tropI;
+        undoSetOptionRedSB();
+        id_Delete(&stdI,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
     }
     if ((v!=NULL) && (v->Typ()==NUMBER_CMD))
     {
-      number p = (number) v->Data();
-      // ideal stdI;
-      // if (!hasFlag(u,FLAG_STD))
-      //   stdI = gfanlib_kStd_wrapper(I,currRing);
-      // else
-      //   stdI = id_Copy(I,currRing);
-      // tropicalStrategy currentStrategy(stdI,p,currRing);
-      tropicalStrategy currentStrategy(I,p,currRing);
-      gfan::ZFan* tropI = tropicalVariety(currentStrategy);
-      res->rtyp = fanID;
-      res->data = (char*) tropI;
-      // id_Delete(&stdI,currRing);
-      return FALSE;
+      try
+      {
+        number p = (number) v->Data();
+        ideal stdI;
+        if (!hasFlag(u,FLAG_STD))
+          stdI = gfanlib_kStd_wrapper(I,currRing);
+        else
+          stdI = id_Copy(I,currRing);
+        tropicalStrategy currentStrategy(stdI,p,currRing);
+        gfan::ZFan* tropI = tropicalVariety(currentStrategy);
+        res->rtyp = fanID;
+        res->data = (char*) tropI;
+        id_Delete(&stdI,currRing);
+        return FALSE;
+      }
+      catch (const std::exception& ex)
+      {
+        Werror("ERROR: %s",ex.what());
+        return TRUE;
+      }
     }
     return FALSE;

Singular/extra.cc

@@ -1864 +1864 @@
     if (strcmp(sys_cmd, "Mwalk") == 0)
     {
-      const short t[]={4,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,RING_CMD};
+      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,RING_CMD,INT_CMD,INT_CMD};
       if (!iiCheckTypes(h,t,1)) return TRUE;
       if (((intvec*) h->next->Data())->length() != currRing->N &&
@@ -1875 +1875 @@
       ideal arg1 = (ideal) h->Data();
       intvec* arg2 = (intvec*) h->next->Data();
-      intvec* arg3   =  (intvec*) h->next->next->Data();
-      ring arg4   =  (ring) h->next->next->next->Data();
-      ideal result = (ideal) Mwalk(arg1, arg2, arg3,arg4);
+      intvec* arg3 = (intvec*) h->next->next->Data();
+      ring arg4 = (ring) h->next->next->next->Data();
+      int arg5 = (int) (long) h->next->next->next->next->Data();
+      int arg6 = (int) (long) h->next->next->next->next->next->Data();
+      ideal result = (ideal) Mwalk(arg1, arg2, arg3, arg4, arg5, arg6);
       res->rtyp = IDEAL_CMD;
       res->data =  result;
@@ -1913 +1915 @@
     if (strcmp(sys_cmd, "Mpwalk") == 0)
     {
-      const short t[]={6,IDEAL_CMD,INT_CMD,INT_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD};
+      const short t[]={8,IDEAL_CMD,INT_CMD,INT_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD};
       if (!iiCheckTypes(h,t,1)) return TRUE;
       if(((intvec*) h->next->next->next->Data())->length() != currRing->N &&
@@ -1927 +1929 @@
       intvec* arg5 = (intvec*) h->next->next->next->next->Data();
       int arg6 = (int) (long) h->next->next->next->next->next->Data();
-      ideal result = (ideal) Mpwalk(arg1, arg2, arg3, arg4, arg5,arg6);
+      int arg7 = (int) (long) h->next->next->next->next->next->next->Data();
+      int arg8 = (int) (long) h->next->next->next->next->next->next->next->Data();
+      ideal result = (ideal) Mpwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8);
       res->rtyp = IDEAL_CMD;
       res->data =  result;
@@ -1939 +1943 @@
     if (strcmp(sys_cmd, "Mrwalk") == 0)
     {
-      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,RING_CMD};
+      const short t[]={7,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD};
       if (!iiCheckTypes(h,t,1)) return TRUE;
-      if((((intvec*) h->next->Data())->length() != currRing->N &&
-         ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
-         (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
-         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
+      if(((intvec*) h->next->Data())->length() != currRing->N &&
+         ((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
+         ((intvec*) h->next->next->Data())->length() != currRing->N &&
+         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) )
       {
         Werror("system(\"Mrwalk\" ...) intvecs not of length %d or %d\n",
@@ -1955 +1959 @@
       int arg4 = (int)(long) h->next->next->next->Data();
       int arg5 = (int)(long) h->next->next->next->next->Data();
-      ring arg6 = (ring) h->next->next->next->next->next->Data();
-      ideal result = (ideal) Mrwalk(arg1, arg2, arg3, arg4, arg5, arg6);
+      int arg6 = (int)(long) h->next->next->next->next->next->Data();
+      int arg7 = (int)(long) h->next->next->next->next->next->next->Data();
+      ideal result = (ideal) Mrwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7);
       res->rtyp = IDEAL_CMD;
       res->data =  result;
@@ -2018 +2023 @@
     if (strcmp(sys_cmd, "Mfwalk") == 0)
     {
-      const short t[]={3,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD};
+      const short t[]={5,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD};
       if (!iiCheckTypes(h,t,1)) return TRUE;
       if (((intvec*) h->next->Data())->length() != currRing->N &&
@@ -2025 +2030 @@
         Werror("system(\"Mfwalk\" ...) intvecs not of length %d\n",
                  currRing->N);
-        return TRUE;
-      }
-      ideal arg1 = (ideal) h->Data();
-      intvec* arg2 = (intvec*) h->next->Data();
-      intvec* arg3   =  (intvec*) h->next->next->Data();
-      ideal result = (ideal) Mfwalk(arg1, arg2, arg3);
-      res->rtyp = IDEAL_CMD;
-      res->data =  result;
-      return FALSE;
-    }
-    else
-  #endif
-  /*==================== Mfrwalk =================*/
-  #ifdef HAVE_WALK
-    if (strcmp(sys_cmd, "Mfrwalk") == 0)
-    {
-      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,RING_CMD};
-      if (!iiCheckTypes(h,t,1)) return TRUE;
-      if (((intvec*) h->next->Data())->length() != currRing->N &&
-          ((intvec*) h->next->next->Data())->length() != currRing->N)
-      {
-        Werror("system(\"Mfrwalk\" ...) intvecs not of length %d\n",currRing->N);
         return TRUE;
       }
@@ -2053 +2036 @@
       intvec* arg3 = (intvec*) h->next->next->Data();
       int arg4 = (int)(long) h->next->next->next->Data();
-      ideal result = (ideal) Mfrwalk(arg1, arg2, arg3, arg4);
+      int arg5 = (int)(long) h->next->next->next->next->Data();
+      ideal result = (ideal) Mfwalk(arg1, arg2, arg3, arg4, arg5);
       res->rtyp = IDEAL_CMD;
       res->data =  result;
@@ -2059 +2043 @@
     }
     else
+  #endif
+  /*==================== Mfrwalk =================*/
+  #ifdef HAVE_WALK
+    if (strcmp(sys_cmd, "Mfrwalk") == 0)
+    {
+      const short t[]={6,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD};
+      if (!iiCheckTypes(h,t,1)) return TRUE;
+/*
+      if (((intvec*) h->next->Data())->length() != currRing->N &&
+          ((intvec*) h->next->next->Data())->length() != currRing->N)
+      {
+        Werror("system(\"Mfrwalk\" ...) intvecs not of length %d\n",currRing->N);
+        return TRUE;
+      }
+*/
+      if((((intvec*) h->next->Data())->length() != currRing->N &&
+         ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
+         (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
+         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
+      {
+        Werror("system(\"Mfrwalk\" ...) intvecs not of length %d or %d\n",
+               currRing->N,(currRing->N)*(currRing->N));
+        return TRUE;
+      }
+
+      ideal arg1 = (ideal) h->Data();
+      intvec* arg2 = (intvec*) h->next->Data();
+      intvec* arg3 = (intvec*) h->next->next->Data();
+      int arg4 = (int)(long) h->next->next->next->Data();
+      int arg5 = (int)(long) h->next->next->next->next->Data();
+      int arg6 = (int)(long) h->next->next->next->next->next->Data();
+      ideal result = (ideal) Mfrwalk(arg1, arg2, arg3, arg4, arg5, arg6);
+      res->rtyp = IDEAL_CMD;
+      res->data =  result;
+      return FALSE;
+    }
+    else
   /*==================== Mprwalk =================*/
     if (strcmp(sys_cmd, "Mprwalk") == 0)
     {
-      const short t[]={7,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,RING_CMD};
+      const short t[]={9,IDEAL_CMD,INTVEC_CMD,INTVEC_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD,INT_CMD};
       if (!iiCheckTypes(h,t,1)) return TRUE;
-      if (((intvec*) h->next->Data())->length() != currRing->N &&
-          ((intvec*) h->next->next->Data())->length() != currRing->N )
-      {
-        Werror("system(\"Mrwalk\" ...) intvecs not of length %d\n",
-               currRing->N);
+      if((((intvec*) h->next->Data())->length() != currRing->N &&
+         ((intvec*) h->next->next->Data())->length() != currRing->N ) &&
+         (((intvec*) h->next->Data())->length() != (currRing->N)*(currRing->N) &&
+         ((intvec*) h->next->next->Data())->length() != (currRing->N)*(currRing->N) ))
+      {
+        Werror("system(\"Mrwalk\" ...) intvecs not of length %d or %d\n",
+               currRing->N,(currRing->N)*(currRing->N));
         return TRUE;
       }
@@ -2077 +2100 @@
       int arg5 = (int)(long) h->next->next->next->next->Data();
       int arg6 = (int)(long) h->next->next->next->next->next->Data();
-      ring arg7 = (ring) h->next->next->next->next->next->next->Data();
-      ideal result = (ideal) Mprwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7);
+      int arg7 = (int)(long) h->next->next->next->next->next->next->Data();
+      int arg8 = (int)(long) h->next->next->next->next->next->next->next->Data();
+      int arg9 = (int)(long) h->next->next->next->next->next->next->next->next->Data();
+      ideal result = (ideal) Mprwalk(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9);
       res->rtyp = IDEAL_CMD;
       res->data =  result;

