===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v
retrieving revision 1.5
retrieving revision 1.10
diff -u -p -r1.5 -r1.10
--- OpenXM/src/k097/lib/minimal/minimal.k	2000/05/05 08:13:49	1.5
+++ OpenXM/src/k097/lib/minimal/minimal.k	2000/05/07 02:10:44	1.10
@@ -1,10 +1,13 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.4 2000/05/04 11:05:20 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.9 2000/05/06 13:41:12 takayama Exp $ */
 #define DEBUG 1 
 /* #define ORDINARY 1 */
 /* If you run this program on openxm version 1.1.2 (FreeBSD),
    make a symbolic link by the command
    ln -s /usr/bin/cpp /lib/cpp
 */
+#define OFFSET 0 
+#define TOTAL_STRATEGY
+/* #define OFFSET 20*/
 /* Test sequences. 
    Use load["minimal.k"];;
 
@@ -34,6 +37,7 @@ def load_tower() {
     sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
     sm1(" /k0-tower.sm1.loaded 1 def ");
   }
+  sm1(" oxNoX ");
 }
 load_tower();
 SonAutoReduce = true;
@@ -336,11 +340,21 @@ def test_SinitOfArray() {
 
 /* f is assumed to be a monomial with toes. */
 def Sdegree(f,tower,level) {
-  local i;
+  local i,ww, wd;
+  /* extern WeightOfSweyl; */
+  ww = WeightOfSweyl;
   f = Init(f);
   if (level <= 1) return(StotalDegree(f));
   i = Degree(f,es);
-  return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1));
+#ifdef TOTAL_STRATEGY
+  return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1)); 
+#endif
+  /* Strategy must be compatible with ordering.  */
+  /* Weight vector must be non-negative, too.  */
+  /* See Sdegree, SgenerateTable, reductionTable. */
+  wd = Sord_w(f,ww);
+  return(wd+Sdegree(tower[level-2,i],tower,level-1));
+    
 }
 
 def SgenerateTable(tower) {
@@ -351,7 +365,8 @@ def SgenerateTable(tower) {
     n = Length(tower[i]);
     ans_at_each_floor=NewArray(n);
     for (j=0; j<n; j++) {
-      ans_at_each_floor[j] = Sdegree(tower[i,j],tower,i+1)-(i+1);
+      ans_at_each_floor[j] = Sdegree(tower[i,j],tower,i+1)-(i+1)
+                            + OFFSET;
       /* Println([i,j,ans_at_each_floor[j]]); */
     }
     ans[i] = ans_at_each_floor;
@@ -427,7 +442,7 @@ def SlaScala(g) {
         reductionTable_tmp;
   /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;
-  Print("WeghtOfSweyl="); Println(WeightOfSweyl);
+  Print("WeightOfSweyl="); Println(WeightOfSweyl);
   rf = SresolutionFrameWithTower(g);
   redundant_seq = 1;   redundant_seq_ordinary = 1;
   tower = rf[1];
@@ -1024,10 +1039,39 @@ def Sannfs(f,v) {
 def Sannfs2(f) {
   local p,pp;
   p = Sannfs(f,"x,y");
+  sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set ");
 /*
   Sweyl("x,y",[["x",1,"y",1,"Dx",1,"Dy",1,"h",1],
                ["x",-1,"y",-1,"Dx",1,"Dy",1]]); */
-  Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
+  /* Sweyl("x,y",[["x",1,"y",1,"Dx",1,"Dy",1,"h",1]]); */
+
+  Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); 
+  pp = Map(p,"Spoly");
+  return(Sminimal_v(pp));
+  /* return(Sminimal(pp)); */
+}
+
+HelpAdd(["Sannfs2",
+["Sannfs2(f) constructs the V-minimal free resolution for the weight (-1,1)",
+ "of the Laplace transform of the annihilating ideal of the polynomial f in x,y.",
+ "See also Sminimal_v, Sannfs3.",
+ "Example: a=Sannfs2(\"x^3-y^2\");",
+ "         b=a[0]; sm1_pmat(b);",
+ "         b[1]*b[0]:",
+ "Example: a=Sannfs2(\"x*y*(x-y)*(x+y)\");",
+ "         b=a[0]; sm1_pmat(b);",
+ "         b[1]*b[0]:"
+]]);
+
+/* Do not forget to turn on TOTAL_STRATEGY */ 
+def Sannfs2_laScala(f) {
+  local p,pp;
+  p = Sannfs(f,"x,y");
+  /*   Do not make laplace transform. 
+    sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set ");
+    p = [p];
+  */
+  Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); 
   pp = Map(p[0],"Spoly");
   return(Sminimal(pp));
 }
@@ -1035,11 +1079,20 @@ def Sannfs2(f) {
 def Sannfs3(f) {
   local p,pp;
   p = Sannfs(f,"x,y,z");
+  sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
   Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
-  pp = Map(p[0],"Spoly");
-  return(Sminimal(pp));
+  pp = Map(p,"Spoly");
+  return(Sminimal_v(pp));
 }
 
