Changeset d853f2 in git

Timestamp:

Jan 6, 2015, 5:40:44 PM (9 years ago)

Author:

Oleksandr Motsak <motsak@…>

Branches:

(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')

Children:

7edaa7ea4b76e631c82942be8f69920eebe4a5a3

Parents:

404f45e7f2bbd4ead6ed034b30dbd5cd299dcb47

git-author:

Oleksandr Motsak <motsak@mathematik.uni-kl.de>2015-01-06 17:40:44+01:00

git-committer:

Oleksandr Motsak <motsak@mathematik.uni-kl.de>2015-01-06 17:56:39+01:00

Message:

Added grtranspose & grorder for lists of/and individual GRADED modules

File:

• Singular/LIB/schreyer.lib (modified) (7 diffs)

Singular/LIB/schreyer.lib

@@ -3080 +3080 @@
   print                                     (
       corner + "  " + head  + "  " + corner + newline +
-      corner + "  " + dash  + "  " + corner + newline +
+      corner + "  " + dash  +  " " + corner + newline +
                       middle                          +
-      corner + "  " + dash2 + "  " + corner + newline +
+      corner + "  " + dash2 +  " " + corner + newline +
       corner + "  " + foot  + "  " + corner );
 }
@@ -3269 +3269 @@
 
 
-proc grtranspose(def M, list #)
+proc reorder(module M, list #)
 "
-transpose graded module/map or a chain complex?...
+Reorder gens of M 
 "
 {
-  if( typeof( M ) == "list" )
-  {
-    if( size(M) == 0 ) { return (); }
-    list L; int i = 1; int j = size(M);
-    
-    if( size(#) > 0 )
-    {  L[j] = grtranspose(M[i], #); }
-    else {  L[j] = grtranspose(M[i]); }
-
-    j--; i++;
-    while( j > 0 )
-    {
-      L[j] = grtranspose(M[i]);
-      j--;
-      i++;
-    };
-    return (ordres(L));    
-  }
-
  // use initial grading if given
  if( size(#) == 1 )
@@ -3312 +3293 @@
    if( !homog( M ) ) { ERROR( "Cannot compute homogenizing grading!"); }
  }
-
+ 
+ 
  def w = attrib(M, "isHomog");
 
@@ -3325 +3307 @@
  }
 
- intvec d, p, pp;
+// view(M);
+
+ intvec d, p;
  (d, p) = order( M, w ); // grades & ordering permutation for N.  d[p] should be sorted!
  module N = module(M[p]);  // reorder the starting ideal/module
  attrib( N, "isHomog", w ); // set the grading
-
-
-// ""; "input: "; view(N);
-
- // and transpose now...
- d = d[p]; M = transpose(N); 
  
- attrib( M, "isHomog", -d ); // set the grading 
+ d = d[p];
+
+// view(N);
  