Singular/iparith.cc

@@ -6154 +6154 @@
     return TRUE;
   }
+  res->rtyp=IDEAL_CMD;
   if ((mk < 1) || (mk > m->rows()) || (mk > m->cols()))
   {
-    Werror("invalid size of minors: %d (matrix is (%d x %d))", mk,
-           m->rows(), m->cols());
-    return TRUE;
+    ideal I=idInit(1,1);
+    if (mk<1) I->m[0]=p_One(currRing);
+    //Werror("invalid size of minors: %d (matrix is (%d x %d))", mk,
+    //       m->rows(), m->cols());
+    res->data=(void*)I;
+    return FALSE;
   }
   if ((!noAlgorithm) && (strcmp(algorithm, "Cache") == 0)
@@ -6179 +6183 @@
                               (noIdeal ? 0 : IasSB), false);
   if (v_typ!=MATRIX_CMD) idDelete((ideal *)&m);
-  res->rtyp = IDEAL_CMD;
   return FALSE;
 }

Singular/ipassign.cc

@@ -974 +974 @@
   }
 
-  int i=0;
   if (lt==DEF_CMD)
   {
@@ -1028 +1027 @@
     return (bb==NULL) || bb->blackbox_Assign(l,r);
   }
-  while (((dAssign[i].res!=lt)
-      || (dAssign[i].arg!=rt))
-    && (dAssign[i].res!=0)) i++;
-  if (dAssign[i].res!=0)
+  int start=0;
+  while ((dAssign[start].res!=lt)
+      && (dAssign[start].res!=0)) start++;
+  int i=start;
+  while ((dAssign[i].res==lt)
+      && (dAssign[i].arg!=rt)) i++;
+  if (dAssign[i].res==lt)
   {
     if (traceit&TRACE_ASSIGN) Print("assign %s=%s\n",Tok2Cmdname(lt),Tok2Cmdname(rt));
@@ -1044 +1046 @@
   }
   // implicite type conversion ----------------------------------------------
-  if (dAssign[i].res==0)
+  if (dAssign[i].res!=lt)
   {
     int ri;
     leftv rn = (leftv)omAlloc0Bin(sleftv_bin);
     BOOLEAN failed=FALSE;
-    i=0;
-    while ((dAssign[i].res!=lt)
-      && (dAssign[i].res!=0)) i++;
+    i=start;
+    //while ((dAssign[i].res!=lt)
+    //  && (dAssign[i].res!=0)) i++;
     while (dAssign[i].res==lt)
     {

Singular/misc_ip.cc

@@ -1216 +1216 @@
     omInitInfo();
 
+// options ---------------------------------------------------------------
+  si_opt_1=0;
 // interpreter tables etc.: -----------------------------------------------
   memset(&sLastPrinted,0,sizeof(sleftv));

Singular/table.h

@@ -1185 +1185 @@
 struct sValAssign dAssign[]=
 {
+// same res types must be grouped together
 // proc         res             arg
  {D(jiA_IDEAL),    IDEAL_CMD,      IDEAL_CMD }
@@ -1198 +1199 @@
 ,{D(jiA_POLY),     POLY_CMD,       POLY_CMD }
 ,{D(jiA_1x1MATRIX),POLY_CMD,       MATRIX_CMD }
+,{D(jiA_RING),     RING_CMD,       RING_CMD }
 ,{D(jiA_QRING),    QRING_CMD,      IDEAL_CMD }
-,{D(jiA_RING),     RING_CMD,       RING_CMD }
 ,{D(jiA_RING),     QRING_CMD,      QRING_CMD }
 ,{D(jiA_RING),     QRING_CMD,      RING_CMD }
@@ -1208 +1209 @@
 ,{D(jiA_INTVEC),   INTVEC_CMD,     INTVEC_CMD }
 ,{D(jiA_INTVEC),   INTMAT_CMD,     INTMAT_CMD }
-//,{D(jiA_INTVEC),   INTMAT_CMD,     INTVEC_CMD }
 ,{D(jiA_BIGINTMAT),BIGINTMAT_CMD,  BIGINTMAT_CMD}
 ,{D(jiA_NUMBER),   NUMBER_CMD,     NUMBER_CMD }

Singular/walk.cc

@@ -27 +27 @@
 
 #define FIRST_STEP_FRACTAL // to define the first step of the fractal
-//#define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if
+#define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if
 //                          tau doesn't stay in the correct cone
 
@@ -42 +42 @@
 #include <Singular/ipshell.h>
 #include <Singular/ipconv.h>
+#include <coeffs/ffields.h>
 #include <coeffs/coeffs.h>
 #include <Singular/subexpr.h>
+#include <polys/templates/p_Procs.h>
 
 #include <polys/monomials/maps.h>
@@ -429 +431 @@
 #endif
 
-#ifdef CHECK_IDEAL_MWALK
+//#ifdef CHECK_IDEAL_MWALK
 static void idString(ideal L, const char* st)
 {
@@ -441 +443 @@
   Print(" %s;", pString(L->m[nL-1]));
 }
-#endif
+//#endif
 
 #if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS)
@@ -558 +560 @@
   }
   return p0;
+}
+
+/*****************************************************************************
+ * compute the gcd of the entries of the vectors curr_weight and diff_weight *
+ *****************************************************************************/
+static int simplify_gcd(intvec* curr_weight, intvec* diff_weight)
+{
+  int j;
+  int nRing = currRing->N;
+  int gcd_tmp = (*curr_weight)[0];
+  for (j=1; j<nRing; j++)
+  {
+    gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]);
+    if(gcd_tmp == 1)
+    {
+      break;
+    }
+  }
+  if(gcd_tmp != 1)
+  {
+    for (j=0; j<nRing; j++)
+    {
+    gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]);
+    if(gcd_tmp == 1)
+      {
+        break;
+      }
+    }
+  }
+  return gcd_tmp;
 }
 
@@ -953 +985 @@
 }
 
-/*****************************************************************************
-* create a weight matrix order as intvec of an extra weight vector (a(iv),lp)*
-******************************************************************************/
+/*********************************************************************************
+* create a weight matrix order as intvec of an extra weight vector (a(iv),M(iw)) *
+**********************************************************************************/
 intvec* MivMatrixOrderRefine(intvec* iv, intvec* iw)
 {
-  assume(iv->length() == iw->length());
-  int i, nR = iv->length();
-
+  assume((iv->length())*(iv->length()) == iw->length());
+  int i,j, nR = iv->length();
+  
   intvec* ivm = new intvec(nR*nR);
 
@@ -966 +998 @@
   {
     (*ivm)[i] = (*iv)[i];
-    (*ivm)[i+nR] = (*iw)[i];
-  }
-  for(i=2; i<nR; i++)
-  {
-    (*ivm)[i*nR+i-2] = 1;
+  }
+  for(i=1; i<nR; i++)
+  {
+    for(j=0; j<nR; j++)
+    {
+      (*ivm)[j+i*nR] = (*iw)[j+i*nR];
+    }
   }
   return ivm;
@@ -1859 +1893 @@
 }
 