+HelpAdd(["Sannfs3",
+["Sannfs3(f) constructs the V-minimal free resolution for the weight (-1,1)",
+ "of the Laplace transform of the annihilating ideal of the polynomial f in x,y,z.",
+ "See also Sminimal_v, Sannfs2.",
+ "Example: a=Sannfs3(\"x^3-y^2*z^2\");",
+ "         b=a[0]; sm1_pmat(b);",
+ "         b[1]*b[0]: b[2]*b[1]:"]]);
+
 /*
   The betti numbers of most examples are 2,1. (0-th and 1-th).
   a=Sannfs2("x*y*(x+y-1)"); ==> The betti numbers are 3, 2. 
@@ -1050,13 +1103,13 @@ def Sannfs3(f) {
      
 
 
-/*  The below is under construction. */
+/*  The below does not use LaScala-Stillman's algorithm. */
 def Sschreyer(g) {
   local rf, tower, reductionTable, skel, redundantTable, bases,
         strategy, maxOfStrategy, height, level, n, i,
         freeRes,place, f, reducer,pos, redundant_seq,bettiTable,freeResV,ww,
         redundantTable_ordinary, redundant_seq_ordinary,
-        reductionTable_tmp,c2,ii,nn;
+        reductionTable_tmp,c2,ii,nn, m,ii, jj, reducerBase;
   /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;
   Print("WeghtOfSweyl="); Println(WeightOfSweyl);
@@ -1121,19 +1174,49 @@ def Sschreyer(g) {
                   /* i must be equal to f[2], I think. Double check. */
 
                   /* Correction Of Constant */
-                  c2 = f[6];
+                  /* Correction of syzygy */
+                  c2 = f[6];  /* or -f[6]?  Double check. */
+                  Print("c2="); Println(c2);
                   nn = Length(bases);
                   for (ii=0; ii<nn;ii++) {
-                     if (ii != place) {
-                       bases[ii] = bases[ii]*c2;
+                     if ((ii != i) && (! IsNull(bases[ii]))) {
+                       m = Length(bases[ii]);
+                       for (jj=0; jj<m; jj++) {
+                         if (jj != place) {
+                           bases[ii,jj] = bases[ii,jj]*c2;
+                         }
+                       } 
                      }
                   }
 