-// "0-gr.transpose??"; view( M );
+ return (N, d);
+}
+
+proc rreorder(module M, list #)
+"
+Reverse-order gens of M 
+"
+{
+ // 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;
+ }
+ 
+ // try to homogenize otherwise 
+ if( typeof(attrib( M, "isHomog")) == "string" )  
+ { // no such attribute? //   ERROR("No grading!");
+   if( !homog( M ) ) { ERROR( "Cannot compute homogenizing grading!"); }
+ }
+ 
+ 
+ def w = attrib(M, "isHomog");
+
+ // input should be graded:
+ if( typeof(w) != "intvec" )
+ {
+   ERROR("Non-graded input!");
+ }
+ if( nrows(M) != size(w) )
+ {
+   ERROR("Wrong grading!");
+ }
+
+// view(M);
+
+ intvec d, p;
+ (d, p) = order( M, w ); // grades & ordering permutation for N.  d[p] should be sorted!
+ p = p[size(p)..1]; // reverse!
+ module N = module(M[p]);  // reorder the starting ideal/module
+ attrib( N, "isHomog", w ); // set the grading
+ 
+ d = d[p];
+
+// view(N);
+ 
+ return (N, d);
+}
+
+
+proc grtranspose(def M) // , list #)
+"
+transpose graded module/map or a chain complex?...
+"
+{ // TODO: extra grading argument??? 
+  if( typeof( M ) == "list" )
+  {
+    if( size(M) == 0 ) { return (); }
+    
+    int j = size(M); 
+
+    int i = 1;
+    while( i < j )
+    {
+     if( size(M[i]) == 0 ){ break; }
+     i++;
+    }
+    
+    if( size(M[i]) == 0 ) { i--; }
+   
+    j = i; i = 1;
+    
+    list L; 
+    while( j > 0 )
+    {
+      L[j] = grtranspose(M[i]);
+      j--; i++;
+    };
+    return (L); // ?
+  }
+
+//////
+// "a";  view(M);
+ 
+ intvec d; module N;  
+ (N,d) = reorder(M); // , #); 
+ kill M;
+ module M = transpose(N);  
+ attrib( M, "isHomog", -d ); // set the grading
+
+// "b";  view(M);
+ 
+ kill N,d; module N; intvec d;
+ // reverse order:
+ (N,d) = rreorder(M); kill M;
+ module M = transpose(N); 
+ attrib( M, "isHomog", -d ); // set the grading
+
+//
+ kill N,d; module N; intvec d;
+ // reverse order:
+ (N,d) = rreorder(M); kill M;
+ module M = transpose(N); 
+ attrib( M, "isHomog", -d ); // set the grading
+ 
+ kill N,d; module N; intvec d;
+ // reverse order:
+ (N,d) = reorder(M);
+ 
+ kill M;
+ 
+
+ return (N);
+}
+
+
+
+proc grorder(def M) // , list #)
+"
+reorder graded module/map or a chain complex?...
+"
+{  
+  if( typeof(M) == "list" )
+  { // TODO: extra grading argument??? 
+    if( size(M) == 0 ) { return (); }
+    list L; 
+    int j = size(M); 
+
+    int i = 1;
+    while( i < j )
+    {
+     if( size(M[i]) == 0 ){ break; }
+     i++;
+    }
+    
+    if( size(M[i]) == 0 ) { i--; }
+    
+    while( i > 0 )
+    {
+//      "i: ", i;      "A"; view(M[i]);
+      L[i] = grorder(M[i]); 
+//      "B"; view(L[i]);
+      i--;
+    };
+
+    return (L); // ?
+  }
+
+// "a";  view(M);
+  
+ intvec d; module N;  
+ (N,d) = reorder(M); // , #); 
+ kill M;
+ module M = transpose(N);  
+ attrib( M, "isHomog", -d ); // set the grading
+
+// "b";  view(M);
+ 
+ kill N,d; module N; intvec d;
+ // reverse order:
+ (N,d) = rreorder(M); kill M;
+// int i = ncols(N); N = N[i..1]; d = d[i..1]; kill i;
+ module M = transpose(N); 
+ attrib( M, "isHomog", -d ); // set the grading
+
+// "c";  view(M);
+  
  return (M);
 }
@@ -3346 +3499 @@
 test/output reordering res(I) & gr-traspose of res 
 "
-{
+{ 
+  "==============================================";
   "";
   "=== Example: [", Name, "]";
@@ -3352 +3506 @@
 
   I = groebner(I); attrib(I, "isHomog", intvec(0));
-  " = Input degrees: "; view(I);
+//  " = Input degrees: "; view(I);
 
   " ! Resolution via 'mres': ";
@@ -3358 +3512 @@
   
   " = Non-minimal betti numbers: ";
-  print(betti(R, 0), "betti");  
-
-  list L = R; 
-//  " = Degrees of maps: "; view(L);
-
-  " = Degrees of (ordered) maps: "; 
-  def LL = ordres(L, intvec(0));
+  print(betti(R, 0), "betti");
+
+  list L = R ; // SRES_list(R); //  " = Degrees of maps: "; view(L);
+
+  view( L ); // MUST BE GRADED!!!
+
+  " = Degrees of (ordered) maps: ";
+  def LL = grorder(L); // MUST BE GRADED
   
-  "==============================================";
+  // ordres(L, intvec(0)); // ?
+
+  view( LL );
   
-  view( LL ); 
+  "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%";
+  list LLL = grtranspose( LL ); //  resolution RR = LLL;  
+  print(betti(LLL, 0), "betti");  
+  view( LLL );  
+  ""; //  "==============================================";
   