+
+/**************************************************************
+ * Look for the position of the smallest absolut value in vec *
+ **************************************************************/
+static int MivAbsMaxArg(intvec* vec)
+{
+  int k = MivAbsMax(vec);
+  int i=0;
+  while(1)
+  {
+    if((*vec)[i] == k || (*vec)[i] == -k)
+    {
+      break;
+    }
+    i++;
+  }
+  return i;
+}
+
+
 /**********************************************************************
  * Compute a next weight vector between curr_weight and target_weight *
@@ -1873 +1927 @@
 
   int nRing = currRing->N;
-  int checkRed, j, kkk, nG = IDELEMS(G);
+  int checkRed, j, nG = IDELEMS(G);
   intvec* ivtemp;
 
@@ -1911 +1965 @@
   mpz_init(dcw);
 
-  //int tn0, tn1, tz1, ncmp, gcd_tmp, ntmp;
   int gcd_tmp;
   intvec* diff_weight = MivSub(target_weight, curr_weight);
@@ -1917 +1970 @@
   intvec* diff_weight1 = MivSub(target_weight, curr_weight);
   poly g;
-  //poly g, gw;
+
   for (j=0; j<nG; j++)
   {
@@ -1979 +2032 @@
     }
   }
-//Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t));
+  //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t));
   mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t));
 
 
-  // there is no 0<t<1 and define the next weight vector that is equal to the current weight vector
+  // there is no 0<t<1 and define the next weight vector that is equal
+  // to the current weight vector
   if(mpz_cmp(t_nenner, t_null) == 0)
   {
@@ -2054 +2108 @@
 #endif
 
-  //  BOOLEAN isdwpos;
-
-  // construct a new weight vector
+// construct a new weight vector and check whether vec[j] is overflow,
+// i.e. vec[j] > 2^31.
+// If vec[j] doesn't overflow, define a weight vector. Otherwise,
+// report that overflow appears. In the second case, test whether the
+// the correctness of the new vector plays an important role
+
   for (j=0; j<nRing; j++)
   {
@@ -2100 +2157 @@
     }
   }
-
+  // reduce the vector with the gcd
+  if(mpz_cmp_si(ggt,1) != 0)
+  {
+    for (j=0; j<nRing; j++)
+    {
+      mpz_divexact(vec[j], vec[j], ggt);
+    }
+  }
 #ifdef  NEXT_VECTORS_CC
   PrintS("\n// gcd of elements of the vector: ");
@@ -2106 +2170 @@
 #endif
 
-/**********************************************************************
-* construct a new weight vector and check whether vec[j] is overflow, *
-* i.e. vec[j] > 2^31.                                                 *
-* If vec[j] doesn't overflow, define a weight vector. Otherwise,      *
-* report that overflow appears. In the second case, test whether the  *
-* the correctness of the new vector plays an important role           *
-**********************************************************************/
-  kkk=0;
   for(j=0; j<nRing; j++)
     {
@@ -2129 +2185 @@
 
   REDUCTION:
+  checkRed = 1;
   for (j=0; j<nRing; j++)
   {
-    (*diff_weight)[j] = mpz_get_si(vec[j]);
-  }
-  while(MivAbsMax(diff_weight) >= 5)
-  {
-    for (j=0; j<nRing; j++)
-    {
-      if(mpz_cmp_si(ggt,1)==0)
-      {
-        (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
-        // Print("\n//  vector[%d] = %d \n",j+1, (*diff_weight1)[j]);
-      }
-      else
-      {
-        mpz_divexact(vec[j], vec[j], ggt);
-        (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
-        // Print("\n//  vector[%d] = %d \n",j+1, (*diff_weight1)[j]);
-      }
-/*
-      if((*diff_weight1)[j] == 0)
-      {
-        kkk = kkk + 1;
-      }
-*/
-    }
-
-
-/*
-    if(kkk > nRing - 1)
-    {
-      // diff_weight was reduced to zero
-      // Print("\n // MwalkNextWeightCC: geaenderter Vector gleich Null! \n");
-      goto TEST_OVERFLOW;
-    }
-*/
-
-    if(test_w_in_ConeCC(G,diff_weight1) != 0)
-    {
-      Print("\n// MwalkNextWeightCC: geaenderter vector liegt in Groebnerkegel! \n");
-      for (j=0; j<nRing; j++)
-      {
-        (*diff_weight)[j] = (*diff_weight1)[j];
-      }
-      if(MivAbsMax(diff_weight) < 5)
-      {
-        checkRed = 1;
-        goto SIMPLIFY_GCD;
-      }
-    }
-    else
-    {
-      // Print("\n// MwalkNextWeightCC: geaenderter vector liegt nicht in Groebnerkegel! \n");
-      break;
-    }
+    (*diff_weight1)[j] = mpz_get_si(vec[j]);
+  }
+  while(test_w_in_ConeCC(G,diff_weight1))
+  {
+    for(j=0; j<nRing; j++)
+    {
+      (*diff_weight)[j] = (*diff_weight1)[j];
+      mpz_set_si(vec[j], (*diff_weight)[j]);      
+    }
+    for(j=0; j<nRing; j++)
+    {
+      (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5);
+    }
+  }
+  if(MivAbsMax(diff_weight)>10000)
+  {
+    for(j=0; j<nRing; j++)
+    {
+      (*diff_weight1)[j] = (*diff_weight)[j];
+    }
+    j = 0;
+    while(test_w_in_ConeCC(G,diff_weight1))
+    {
+      (*diff_weight)[j] = (*diff_weight1)[j];
+      mpz_set_si(vec[j], (*diff_weight)[j]);
+      j = MivAbsMaxArg(diff_weight1);
+      (*diff_weight1)[j] = floor(0.1*(*diff_weight1)[j] + 0.5);
+    }
+    goto SIMPLIFY_GCD;
   }
 
@@ -2222 +2255 @@
    mpz_clear(t_null);
 
-
-
   if(Overflow_Error == FALSE)
   {
     Overflow_Error = nError;
   }
- rComplete(currRing);
-  for(kkk=0; kkk<IDELEMS(G);kkk++)
-  {
-    poly p=G->m[kkk];
+  rComplete(currRing);
+  for(j=0; j<IDELEMS(G); j++)
+  {
+    poly p=G->m[j];
     while(p!=NULL)
     {
@@ -2271 +2302 @@
 }
 
-/**************************************************************
+/********************************************************************
  * define and execute a new ring which order is (a(vb),a(va),lp,C)  *
- * ************************************************************/
+ * ******************************************************************/
 static void VMrHomogeneous(intvec* va, intvec* vb)
 {
@@ -2426 +2457 @@
 }
 
-static ring VMrDefault1(intvec* va)
-{
-
-  if ((currRing->ppNoether)!=NULL)
-  {
-    pDelete(&(currRing->ppNoether));
-  }
-  if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) ||
-      ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data))))
-  {
-    sLastPrinted.CleanUp();
-  }
-
-  ring r = (ring) omAlloc0Bin(sip_sring_bin);
-  int i, nv = currRing->N;
-
-  r->cf  = currRing->cf;
-  r->N   = currRing->N;
-
-  int nb = 4;
-
-  //names
-  char* Q; // In order to avoid the corrupted memory, do not change.
-  r->names = (char **) omAlloc0(nv * sizeof(char_ptr));
-  for(i=0; i<nv; i++)
-  {
-    Q = currRing->names[i];
-    r->names[i]  = omStrDup(Q);
-  }
-
-  /*weights: entries for 3 blocks: NULL Made:???*/
-  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
-  r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
-  for(i=0; i<nv; i++)
-    r->wvhdl[0][i] = (*va)[i];
-
-  /* order: a,lp,C,0 */
-  r->order = (int *) omAlloc(nb * sizeof(int *));
-  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
-  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
-
-  // ringorder a for the first block: var 1..nv
-  r->order[0]  = ringorder_a;
-  r->block0[0] = 1;
-  r->block1[0] = nv;
-
-  // ringorder lp for the second block: var 1..nv
-  r->order[1]  = ringorder_lp;
-  r->block0[1] = 1;
-  r->block1[1] = nv;
-
-  // ringorder C for the third block
-  // it is very important within "idLift",
-  // especially, by ring syz_ring=rCurrRingAssure_SyzComp();
-  // therefore, nb  must be (nBlocks(currRing)  + 1)
-  r->order[2]  = ringorder_C;
-
-  // the last block: everything is 0
-  r->order[3]  = 0;
-
-  // polynomial ring
-  r->OrdSgn    = 1;
-
-  // complete ring intializations
-
-  rComplete(r);
-
-  //rChangeCurrRing(r);
-  return r;
-}
-
 /****************************************************************
  * define and execute a new ring with ordering (a(va),Wp(vb),C) *
  * **************************************************************/
-
 static ring VMrRefine(intvec* va, intvec* vb)
 {
@@ -2574 +2533 @@
 
   // complete ring intializations
-
+  
   rComplete(r);
 