+                  Print("Old freeRes[level] = "); sm1_pmat(freeRes[level]);
                   freeRes[level] = bases;
-                  /* bases = freeRes[level-1];
-                     bases[place] = f[0];
-                     freeRes[level-1] = bases;  It is already set. */
-                  reducer[level-1,place] = f[1];
+                  Print("New freeRes[level] = "); sm1_pmat(freeRes[level]);
+
+                 /* Update the freeRes[level-1] */
+                  Print("Old freeRes[level-1] = "); sm1_pmat(freeRes[level-1]);
+                  bases = freeRes[level-1];
+                  bases[place] = f[0];
+                  freeRes[level-1] = bases; 
+                  Print("New freeRes[level-1] = "); sm1_pmat(freeRes[level-1]);
+
+                  reducer[level-1,place] = f[1]-SunitOfFormat(place,f[1]);
+                   /* This reducer is different from that of SlaScala(). */
+
+                  reducerBasis = reducer[level-1];
+                  nn = Length(reducerBasis);
+                  for (ii=0; ii<nn;ii++) {
+                     if ((ii != place) && (! IsNull(reducerBasis[ii]))) {
+                       m = Length(reducerBasis[ii]);
+                       for (jj=0; jj<m; jj++) {
+                         if (jj != place) {
+                           reducerBasis[ii,jj] = reducerBasis[ii,jj]*c2;
+                         }
+                       } 
+                     }
+                  }
+                  reducer[level-1] = reducerBasis;
+
                }else{
                   /* redundantTable[level,i] = 0; */
                   bases = freeRes[level];
@@ -1143,6 +1226,33 @@ def Sschreyer(g) {
              }  /* end of level >= 1 */
           }
     } /* i loop */
+
+    /* Triangulate reducer */
+    if (level >= 1) {
+      Println(" ");
+      Print("Triangulating reducer at level "); Println(level-1);
+      Println("freeRes[level]="); sm1_pmat(freeRes[level]);
+      reducerBase = reducer[level-1];
+      Print("reducerBase=");  Println(reducerBase);
+      Println("Compare freeRes[level] and reducerBase (put -1)");
+      m = Length(reducerBase);
+      for (ii=m-1; ii>=0; ii--) {
+        if (!IsNull(reducerBase[ii])) {
+           for (jj=ii-1; jj>=0; jj--) {
+             if (!IsNull(reducerBase[jj])) {
+              if (!IsZero(reducerBase[jj,ii])) {
+                /* reducerBase[ii,ii] should be always constant. */  
+                reducerBase[jj] = reducerBase[ii,ii]*reducerBase[jj]-reducerBase[jj,ii]*reducerBase[ii];
+              }
+             }
+           }
+         }
+       }
+       Println("New reducer");
+       sm1_pmat(reducerBase);
+       reducer[level-1] = reducerBase;
+    }
+
   } /* level loop */
   n = Length(freeRes);
   freeResV = SnewArrayOfFormat(freeRes);
@@ -1151,6 +1261,18 @@ def Sschreyer(g) {
     bases = Sbases_to_vec(bases,bettiTable[i]);
     freeResV[i] = bases;
   }
+
+  /* Mark the non-redundant elements. */
+  for (i=0; i<n; i++) {
+    m = Length(redundantTable[i]);
+    for (jj=0; jj<m; jj++) {
+      if (IsNull(redundantTable[i,jj])) {
+        redundantTable[i,jj] = 0;
+      }
+    }
+  }
+
+
   return([freeResV, redundantTable,reducer,bettiTable,redundantTable_ordinary]);
 }
 
@@ -1158,7 +1280,7 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   local i, j, myindex, p, bases, tower2, gi, gj,
        si, sj, tmp, t_syz, pos, ans, ssp, syzHead,pos2,
        vdeg,vdeg_reduced,n,c2;
-  Println("SpairAndReduction2:");
+  Println("SpairAndReduction2 : -------------------------");
 
   if (level < 1) Error("level should be >= 1 in SpairAndReduction.");
   p = skel[level,ii];
@@ -1193,6 +1315,11 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   tmp = Sreduction(si*gi+sj*gj, bases);
 