-  "==============================================";
-  list LLL = grtranspose( LL );
-  view( LLL );
-//  resolution RR = LLL; 
-  print(betti(LLL, 0), "betti"); 
-  "==============================================";
-
-"";
   kill L, R;
 }
 example
 { "EXAMPLE:"; echo = 2;
-
-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 = "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.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 = "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 = "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 = "k3.d11.g12"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;
-ideal I = 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2uv+5603xyuv-975y2uv-8680xzuv+3973yzuv-5795z2uv+2486xu2v+8136yu2v-34/87zu2v-11205u3v-10372x2v2-9501xyv2+2121y2v2+15744xzv2+455yzv2-97/107z2v2-25/118xuv2-10580yuv2+91/6zuv2-11835u2v2-68/93xv3-9566yv3+117/14zv3+13917uv3-67/44v4;
-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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-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 = "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 = "k3.d14.g19"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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/61yz4+83/98z5+9973x4u+67/101x3yu+25/19x2y2u+7517xy3u-59/117y4u-1/86x3zu-10/119x2yzu+2552xy2zu-2448y3zu-112/45x2z2u+35/71xyz2u+12328y2z2u+124/65xz3u-15531yz3u-39/16z4u+4678x3u2-44/103x2yu2-9303xy2u2+59/20y3u2-45/97x2zu2+2707xyzu2+65/61y2zu2+75/68xz2u2+2853yz2u2-12748z3u2-17/18x2u3-115/121xyu3+72/71y2u3-12194xzu3-14204yzu3-63/17z2u3+5772xu4-99/16yu4-51/43zu4+49/43u5-2588x4v+89/44x3yv+32/107x2y2v-117/76xy3v-84/115y4v+113/30x3zv-13/68x2yzv+15120xy2zv-59/28y3zv+61/52x2z2v+12390xyz2v+11436y2z2v+109/40xz3v+40/61yz3v+65/31z4v+12764x3uv+15885x2yuv-11299xy2uv-113/66y3uv+2887x2zuv-918xyzuv+12579y2zuv+39/10xz2uv-119/53yz2uv-62/115z3uv-10887x2u2v+115/122xyu2v-8863y2u2v-30/79xzu2v-26/5yzu2v+15294z2u2v-15701xu3v-11/19yu3v+25/14zu3v-48/55u4v+1341x3v2-4973x2yv2+55/117xy2v2-1787y3v2-115/57x2zv2+28/29xyzv2-184y2zv2+11738xz2v2-8375yz2v2-5962z3v2+52/55x2uv2+17/48xyuv2-103/52y2uv2-53/25xzuv2-101/3yzuv2-123/35z2uv2-14815xu2v2-103/14yu2v2-68/81zu2v2-81/22u3v2-121/56x2v3-12609xyv3+5555y2v3+8/17xzv3-741yzv3-73/103z2v3-12550xuv3-17/78yuv3+7817zuv3+6534u2v3-15384xv4+1807yv4-4677zv4-101/115uv4-83/19v5,-53/83x5+107/75x4y+26/51x3y2+45/109x2y3-3009xy4-27/61y5+16/85x4z-14859x3yz-20/27x2y2z+6326xy3z-4508y4z-10006x3z2-11979x2yz2+8579xy2z2+14669y3z2+67/79x2z3-2551xyz3-61/124y2z3+83/10xz4+12698yz4+15/113z5+123/86x4u-77/6x3yu+15113x2y2u+79/117xy3u-115/88y4u+101/95x3zu+56/13x2yzu-25/62xy2zu+1955y3zu+70/33x2z2u+7470xyz2u-2148y2z2u-14263xz3u-3962yz3u+47/35z4u+441x3u2+14944x2yu2