@@ -2804 +2763 @@
 }
 
-
-/* define a ring with parameters und change to it */
-/* DefRingPar and DefRingParlp corrupt still memory */
+/***************************************************
+* define a ring with parameters und change to it   *
+* DefRingPar and DefRingParlp corrupt still memory *
+****************************************************/
 static void DefRingPar(intvec* va)
 {
@@ -2954 +2914 @@
 }
 
-//unused
-/**************************************************************
- * check wheather one or more components of a vector are zero *
- **************************************************************/
-//#if 0
+/*************************************************************
+ * check whether one or more components of a vector are zero *
+ *************************************************************/
 static int isNolVector(intvec* hilb)
 {
@@ -2971 +2929 @@
   return 0;
 }
-//#endif
+
+/*************************************************************
+ * check whether one or more components of a vector are <= 0 *
+ *************************************************************/
+static int isNegNolVector(intvec* hilb)
+{
+  int i;
+  for(i=hilb->length()-1; i>=0; i--)
+  {
+    if((* hilb)[i]<=0)
+    {
+      return 1;
+    }
+  }
+  return 0;
+}
+
+/**************************************************************************
+* Gomega is the initial ideal of G w. r. t. the current weight vector     *
+* curr_weight. Check whether curr_weight lies on a border of the Groebner *
+* cone, i. e. check whether a monomial is divisible by a leading monomial *
+***************************************************************************/
+static ideal middleOfCone(ideal G, ideal Gomega)
+{
+  BOOLEAN middle = FALSE;
+  int i,j,N = IDELEMS(Gomega);
+  poly p,lm,factor1,factor2;
+  PrintS("\n//** idCopy\n");
+  ideal Go = idCopy(G);
+  
+  PrintS("\n//** jetzt for-Loop!\n");
+  for(i=0; i<N; i++)
+  {
+    for(j=0; j<N; j++)
+    {
+      if(i!=j)
+      {
+        p = pCopy(Gomega->m[i]);
+        lm = pCopy(Gomega->m[j]);
+        pIter(p);
+        while(p!=NULL)
+        {
+          if(pDivisibleBy(lm,p))
+          {
+            if(middle == FALSE)
+            {
+              middle = TRUE;
+            }
+            factor1 = singclap_pdivide(pHead(p),lm,currRing);
+            factor2 = pMult(pCopy(factor1),pCopy(Go->m[j]));
+            pDelete(&factor1);
+            Go->m[i] = pAdd((Go->m[i]),pNeg(pCopy(factor2)));
+            pDelete(&factor2);
+          }
+          pIter(p);
+        }
+        pDelete(&lm);
+        pDelete(&p);
+      }
+    }
+  }
+  
+  //PrintS("\n//** jetzt Delete!\n");
+  //pDelete(&p);
+  //pDelete(&factor);
+  //pDelete(&lm);
+  if(middle == TRUE)
+  {
+    PrintS("\n//** middle TRUE!\n");
+    return Go;
+  }
+  PrintS("\n//** middle FALSE!\n");
+  idDelete(&Go);
+  return NULL; 
+}
 
 /******************************  Februar 2002  ****************************
@@ -3126 +3158 @@
     else
     {
-      rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung
+      rChangeCurrRing(VMrDefault(curr_weight));
     }
     newRing = currRing;
@@ -3278 +3310 @@
   }
   return 0;
+}
+
+/*****************************************
+ * return maximal polynomial length of G *
+ *****************************************/
+static int maxlengthpoly(ideal G)
+{
+  int i,k,length=0;
+  for(i=IDELEMS(G)-1; i>=0; i--)
+  {
+    k = pLength(G->m[i]);
+    if(k>length)
+    {
+      length = k;
+    }
+  }
+  return length;
 }
 
@@ -3882 +3931 @@
     else
     {
-      rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung
+      rChangeCurrRing(VMrDefault(curr_weight));
     }
     newRing = currRing;
@@ -4143 +4192 @@
     else
     {
-      rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
+      rChangeCurrRing(VMrDefault(curr_weight));
     }
     newRing = currRing;
@@ -4285 +4334 @@
 intvec* Xivlp;
 
-#if 0
+
 /********************************
  * compute a next weight vector *
  ********************************/
-static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg)
-{
-  int i, weight_norm;
-  int nV = currRing->N;
-  intvec* next_weight2;
-  intvec* next_weight22 = new intvec(nV);
-  intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight, G);
-  if(MivComp(next_weight, target_weight) == 1)
-  {
-    return(next_weight);
-  }
-  else
-  {
-    //compute a perturbed next weight vector "next_weight1"
-    intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G, MivMatrixOrder(curr_weight), pert_deg), target_weight, G);
-    //Print("\n // size of next_weight1 = %d", sizeof((*next_weight1)));
-
-    //compute a random next weight vector "next_weight2"
-    while(1)
-    {
-      weight_norm = 0;
-      while(weight_norm == 0)
-      {
-        for(i=0; i<nV; i++)
-        {
-          //Print("\n//  next_weight[%d]  = %d", i, (*next_weight)[i]);
-          (*next_weight22)[i] = rand() % 60000 - 30000;
-          weight_norm = weight_norm + (*next_weight22)[i]*(*next_weight22)[i];
-        }
-        weight_norm = 1 + floor(sqrt(weight_norm));
-      }
-
-      for(i=nV-1; i>=0; i--)
-      {
-        if((*next_weight22)[i] < 0)
-        {
-          (*next_weight22)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm);
-        }
-        else
-        {
-          (*next_weight22)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm);
-        }
-      //Print("\n//  next_weight22[%d]  = %d", i, (*next_weight22)[i]);
-      }
-
-      if(test_w_in_ConeCC(G, next_weight22) == 1)
-      {
-        //Print("\n//MWalkRandomNextWeight: next_weight2 im Kegel\n");
-        next_weight2 = MkInterRedNextWeight(next_weight22, target_weight, G);
-        delete next_weight22;
-        break;
-      }
-    }
-    intvec* result = new intvec(nV);
-    ideal G_test = MwalkInitialForm(G, next_weight);
-    ideal G_test1 = MwalkInitialForm(G, next_weight1);
-    ideal G_test2 = MwalkInitialForm(G, next_weight2);
-
-    // compare next_weights
-    if(IDELEMS(G_test1) < IDELEMS(G_test))
-    {
-      if(IDELEMS(G_test2) <= IDELEMS(G_test1)) // |G_test2| <= |G_test1| < |G_test|
-      {
-        for(i=0; i<nV; i++)
-        {
-          (*result)[i] = (*next_weight2)[i];
-        }
-      }
-      else // |G_test1| < |G_test|, |G_test1| < |G_test2|
-      {
-        for(i=0; i<nV; i++)
-        {
-          (*result)[i] = (*next_weight1)[i];
-        }
-      }
-    }
-    else
-    {
-      if(IDELEMS(G_test2) <= IDELEMS(G_test)) // |G_test2| <= |G_test| <= |G_test1|
-      {
-        for(i=0; i<nV; i++)
-        {
-          (*result)[i] = (*next_weight2)[i];
-        }
-      }
-      else // |G_test| <= |G_test1|, |G_test| < |G_test2|
-      {
-        for(i=0; i<nV; i++)
-        {
-          (*result)[i] = (*next_weight)[i];
-        }
-      }
-    }
-    delete next_weight;
-    delete next_weight1;
-    idDelete(&G_test);
-    idDelete(&G_test1);
-    idDelete(&G_test2);
-    if(test_w_in_ConeCC(G, result) == 1)
-    {
-      delete next_weight2;
-      return result;
-    }
-    else
-    {
-      delete result;
-      return next_weight2;
-    }
-  }
-}
-#endif
-
-/********************************
- * compute a next weight vector *
- ********************************/
-static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg)
-{
-  int i, weight_norm;
-  //int randCount=0;
-  int nV = currRing->N;
+static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight,
+               intvec* target_weight, int weight_rad, int pert_deg)
+{
+  assume(currRing != NULL && curr_weight != NULL &&
+         target_weight != NULL && G->m[0] != NULL);
+
+  int i,weight_norm,nV = currRing->N;
   intvec* next_weight2;
   intvec* next_weight22 = new intvec(nV);
   intvec* result = new intvec(nV);
 