   Print("result is "); Println(tmp);
+  if (!IsZero(tmp[0])) {
+    Print("Error: base = ");
+    Println(Map(bases,"Stoes_vec"));
+    Error("SpairAndReduction2: the remainder should be zero. See tmp. tower2. show_ring.");
+  }
   t_syz = tmp[2];
   si = si*tmp[1]+t_syz[i];
   sj = sj*tmp[1]+t_syz[j];
@@ -1203,15 +1330,18 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   /* tmp[0] must be zero */
   n = Length(t_syz);
   for (i=0; i<n; i++) {
-     if (IsConstant(t_syz[i])) {
+     if (IsConstant(t_syz[i])){
+      if (!IsZero(t_syz[i])) {
        if (IsNull(redundantTable[level-1,i])) {
          /* i must equal to pos2 below. */
          c2 = -t_syz[i];
-         tmp[0] = freeRes[level-1,i];
+         tmp[0] = c2*Stoes_vec(freeRes[level-1,i]);
          t_syz[i] = 0;
+         /* tmp[0] = t_syz . g */
          /* break; does not work. Use */
          i = n;
        }
+      }
      }
   }
 
@@ -1228,5 +1358,194 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   /* pos is the place to put syzygy at level. */
   /* pos2 is the place to put a new GB at level-1. */   
   Println(ans);
+  Println("  ");
   return(ans);
+}
+
+HelpAdd(["Sminimal_v",
+["It constructs the V-minimal free resolution from the Schreyer resolution",
+ "step by step.",
+ "Example:   Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);", 
+ "          v=[[2*x*Dx + 3*y*Dy+6, 0],",
+ "             [3*x^2*Dy + 2*y*Dx, 0],",
+ "             [0,  x^2+y^2],",
+ "             [0,  x*y]];",
+ "         a=Sminimal_v(v);",
+ "         sm1_pmat(a[0]); b=a[0]; b[1]*b[0]:",
+ "Note:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution."]]);
+
+
+def Sminimal_v(g) {
+  local r, freeRes, redundantTable, reducer, maxLevel,
+        minRes, seq, maxSeq, level, betti, q, bases, dr,
+        betti_levelplus, newbases, i, j,qq,tminRes;
+  r = Sschreyer(g);
+  sm1_pmat(r);
+  Debug_Sminimal_v = r;
+  Println(" Return value of Schreyer(g) is set to Debug_Sminimal_v");
+  /* Should I turn off the tower?? */
+  freeRes = r[0];
+  redundantTable = r[1];
+  reducer = r[2];
+  minRes = SnewArrayOfFormat(freeRes);
+  seq = 0;
+  maxSeq = SgetMaxSeq(redundantTable);
+  maxLevel = Length(freeRes);
+  for (level = 0; level < maxLevel; level++) {
+    minRes[level] = freeRes[level];
+  }
+  for (level = 0; level < maxLevel; level++) {
+      betti = Length(freeRes[level]);
+      for (q = betti-1; q>=0; q--) {
+        if (redundantTable[level,q] > 0) {
+          Print("[seq,level,q]="); Println([seq,level,q]);
+          if (level < maxLevel-1) {
+            bases = freeRes[level+1];
+            dr = reducer[level,q];
+            /* dr[q] = -1;  We do not need this in our reducer format. */
+            /* dr[q] should be a non-zero constant. */
+            newbases = SnewArrayOfFormat(bases);
+            betti_levelplus = Length(bases);
+            /*
+               bases[i,j] ---> bases[i,j]+bases[i,q]*dr[j]
+            */
+            for (i=0; i<betti_levelplus; i++) {
+              newbases[i] = dr[q]*bases[i] - bases[i,q]*dr;
+            }
+            Println(["level, q =", level,q]);
+            Println("bases="); sm1_pmat(bases); 
+            Println("dr="); sm1_pmat(dr);