-2/77xy2u2+68/23y3u2-121/43x2zu2-14321xyzu2-35/32y2zu2+34/21xz2u2+11645yz2u2+7131z3u2-3615x2u3-2748xyu3-15200y2u3+81/101xzu3+39/64yzu3-3967z2u3-10346xu4+55/18yu4-8/9zu4+33/68u5-13957x4v+31/116x3yv+58/81x2y2v+36/71xy3v-5706y4v-95/48x3zv+3214x2yzv+14729xy2zv+71/109y3zv+15365x2z2v-5109xyz2v-20/107y2z2v-6/11xz3v+74/55yz3v-76/11z4v+41/72x3uv+7215x2yuv-18/59xy2uv+1741y3uv+7698x2zuv-7299xyzuv+12127y2zuv+7/93xz2uv+71/8yz2uv-123/73z3uv+13657x2u2v-98/13xyu2v+11818y2u2v+22/23xzu2v-3038yzu2v+68/61z2u2v-7173xu3v-7460yu3v+3540zu3v+27/20u4v-37/41x3v2+20x2yv2+107/82xy2v2-2237y3v2+9827x2zv2+124/27xyzv2-18/5y2zv2-77/24xz2v2-10231yz2v2-32/7z3v2-11980x2uv2-36/35xyuv2+8618y2uv2+3174xzuv2-123/2yzuv2-117/38z2uv2+117/115xu2v2+70/3yu2v2-3144zu2v2+815u3v2-116/85x2v3+98/41xyv3-648y2v3-38/5xzv3-9/125yzv3+8710z2v3+48/31xuv3+101/109yuv3+70/11zuv3-51/4u2v3-76/59xv4-93/52yv4+15291zv4+4/55uv4+64/59v5,568x5+4355x4y+48/5x3y2+33/7x2y3-53/111xy4+1749y5-23/4x4z-98/69x3yz-47/56x2y2z-8519xy3z-5/113y4z+11488x3z2+79/21x2yz2+11/89xy2z2-64/83y3z2-15697x2z3-67/86xyz3+11545y2z3+3336xz4-106/39yz4+15466z5+15202x4u-34/63x3yu-121/72x2y2u+1/52xy3u+10800y4u+4993x3zu-55/112x2yzu-26/51xy2zu-114/125y3zu+113/2x2z2u-87/88xyz2u-91/107y2z2u-65/6xz3u+15415yz3u+1373z4u-27/86x3u2-76/93x2yu2+9/22xy2u2+16/91y3u2+10326x2zu2-61/84xyzu2-28/99y2zu2+87/14xz2u2-88/45yz2u2+60/59z3u2-13/60x2u3-10824xyu3-121/119y2u3+14919xzu3-81/25yzu3+11233z2u3+14676xu4-8474yu4+12211zu4+32/83u5+57/52x4v+10/13x3yv-277x2y2v-6961xy3v-4594y4v-13439x3zv-1/30x2yzv-118/43xy2zv-62/15y3zv+76/15x2z2v+3805xyz2v-26/15y2z2v+3081xz3v+662yz3v+13856z4v+107/30x3uv+6063x2yuv+100/37xy2uv+110/107y3uv-10346x2zuv-67/44xyzuv-93/29y2zuv+17/89xz2uv-57/104yz2uv-68/91z3uv+3804x2u2v-75/107xyu2v-11842y2u2v-103/57xzu2v-37/18yzu2v+10795z2u2v-90/31xu3v+14200yu3v+97/124zu3v+5256u4v+52/101x3v2-94/107x2yv2-12841xy2v2+77/72y3v2+93/74x2zv2+7033xyzv2+87/76y2zv2-15415xz2v2-15164yz2v2-14749z3v2+86/53x2uv2+14707xyuv2+9443y2uv2+118/5xzuv2-81/2yzuv2+43/57z2uv2+59/83xu2v2-121/79yu2v2+4449zu2v2-50/63u3v2+79/31x2v3+95/32xyv3+125/107y2v3-9165xzv3+3151yzv3+5006z2v3+45/19xuv3-5194yuv3-82/11zuv3+121/15u2v3-10265xv4-99/118yv4-3162zv4-16/29uv4-37/4v5;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 = "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 = "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 = "k3.d11.g12"; int @p=31991; ring R = (@p),(x,y,z,u,v), dp;ideal I = 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2uv+5603xyuv-975y2uv-8680xzuv+3973yzuv-5795z2uv+2486xu2v+8136yu2v-34/87zu2v-11205u3v-10372x2v2-9501xyv2+2121y2v2+15744xzv2+455yzv2-97/107z2v2-25/118xuv2-10580yuv2+91/6zuv2-11835u2v2-68/93xv3-9566yv3+117/14zv3+13917uv3-67/44v4;TestGRRes(Name, 2, I); kill R, Name, @p;
+  "";
+}
+