-  //compute a perturbed next weight vector "next_weight1"
-  //intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G,MivMatrixOrderRefine(curr_weight,target_weight),pert_deg),target_weight,G);
   intvec* next_weight1 =MkInterRedNextWeight(curr_weight,target_weight,G);
   //compute a random next weight vector "next_weight2"
@@ -4422 +4356 @@
     while(weight_norm == 0)
     {
+
       for(i=0; i<nV; i++)
       {
@@ -4429 +4364 @@
       weight_norm = 1 + floor(sqrt(weight_norm));
     }
+
     for(i=0; i<nV; i++)
     {
@@ -4440 +4376 @@
       }
     }
+
     if(test_w_in_ConeCC(G, next_weight22) == 1)
     {
       next_weight2 = MkInterRedNextWeight(next_weight22,target_weight,G);
+      if(MivAbsMax(next_weight2)>1147483647)
+      {
+        for(i=0; i<nV; i++)
+        {
+          (*next_weight22)[i] = (*next_weight2)[i];
+        }
+        i = 0;
+        /* reduce the size of the maximal entry of the vector*/
+        while(test_w_in_ConeCC(G,next_weight22))
+        {
+          (*next_weight2)[i] = (*next_weight22)[i];
+          i = MivAbsMaxArg(next_weight22);
+          (*next_weight22)[i] = floor(0.1*(*next_weight22)[i] + 0.5);
+        }
+      }
       delete next_weight22;
       break;
     }
   }
+  
   // compute "usual" next weight vector
   intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight, G);
@@ -4456 +4409 @@
   {
     ideal G_test1 = MwalkInitialForm(G, next_weight1);
-    if(IDELEMS(G_test1) < IDELEMS(G_test))
-    {
-      if(IDELEMS(G_test2) < IDELEMS(G_test1))
+    if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test))//if(IDELEMS(G_test1) < IDELEMS(G_test))
+    {
+      if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test1)) //if(IDELEMS(G_test2) < IDELEMS(G_test1))
       {
         // |G_test2| < |G_test1| < |G_test|
@@ -4473 +4426 @@
           (*result)[i] = (*next_weight1)[i];
         }
-      }
+      }    
     }
     else
     {
-      if(IDELEMS(G_test2) < IDELEMS(G_test)) // |G_test2| < |G_test| <= |G_test1|
+      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|
       {
         for(i=0; i<nV; i++)
@@ -4498 +4451 @@
   {
     Overflow_Error = FALSE;
-    if(IDELEMS(G_test2) < IDELEMS(G_test))
+    if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test))//if(IDELEMS(G_test2) < IDELEMS(G_test))
     {
       for(i=1; i<nV; i++)
@@ -4513 +4466 @@
     }
   }
+  PrintS("\n MWalkRandomNextWeight: Ende ok!\n");
   idDelete(&G_test);
   idDelete(&G_test2);
@@ -4573 +4527 @@
     else
     {
-      rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
+      rChangeCurrRing(VMrDefault(orig_target_weight));
     }
     TargetRing = currRing;
@@ -4644 +4598 @@
     else
     {
-      rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
+      rChangeCurrRing(VMrDefault(curr_weight));
     }
     newRing = currRing;
@@ -4753 +4707 @@
     else
     {
-      rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
+      rChangeCurrRing(VMrDefault(orig_target_weight));
     }
     F1 = idrMoveR(G, newRing,currRing);
@@ -4784 +4738 @@
       else
       {
-        rChangeCurrRing(VMrDefault(orig_target_weight)); // Aenderung
+        rChangeCurrRing(VMrDefault(orig_target_weight));
       }
     KSTD_Finish:
@@ -4882 +4836 @@
       tim = clock();
       /*
-        Print("\n// **** Grï¿œbnerwalk took %d steps and ", nwalk);
+        Print("\n// **** Groebnerwalk took %d steps and ", nwalk);
         PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:");
         idElements(Gomega, "G_omega");
@@ -4912 +4866 @@
       oldRing = currRing;
 
-      /* create a new ring newRing */
+      // create a new ring newRing
        if (rParameter(currRing) != NULL)
        {
@@ -4919 +4873 @@
        else
        {
-         rChangeCurrRing(VMrDefault(curr_weight)); // Aenderung
+         rChangeCurrRing(VMrDefault(curr_weight));
        }
       newRing = currRing;
@@ -4945 +4899 @@
       else
       {
-        rChangeCurrRing(VMrDefault(curr_weight));  //Aenderung
+        rChangeCurrRing(VMrDefault(curr_weight));
       }
       newRing = currRing;
@@ -4957 +4911 @@
       M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
       delete hilb_func;
-#endif // BUCHBERGER_ALG
+#endif
       tstd = tstd + clock() - to;
 
@@ -4966 +4920 @@
 
       to = clock();
-      // 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.
+      // 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.
       F = MLifttwoIdeal(Gomega2, M1, G);
       tlift = tlift + clock() - to;
@@ -5016 +4972 @@
       else
       {
-        rChangeCurrRing(VMrDefault(target_weight)); // Aenderung
+        rChangeCurrRing(VMrDefault(target_weight));
       }
       F1 = idrMoveR(G, newRing,currRing);
@@ -5063 +5019 @@
  * THE GROEBNER WALK ALGORITHM *
  *******************************/
-ideal Mwalk(ideal Go, intvec* orig_M, intvec* target_M, ring baseRing)
-{
-  BITSET save1 = si_opt_1; // save current options
-  //si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
-  //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
-  //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
+ideal Mwalk(ideal Go, intvec* orig_M, intvec* target_M,
+            ring baseRing, int reduction, int printout)
+{
+  // save current options
+  BITSET save1 = si_opt_1;
+  if(reduction == 0)
+  {
+    // no reduced Groebner basis
+    si_opt_1 &= (~Sy_bit(OPT_REDSB));
+    // not tail reductions
+    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL));
+  }
   Set_Error(FALSE);
   Overflow_Error = FALSE;
@@ -5081 +5043 @@
   int nV = baseRing->N;
 