+            Println("newbases="); sm1_pmat(newbases);
+            minRes[level+1] = newbases;
+            freeRes = minRes;
+#ifdef DEBUG
+            for (qq=q; qq<betti; qq++) {
+                for (i=0; i<betti_levelplus; i++) {
+                  if ((!IsZero(newbases[i,qq])) && (redundantTable[level,qq] >0)) {
+                    Println(["[i,qq]=",[i,qq]," is not zero in newbases."]);
+                    Print("redundantTable ="); sm1_pmat(redundantTable[level]);
+                    Error("Stop in Sminimal for debugging.");
+                  }
+                }
+            }
+#endif
+          }
+        }
+      }
+   }
+   tminRes = Stetris(minRes,redundantTable);
+   return([SpruneZeroRow(tminRes), tminRes,
+          [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]);
+  /* r[4] is the redundantTable_ordinary */
+  /* r[0] is the freeResolution */
+}  
+
+/* Sannfs2("x*y*(x-y)*(x+y)"); is a test problem */
+/* x y (x+y-1)(x-2),  x^3-y^2, x^3 - y^2 z^2,
+   x y z (x+y+z-1) seems to be interesting, because the first syzygy
+  contains 1.
+*/
+
+def CopyArray(m) {
+  local ans,i,n;
+  if (IsArray(m)) {
+     n = Length(m);
+     ans = NewArray(n);
+     for (i=0; i<n; i++) {
+       ans[i] = CopyArray(m[i]);
+     }
+     return(ans);
+  }else{
+     return(m);
+  }
+}
+HelpAdd(["CopyArray",
+["It duplicates the argument array recursively.",
+ "Example: m=[1,[2,3]];",
+ "         a=CopyArray(m); a[1] = \"Hello\";",
+ "         Println(m); Println(a);"]]);
+
+def IsZeroVector(m) {
+  local n,i;
+  n = Length(m);
+  for (i=0; i<n; i++) {
+    if (!IsZero(m[i])) { 
+      return(false);
+    }
+  }
+  return(true);
+}
+
+def SpruneZeroRow(res) {
+  local minRes, n,i,j,m, base,base2,newbase,newbase2, newMinRes;
+
+  minRes = CopyArray(res);
+  n = Length(minRes);
+  for (i=0; i<n; i++) {
+    base = minRes[i];
+    m = Length(base);
+    if (i != n-1) {
+      base2 = minRes[i+1];
+      base2 = Transpose(base2);
+    }
+    newbase = [ ];
+    newbase2 = [ ];
+    for (j=0; j<m; j++) {
+      if (!IsZeroVector(base[j])) {
+        newbase = Append(newbase,base[j]);
+        if (i != n-1) {
+          newbase2 = Append(newbase2,base2[j]);
+        }
+      }
+    }
+    minRes[i] = newbase;
+    if (i != n-1) {
+      if (newbase2 == [ ]) {
+        minRes[i+1] = [ ];
+      }else{
+        minRes[i+1] = Transpose(newbase2);
+      }
+    }
+  }
+  
+  newMinRes = [ ];
+  n = Length(minRes);
+  i = 0;
+  while (i < n ) {
+    base = minRes[i];
+    if (base == [ ]) {
+      i = n; /* break; */
+    }else{
+      newMinRes = Append(newMinRes,base);
+    }
+    i++;
+  }
+  return(newMinRes);
+}
+
+def testAnnfs2(f) {
+  local a,i,n;
+  a = Sannfs2(f);
+  b=a[0];
+  n = Length(b);
+  Println("------ V-minimal free resolution -----");
+  sm1_pmat(b);
+  Println("----- Is it complex?  ---------------");
+  for (i=0; i<n-1; i++) {
+    Println(b[i+1]*b[i]);
+  }
+  return(a);
+}
+def testAnnfs3(f) {
+  local a,i,n;
+  a = Sannfs3(f);
+  b=a[0];
+  n = Length(b);
+  Println("------ V-minimal free resolution -----");
+  sm1_pmat(b);
+  Println("----- Is it complex?  ---------------");
+  for (i=0; i<n-1; i++) {
+    Println(b[i+1]*b[i]);
+  }
+  return(a);
 }