===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v
retrieving revision 1.7
retrieving revision 1.10
diff -u -p -r1.7 -r1.10
--- OpenXM/src/k097/lib/minimal/minimal.k	2000/05/06 10:35:33	1.7
+++ OpenXM/src/k097/lib/minimal/minimal.k	2000/05/07 02:10:44	1.10
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.6 2000/05/06 07:58:37 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),
@@ -1044,12 +1044,25 @@ def Sannfs2(f) {
   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,"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;
@@ -1072,6 +1085,14 @@ def Sannfs3(f) {
   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. 
@@ -1153,11 +1174,12 @@ def Sschreyer(g) {
                   /* i must be equal to f[2], I think. Double check. */
 
                   /* Correction Of Constant */
+                  /* 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) && (! IsNull(bases[ii]))) {
+                     if ((ii != i) && (! IsNull(bases[ii]))) {
                        m = Length(bases[ii]);
                        for (jj=0; jj<m; jj++) {
                          if (jj != place) {
@@ -1178,7 +1200,23 @@ def Sschreyer(g) {
                   freeRes[level-1] = bases; 
                   Print("New freeRes[level-1] = "); sm1_pmat(freeRes[level-1]);
 
-                  reducer[level-1,place] = f[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];
@@ -1193,15 +1231,18 @@ def Sschreyer(g) {
     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[jj] = reducerBase[jj]-reducerBase[jj,ii]*reducerBase[ii];
+                /* reducerBase[ii,ii] should be always constant. */  
+                reducerBase[jj] = reducerBase[ii,ii]*reducerBase[jj]-reducerBase[jj,ii]*reducerBase[ii];
               }
              }
            }
@@ -1321,10 +1362,23 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   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;
+        betti_levelplus, newbases, i, j,qq,tminRes;
   r = Sschreyer(g);
   sm1_pmat(r);
   Debug_Sminimal_v = r;
@@ -1348,14 +1402,15 @@ def Sminimal_v(g) {
           if (level < maxLevel-1) {
             bases = freeRes[level+1];
             dr = reducer[level,q];
-            dr[q] = -1;
+            /* 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] = bases[i] + bases[i,q]*dr;
+              newbases[i] = dr[q]*bases[i] - bases[i,q]*dr;
             }
             Println(["level, q =", level,q]);
             Println("bases="); sm1_pmat(bases); 
@@ -1364,26 +1419,133 @@ def Sminimal_v(g) {
             minRes[level+1] = newbases;
             freeRes = minRes;
 #ifdef DEBUG
-/*  Do it later. 
-            for (qq=0; qq<betti; qq++) {
+            for (qq=q; qq<betti; qq++) {
                 for (i=0; i<betti_levelplus; i++) {
-                  if (!IsZero(newbases[i,qq])) {
+                  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
           }
         }
       }
    }
-   return([Stetris(minRes,redundantTable),
+   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);
+}