-  ideal Gomega, M, F, Gomega1, Gomega2, M1; //, F1;
+  ideal Gomega, M, F, FF, Gomega1, Gomega2, M1; //, F1;
   ring newRing;
   ring XXRing = baseRing;
@@ -5109 +5071 @@
 #endif
   rComplete(currRing);
-#ifdef CHECK_IDEAL_MWALK
-    idString(Go,"Go");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+  if(printout > 2)
+  {
+    idString(Go,"//** Mwalk: Go");
+  }
+//#endif
 #ifdef TIME_TEST
   to = clock();
 #endif
-     if(orig_M->length() == nV)
-      {
-        newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
-      }
-      else
-      {
-        newRing = VMatrDefault(orig_M);
-      }
+  if(orig_M->length() == nV)
+  {
+    // define a new ring with ordering "(a(curr_weight),lp)
+    newRing = VMrDefault(curr_weight);
+  }
+  else
+  {
+    newRing = VMatrDefault(orig_M);
+  }
   rChangeCurrRing(newRing);
-  ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
+  //ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
+  ideal G = idrMoveR(Go,baseRing,currRing);
   baseRing = currRing;
 #ifdef TIME_TEST
@@ -5138 +5105 @@
     to = clock();
 #endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(G,"G");
-#endif
-    Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(G,"//** Mwalk: G");
+    }
+//#endif
+    // compute an initial form ideal of <G> w.r.t. "curr_vector"
+    Gomega = MwalkInitialForm(G, curr_weight);
 #ifdef TIME_TEST
-    tif = tif + clock()-to; //time for computing initial form ideal
-#endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(Gomega,"Gomega");
-#endif
+    //time for computing initial form ideal
+    tif = tif + clock()-to;
+#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 1)
+    {
+      idString(Gomega,"//** Mwalk: Gomega");
+    }
+//#endif
+
+
+    if(reduction == 0)
+    {
+      PrintS("\n//** Mwalk: test middle of cone!\n");
+      FF = middleOfCone(G,Gomega);
+      PrintS("\n//** Mwalk: Test F!\n");
+      if( FF != NULL)
+      {
+        idDelete(&G);
+        G = idCopy(FF);
+        idDelete(&FF);
+        PrintS("\n//** Mwalk: FF nicht NULL! Compue next vector.\n");
+        goto NEXT_VECTOR;
+      } 
+    }
+
 #ifndef  BUCHBERGER_ALG
     if(isNolVector(curr_weight) == 0)
     {
       hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
-    }
+    }   
     else
     {
@@ -5162 +5154 @@
       if(orig_M->length() == nV)
       {
-        newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
+        // define a new ring with ordering "(a(curr_weight),lp)
+        newRing = VMrDefault(curr_weight);
       }
       else
@@ -5173 +5166 @@
      if(target_M->length() == nV)
      {
-       newRing = VMrRefine(curr_weight,target_weight); //define a new ring with ordering "(a(curr_weight),Wp(target_weight))"
+       //define a new ring with ordering "(a(curr_weight),Wp(target_weight))"
+       newRing = VMrRefine(curr_weight,target_weight);
      }
      else
      {
+       //define a new ring with matrix ordering
        newRing = VMatrRefine(target_M,curr_weight);
      }
@@ -5197 +5192 @@
 #endif
     idSkipZeroes(M);
-#ifdef CHECK_IDEAL_MWALK
-    PrintS("\n//** Mwalk: computed M.\n");
-    idString(M, "M");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(M, "//** Mwalk: M");
+    }
+//#endif
     //change the ring to baseRing
     rChangeCurrRing(baseRing);
@@ -5210 +5207 @@
     to = clock();
 #endif
-    // 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
+    // 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
     F = MLifttwoIdeal(Gomega2, M1, G);
 #ifdef TIME_TEST
     tlift = tlift + clock() - to;
 #endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(F, "F");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(F, "//** Mwalk: F");
+    }
+//#endif
     idDelete(&Gomega2);
     idDelete(&M1);
@@ -5227 +5228 @@
     to = clock();
 #endif
-    //G = kStd(F1,NULL,testHomog,NULL,NULL,0,0,NULL);
+
 #ifdef TIME_TEST
     tstd = tstd + clock() - to;
 #endif
     idSkipZeroes(G);
-#ifdef CHECK_IDEAL_MWALK
-    idString(G, "G");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(G, "//** Mwalk: G");
+    }
+//#endif
 #ifdef TIME_TEST
     to = clock();
 #endif
+    NEXT_VECTOR:
+    PrintS("\n//** Mwalk: NEXT_VECTOR!\n");
     intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
 #ifdef TIME_TEST
     tnw = tnw + clock() - to;
 #endif
-#ifdef PRINT_VECTORS
-    MivString(curr_weight, target_weight, next_weight);
-#endif
-    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)
-    {
-#ifdef CHECK_IDEAL_MWALK
-      PrintS("\n//** Mwalk: entering last cone.\n");
-#endif
+//#ifdef PRINT_VECTORS
+    if(printout > 0)
+    {
+      MivString(curr_weight, target_weight, next_weight);
+    }
+//#endif
+    if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1 || test_w_in_ConeCC(G, target_weight) == 1)
+    {
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 0)
+      {
+        PrintS("\n//** Mwalk: entering last cone.\n");
+      }
+//#endif
       Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
       if(target_M->length() == nV)
@@ -5262 +5274 @@
       Gomega1 = idrMoveR(Gomega, baseRing,currRing);
       idDelete(&Gomega);
-#ifdef CHECK_IDEAL_MWALK
-      idString(Gomega1, "Gomega");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 1)
+      {
+        idString(Gomega1, "//** Mwalk: Gomega");
+      }
+      PrintS("\n //** Mwalk: kStd(Gomega)");
+//#endif
       M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
-#ifdef CHECK_IDEAL_MWALK
-      idString(M,"M");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 1)
+      {
+        idString(M,"//** Mwalk: M");
+      }
+//#endif
       rChangeCurrRing(baseRing);
       M1 =  idrMoveR(M, newRing,currRing);
@@ -5274 +5293 @@
       Gomega2 = idrMoveR(Gomega1, newRing,currRing);
       idDelete(&Gomega1);
+      PrintS("\n //** Mwalk: MLifttwoIdeal");
       F = MLifttwoIdeal(Gomega2, M1, G);
-#ifdef CHECK_IDEAL_MWALK
-      idString(F,"F");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(F,"//** Mwalk: F");
+    }
+//#endif
       idDelete(&Gomega2);
       idDelete(&M1);
@@ -5289 +5312 @@
       to = clock();
 #endif
- //     if(si_opt_1 == (Sy_bit(OPT_REDSB)))
-  //    {
-        G = kInterRedCC(G,NULL); //reduce the Groebner basis <G> w.r.t. currRing, if option(redSB) is set
-  //    }
+      //PrintS("\n //**Mwalk: Interreduce");
+      //interreduce the Groebner basis <G> w.r.t. currRing
+      //G = kInterRedCC(G,NULL);
 #ifdef TIME_TEST
       tred = tred + clock() - to;
@@ -5299 +5321 @@
       delete next_weight;
       break;
-#ifdef CHECK_IDEAL_MWALK
-      PrintS("\n//** Mwalk: last cone.\n");
-#endif
-    }
-#ifdef CHECK_IDEAL_MWALK
-    PrintS("\n//** Mwalk: update weight vectors.\n");
-#endif
+    }
     for(i=nV-1; i>=0; i--)
     {
@@ -5316 +5332 @@
   ideal result = idrMoveR(G,baseRing,currRing);
   idDelete(&G);
-/*#ifdef CHECK_IDEAL_MWALK
-  pDelete(&p);
-#endif*/
   delete tmp_weight;
   delete ivNull;
@@ -5326 +5339 @@
 #endif
 #ifdef TIME_TEST
-  Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
   TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
-  Print("\n//** Mwalk: Ergebnis.\n");
   //Print("\n// pSetm_Error = (%d)", ErrorCheck());
   //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
 #endif
+  Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
   return(result);
 }
 
-// 07.11.2012
-// THE RANDOM WALK ALGORITHM  ideal Go, intvec* orig_M, intvec* target_M, ring baseRing
-ideal Mrwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, int pert_deg, ring baseRing)
+// THE RANDOM WALK ALGORITHM
+ideal Mrwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, int pert_deg,
+             int reduction, int printout)
 {
   BITSET save1 = si_opt_1; // save current options
-  //si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
-  //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
-  //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
+  if(reduction == 0)
+  {
+    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
+    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
+    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
+  }
   Set_Error(FALSE);
   Overflow_Error = FALSE;
@@ -5352 +5367 @@
 #endif
   nstep=0;
-  int i,nwalk,endwalks = 0;
-  int nV = baseRing->N;
+  int i,polylength,nwalk,endwalks = 0;
+  int nV = currRing->N;
 
   ideal Gomega, M, F, Gomega1, Gomega2, M1; //, F1;
   ring newRing;
-  ring XXRing = baseRing;
+  ring baseRing = currRing;
+  ring XXRing = currRing;
   intvec* ivNull = new intvec(nV);
   intvec* curr_weight = new intvec(nV);
@@ -5363 +5379 @@
   intvec* exivlp = Mivlp(nV);
   intvec* tmp_weight = new intvec(nV);
+  intvec* next_weight= new intvec(nV);
   for(i=0; i<nV; i++)
   {
@@ -5383 +5400 @@
 #endif
   rComplete(currRing);
-#ifdef CHECK_IDEAL_MWALK
-    idString(Go,"Go");
-#endif
 #ifdef TIME_TEST
   to = clock();
 #endif
-     if(orig_M->length() == nV)
-      {
-        newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
-      }
-      else
-      {
-        newRing = VMatrDefault(orig_M);
-      }
+  if(orig_M->length() == nV)
+  {
+    newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
+  }
+  else
+  {
+    newRing = VMatrDefault(orig_M);
+  }
   rChangeCurrRing(newRing);
-  ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
+  //ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
+  ideal G = idrMoveR(Go,baseRing,currRing);
   baseRing = currRing;
 #ifdef TIME_TEST
@@ -5412 +5427 @@
     to = clock();
 #endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(G,"G");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(G,"//** Mrwalk: G");
+    }
+//#endif
     Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
+    //polylength = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise
+    polylength = lengthpoly(Gomega);
 #ifdef TIME_TEST
     tif = tif + clock()-to; //time for computing initial form ideal
 #endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(Gomega,"Gomega");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 1)
+    {
+      idString(Gomega,"//** Mrwalk: Gomega");
+    }
+//#endif
 #ifndef  BUCHBERGER_ALG
     if(isNolVector(curr_weight) == 0)
     {
       hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
-    }
+    }   
     else
     {
@@ -5471 +5494 @@
 #endif
     idSkipZeroes(M);
-#ifdef CHECK_IDEAL_MWALK
-    PrintS("\n//** Mwalk: computed M.\n");
-    idString(M, "M");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(M, "//** Mrwalk: M");
+    }
+//#endif
     //change the ring to baseRing
     rChangeCurrRing(baseRing);
@@ -5484 +5509 @@
     to = clock();
 #endif
-    // 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
+    // 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
     F = MLifttwoIdeal(Gomega2, M1, G);
 #ifdef TIME_TEST
     tlift = tlift + clock() - to;
 #endif
-#ifdef CHECK_IDEAL_MWALK
-    idString(F, "F");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(F, "//** Mrwalk: F");
+    }
+//#endif
     idDelete(&Gomega2);
     idDelete(&M1);
@@ -5500 +5529 @@
 #ifdef TIME_TEST
     to = clock();
-#endif
-    //G = kStd(F1,NULL,testHomog,NULL,NULL,0,0,NULL);
-#ifdef TIME_TEST
     tstd = tstd + clock() - to;
 #endif
     idSkipZeroes(G);
-#ifdef CHECK_IDEAL_MWALK
-    idString(G, "G");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(G, "//** Mrwalk: G");
+    }
+//#endif
 #ifdef TIME_TEST
     to = clock();
 #endif
-    intvec* next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg);//next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
+    next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
+    if(polylength > 0)
+    {
+      //there is a polynomial in Gomega with at least 3 monomials,
+      //low-dimensional facet of the cone
+      delete next_weight;
+      next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg);
+    }
 #ifdef TIME_TEST
     tnw = tnw + clock() - to;
 #endif
-#ifdef PRINT_VECTORS
-    MivString(curr_weight, target_weight, next_weight);
-#endif
-    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)
+//#ifdef PRINT_VECTORS
+    if(printout > 0)
+    {
+      MivString(curr_weight, target_weight, next_weight);
+    }
+//#endif
+    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)
     {
 #ifdef CHECK_IDEAL_MWALK
@@ -5525 +5564 @@
 #endif
       Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 1)
+      {
+        idString(Gomega, "//** Mrwalk: Gomega");
+      }
+//#endif
       if(target_M->length() == nV)
       {
@@ -5536 +5581 @@
       Gomega1 = idrMoveR(Gomega, baseRing,currRing);
       idDelete(&Gomega);
-#ifdef CHECK_IDEAL_MWALK
-      idString(Gomega1, "Gomega");
-#endif
       M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
-#ifdef CHECK_IDEAL_MWALK
-      idString(M,"M");
-#endif
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 2)
+      {
+        idString(M,"//** Mrwalk: M");
+      }
+//#endif
       rChangeCurrRing(baseRing);
       M1 =  idrMoveR(M, newRing,currRing);
@@ -5549 +5594 @@
       idDelete(&Gomega1);
       F = MLifttwoIdeal(Gomega2, M1, G);
-#ifdef CHECK_IDEAL_MWALK
-      idString(F,"F");
-#endif
       idDelete(&Gomega2);
       idDelete(&M1);
@@ -5558 +5600 @@
       idDelete(&F);
       baseRing = currRing;
-      si_opt_1 = save1; //set original options, e. g. option(RedSB)
       idSkipZeroes(G);
 #ifdef TIME_TEST
       to = clock();
 #endif
- //     if(si_opt_1 == (Sy_bit(OPT_REDSB)))
-  //    {
-        //G = kInterRedCC(G,NULL); //reduce the Groebner basis <G> w.r.t. currRing, if option(redSB) is set
-  //    }
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 2)
+      {
+        idString(G,"//** Mrwalk: G");
+      }
+///#endif
+      if(si_opt_1 == (Sy_bit(OPT_REDSB)))
+      {
+        //G = kInterRedCC(G,NULL); //interreduce the Groebner basis <G> w.r.t. currRing
+      }
 #ifdef TIME_TEST
       tred = tred + clock() - to;
@@ -5573 +5620 @@
       delete next_weight;
       break;
-#ifdef CHECK_IDEAL_MWALK
-      PrintS("\n//** Mwalk: last cone.\n");
-#endif
-    }
-#ifdef CHECK_IDEAL_MWALK
-    PrintS("\n//** Mwalk: update weight vectors.\n");
-#endif
+    }
     for(i=nV-1; i>=0; i--)
     {
@@ -5587 +5628 @@
     delete next_weight;
   }
+  baseRing = currRing;
   rChangeCurrRing(XXRing);
   ideal result = idrMoveR(G,baseRing,currRing);
   idDelete(&G);
-/*#ifdef CHECK_IDEAL_MWALK
-  pDelete(&p);
-#endif*/
+  si_opt_1 = save1; //set original options, e. g. option(RedSB)
   delete tmp_weight;
   delete ivNull;
@@ -5599 +5639 @@
   delete last_omega;
 #endif
+  Print("\n//** Mrwalk: Groebner Walk took %d steps.\n", nstep);
 #ifdef TIME_TEST
-  Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
   TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
-  Print("\n//** Mwalk: Ergebnis.\n");
   //Print("\n// pSetm_Error = (%d)", ErrorCheck());
   //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
@@ -5749 +5788 @@
 // use kStd, if nP = 0, else call LastGB
 ideal Mpwalk(ideal Go, int op_deg, int tp_deg,intvec* curr_weight,
-             intvec* target_weight, int nP)
-{
+             intvec* target_weight, int nP, int reduction, int printout)
+{
+  BITSET save1 = si_opt_1; // save current options
+  if(reduction == 0)
+  {
+    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
+    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
+    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
+  }
   Set_Error(FALSE  );
   Overflow_Error = FALSE;
@@ -5788 +5834 @@
   ring XXRing = currRing;
 
-
   to = clock();
-  /* perturbs the original vector */
+  // perturbs the original vector
   if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
   {
@@ -5807 +5852 @@
       DefRingPar(curr_weight);
     else
-      rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung 1
+      rChangeCurrRing(VMrDefault(curr_weight));
 
     G = idrMoveR(Go, XXRing,currRing);
@@ -5822 +5867 @@
   ring HelpRing = currRing;
 
-  /* perturbs the target weight vector */
+  // perturbs the target weight vector
   if(tp_deg > 1 && tp_deg <= nV)
   {
@@ -5828 +5873 @@
       DefRingPar(target_weight);
     else
-      rChangeCurrRing(VMrDefault(target_weight)); // Aenderung 2
+      rChangeCurrRing(VMrDefault(target_weight));
 
     TargetRing = currRing;
@@ -5850 +5895 @@
     G = idrMoveR(ssG, TargetRing,currRing);
   }
-  /*
-    Print("\n// Perturbationwalkalg. vom Gradpaar (%d,%d):",op_deg,tp_deg);
-    ivString(curr_weight, "new sigma");
-    ivString(target_weight, "new tau");
-  */
+    if(printout > 0)
+    {
+      Print("\n//** Mpwalk: Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
+      ivString(curr_weight, "//** Mpwalk: new current weight");
+      ivString(target_weight, "//** Mpwalk: new target weight");
+    }
   while(1)
   {
     nstep ++;
     to = clock();
-    /* compute an initial form ideal of <G> w.r.t. the weight vector
-       "curr_weight" */
+    // compute an initial form ideal of <G> w.r.t. the weight vector
+    // "curr_weight"
     Gomega = MwalkInitialForm(G, curr_weight);
-
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 1)
+    {
+      idString(Gomega,"//** Mpwalk: Gomega");
+    }
+//#endif
 
 #ifdef ENDWALKS
-    if(endwalks == 1){
+    if(endwalks == 1)
+    {
       Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
       idElements(G, "G");
-      // idElements(Gomega, "Gw");
       headidString(G, "G");
-      //headidString(Gomega, "Gw");
     }
 #endif
@@ -5889 +5939 @@
       DefRingPar(curr_weight);
     else
-      rChangeCurrRing(VMrDefault(curr_weight)); //Aenderung 3
+      rChangeCurrRing(VMrDefault(curr_weight));
 
     newRing = currRing;
@@ -5910 +5960 @@
     tim = clock();
     to = clock();
-    /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */
+    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
 #ifdef  BUCHBERGER_ALG
     M = MstdhomCC(Gomega1);
@@ -5916 +5966 @@
     M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
     delete hilb_func;
-#endif // BUCHBERGER_ALG
+#endif
+//#ifdef CHECK_IDEAL_MWALK
+      if(printout > 2)
+      {
+        idString(M,"//** Mpwalk: M");
+      }
+//#endif
 
     if(endwalks == 1){
@@ -5928 +5984 @@
       tstd=tstd+clock()-to;
 
-    /* change the ring to oldRing */
+    // change the ring to oldRing
     rChangeCurrRing(oldRing);
     M1 =  idrMoveR(M, newRing,currRing);
     Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
-
-    //if(endwalks==1)  PrintS("\n// Lifting is working:..");
 
     to=clock();
@@ -5945 +5999 @@
       xtlift=clock()-to;
 
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)
+    {
+      idString(F,"//** Mpwalk: F");
+    }
+//#endif
+
     idDelete(&M1);
     idDelete(&Gomega2);
     idDelete(&G);
 
-    /* change the ring to newRing */
+    // change the ring to newRing
     rChangeCurrRing(newRing);
     F1 = idrMoveR(F, oldRing,currRing);
-
-    //if(endwalks==1)PrintS("\n// InterRed is working now:");
-
+    //G = idrMoveR(F,oldRing,currRing);
     to=clock();
-    /* reduce the Groebner basis <G> w.r.t. new ring */
+    PrintS("\n //** Mpwalk: reduce the Groebner basis.\n");
     G = kInterRedCC(F1, NULL);
     if(endwalks != 1)
@@ -5969 +6028 @@
 
     to=clock();
-    /* compute a next weight vector */
+    // compute a next weight vector
     next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
     tnw=tnw+clock()-to;
-#ifdef PRINT_VECTORS
-    MivString(curr_weight, target_weight, next_weight);
-#endif
+//#ifdef PRINT_VECTORS
+    if(printout > 0)
+    {
+      MivString(curr_weight, target_weight, next_weight);
+    }
+//#endif
 
     if(Overflow_Error == TRUE)
@@ -5998 +6060 @@
 
     delete next_weight;
-  }//while
+  }//end of while-loop
 
   if(tp_deg != 1)
@@ -6012 +6074 @@
         DefRingPar(orig_target);
       else
-        rChangeCurrRing(VMrDefault(orig_target)); //Aenderung
+        rChangeCurrRing(VMrDefault(orig_target));
 
     TargetRing=currRing;
@@ -6066 +6128 @@
     Eresult = idrMoveR(G, newRing,currRing);
   }
+  si_opt_1 = save1; //set original options, e. g. option(RedSB)
   delete ivNull;
   if(tp_deg != 1)
@@ -6080 +6143 @@
              tnw+xtnw);
 
-  Print("\n// pSetm_Error = (%d)", ErrorCheck());
-  Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
-#endif
+  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
+  //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
+#endif
+  Print("\n//** Mpwalk: Perturbation Walk took %d steps.\n", nstep);
+  return(Eresult);
+}
+
+/*******************************************************
+ * THE PERTURBATION WALK ALGORITHM WITH RANDOM ELEMENT *
+ *******************************************************/
+ideal Mprwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad,
+              int op_deg, int tp_deg, int nP, int reduction, int printout)
+{
+  BITSET save1 = si_opt_1; // save current options
+  if(reduction == 0)
+  {
+    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
+    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
+    //si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
+  }
+  Set_Error(FALSE);
+  Overflow_Error = FALSE;
+  //Print("// pSetm_Error = (%d)", ErrorCheck());
+
+  clock_t  tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
+  xtextra=0;
+  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
+  tinput = clock();
+
+  clock_t tim;
+
+  nstep = 0;
+  int i, ntwC=1, ntestw=1, polylength, nV = currRing->N;
+  int endwalks=0;
+
+  ideal Gomega, M, F, G, Gomega1, Gomega2, M1,F1,Eresult,ssG;
+  ring newRing, oldRing, TargetRing;
+  intvec* iv_M_dp;
+  intvec* iv_M_lp;
+  intvec* exivlp = Mivlp(nV);
+  intvec* curr_weight = new intvec(nV);
+  intvec* target_weight = new intvec(nV);
+  for(i=0; i<nV; i++)
+  {
+    (*curr_weight)[i] = (*orig_M)[i];
+    (*target_weight)[i] = (*target_M)[i];
+  }
+  intvec* orig_target = target_weight;
+  intvec* pert_target_vector = target_weight;
+  intvec* ivNull = new intvec(nV);
+  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
+#ifndef BUCHBERGER_ALG
+  intvec* hilb_func;
+#endif
+  intvec* next_weight;
+
+  // to avoid (1,0,...,0) as the target vector
+  intvec* last_omega = new intvec(nV);
+  for(i=nV-1; i>0; i--)
+    (*last_omega)[i] = 1;
+  (*last_omega)[0] = 10000;
+
+  ring XXRing = currRing;
+
+  to = clock();
+  // perturbs the original vector
+  if(orig_M->length() == nV)
+  {
+    if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
+    {
+      G = MstdCC(Go);
+      tostd = clock()-to;
+      if(op_deg != 1)
+      {
+        iv_M_dp = MivMatrixOrderdp(nV);
+        //ivString(iv_M_dp, "iv_M_dp");
+        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
+      }
+    }
+    else
+    {
+      //define ring order := (a(curr_weight),lp);
+      if (rParameter(currRing) != NULL)
+        DefRingPar(curr_weight);
+      else
+        rChangeCurrRing(VMrDefault(curr_weight));
+
+      G = idrMoveR(Go, XXRing,currRing);
+      G = MstdCC(G);
+      tostd = clock()-to;
+      if(op_deg != 1)
+      {
+        iv_M_dp = MivMatrixOrder(curr_weight);
+        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
+      }
+    }
+  }
+  else
+  {
+    rChangeCurrRing(VMatrDefault(orig_M));
+    G = idrMoveR(Go, XXRing,currRing);
+    G = MstdCC(G);
+    tostd = clock()-to;
+    if(op_deg != 1)
+    {
+      curr_weight = MPertVectors(G, orig_M, op_deg);
+    }
+  }
+
+  delete iv_dp;
+  if(op_deg != 1) delete iv_M_dp;
+
+  ring HelpRing = currRing;
+
+  // perturbs the target weight vector
+  if(target_M->length() == nV)
+  {
+    if(tp_deg > 1 && tp_deg <= nV)
+    {
+      if (rParameter(currRing) != NULL)
+        DefRingPar(target_weight);
+      else
+        rChangeCurrRing(VMrDefault(target_weight));
+
+      TargetRing = currRing;
+      ssG = idrMoveR(G,HelpRing,currRing);
+      if(MivSame(target_weight, exivlp) == 1)
+      {
+        iv_M_lp = MivMatrixOrderlp(nV);
+        //ivString(iv_M_lp, "iv_M_lp");
+        //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg);
+        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
+      }
+      else
+      {
+        iv_M_lp = MivMatrixOrder(target_weight);
+        //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg);
+        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
+      }
+      delete iv_M_lp;
+      pert_target_vector = target_weight;
+      rChangeCurrRing(HelpRing);
+      G = idrMoveR(ssG, TargetRing,currRing);
+    }
+  }
+  else
+  {
+    if(tp_deg > 1 && tp_deg <= nV)
+    {
+      rChangeCurrRing(VMatrDefault(target_M));
+      TargetRing = currRing;
+      ssG = idrMoveR(G,HelpRing,currRing);
+      target_weight = MPertVectors(ssG, target_M, tp_deg);
+    }
+  }
+  if(printout > 0)
+  {
+    Print("\n//** Mprwalk: Random Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
+    ivString(curr_weight, "//** Mprwalk: new current weight");
+    ivString(target_weight, "//** Mprwalk: new target weight");
+  }
+  while(1)
+  {
+    nstep ++;
+    to = clock();
+    // compute an initial form ideal of <G> w.r.t. the weight vector
+    // "curr_weight"
+    Gomega = MwalkInitialForm(G, curr_weight);
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 0)
+    {
+      idString(Gomega,"//** Mprwalk: Gomega");
+    }
+//#endif
+    polylength = lengthpoly(Gomega);
+#ifdef ENDWALKS
+    if(endwalks == 1)
+    {
+      Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
+      idElements(G, "G");
+      headidString(G, "G");
+    }
+#endif
+
+    tif = tif + clock()-to;
+
+#ifndef  BUCHBERGER_ALG
+    if(isNolVector(curr_weight) == 0)
+      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
+    else
+      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
+#endif // BUCHBERGER_ALG
+
+    oldRing = currRing;
+
+    if(target_M->length() == nV)
+    {
+      // define a new ring with ordering "(a(curr_weight),lp)
+      if (rParameter(currRing) != NULL)
+        DefRingPar(curr_weight);
+      else
+        rChangeCurrRing(VMrDefault(curr_weight));
+    }
+    else
+    {
+      rChangeCurrRing(VMatrRefine(target_M,curr_weight));
+    }
+    newRing = currRing;
+    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
+    PrintS("\n //** Mprwalk: Changed ring.\n");
+#ifdef ENDWALKS
+    if(endwalks==1)
+    {
+      Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
+      idElements(Gomega1, "Gw");
+      headidString(Gomega1, "headGw");
+      PrintS("\n// compute a rGB of Gw:\n");
+
+#ifndef  BUCHBERGER_ALG
+      ivString(hilb_func, "w");
+#endif
+    }
+#endif
+
+    tim = clock();
+    to = clock();
+    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
+#ifdef  BUCHBERGER_ALG
+    M = MstdhomCC(Gomega1);
+#else
+    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
+    delete hilb_func;
+#endif
+//#ifdef CHECK_IDEAL_MWALK
+    Print("\n //** Mprwalk: M");
+    if(printout > 2)
+    {
+      idString(M,"//** Mprwalk: M");
+    }
+//#endif
+
+    if(endwalks == 1)
+    {
+      xtstd = xtstd+clock()-to;
+#ifdef ENDWALKS
+      Print("\n// time for the last std(Gw)  = %.2f sec\n",
+            ((double) clock())/1000000 -((double)tim) /1000000);
+#endif
+    }
+    else
+      tstd=tstd+clock()-to;
+
+    /* change the ring to oldRing */
+    rChangeCurrRing(oldRing);
+    M1 =  idrMoveR(M, newRing,currRing);
+    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
+
+    to=clock();
+    /* 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 */
+    F = MLifttwoIdeal(Gomega2, M1, G);
+    if(endwalks != 1)
+      tlift = tlift+clock()-to;
+    else
+      xtlift=clock()-to;
+    Print("\n //** Mprwalk: F.\n");
+//#ifdef CHECK_IDEAL_MWALK
+    if(printout > 2)