===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v
retrieving revision 1.19
retrieving revision 1.31
diff -u -p -r1.19 -r1.31
--- OpenXM/src/k097/lib/minimal/minimal.k	2000/07/31 01:21:41	1.19
+++ OpenXM/src/k097/lib/minimal/minimal.k	2000/12/10 03:12:20	1.31
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.18 2000/07/30 02:26:25 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.30 2000/11/19 05:50:30 takayama Exp $ */
 #define DEBUG 1 
 Sordinary = false;
 /* If you run this program on openxm version 1.1.2 (FreeBSD),
@@ -7,6 +7,22 @@ Sordinary = false;
 */
 #define OFFSET 0 
 /* #define OFFSET 20*/
+Sverbose = false; /* Be extreamly verbose     */
+Sverbose2 = true; /* Don't be quiet and show minimal information */
+def Sprintln(s) {
+  if (Sverbose) Println(s);
+}
+def Sprint(s) {
+  if (Sverbose) Print(s);
+}
+def Sprintln2(s) {
+  if (Sverbose2) Println(s);
+}
+def Sprint2(s) {
+  if (Sverbose2) Print(s);
+  sm1(" [(flush)] extension ");
+}
+
 /* Test sequences. 
    Use load["minimal.k"];;
 
@@ -28,12 +44,25 @@ Sordinary = false;
      
 */
 
+/* We cannot use load command in the if statement. */
+load("lib/minimal/cohom.k");
 
-load("cohom.k");
 def load_tower() {
+  local ppp;
   if (Boundp("k0-tower.sm1.loaded")) {
   }else{
-    sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
+    if (Tag(GetPathName("k0-tower.sm1")) == 0) {
+      ppp = GetPathName("lib/minimal/k0-tower.sm1");
+      sm1(" [(parse) ppp pushfile ] extension ");
+    }else{
+      sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
+    }
+    if (Tag(GetPathName("new.sm1")) == 0) {
+      ppp = GetPathName("lib/minimal/new.sm1");
+      sm1(" [(parse) ppp pushfile ] extension ");
+    }else{
+      sm1(" [(parse) (new.sm1) pushfile ] extension ");
+    }
     sm1(" /k0-tower.sm1.loaded 1 def ");
   }
   sm1(" oxNoX ");
@@ -50,7 +79,20 @@ def Sgroebner(f) {
    sm1(" [f] groebner /FunctionValue set");
 }
 
+def Sinvolutive(f,w) {
+  local g,m;
+  if (IsArray(f[0])) {
+    m = NewArray(Length(f[0]));
+  }else{
+    m = [0];
+  }
+  g = Sgroebner(f);
+  /* This is a temporary code. */
+  sm1(" g 0 get { w m init_w<m>} map /FunctionValue set ");
+}
 
+
+
 def Error(s) {
   sm1(" s error ");
 }
@@ -83,6 +125,60 @@ def RingOf(f) {
   return(r);
 }
 
+def Ord_w_m(f,w,m) {
+  sm1(" f  w  m ord_w<m> { (universalNumber) dc } map /FunctionValue set ");
+}
+HelpAdd(["Ord_w_m",
+["Ord_w_m(f,w,m) returns the order of f with respect to w with the shift m.",
+ "Note that the order of the ring and the weight w must be the same.",
+ "When f is zero, it returns -intInfinity = -999999999.",
+ "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+ "          Ord_w_m([x*Dx+1,Dx^2+x^5],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+
+def Init_w_m(f,w,m) {
+  sm1(" f w m init_w<m> /FunctionValue set ");
+}
+HelpAdd(["Init_w_m",
+["Init_w_m(f,w,m) returns the initial of f with respect to w with the shift m.",
+ "Note that the order of the ring and the weight w must be the same.",
+ "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+ "          Init_w_m([x*Dx+1,Dx^2+x^5],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+
+def Max(v) {
+  local i,t,n;
+  n = Length(v);
+  if (n == 0) return(null);
+  t = v[0];
+  for (i=0; i<n; i++) {
+    if (v[i] > t) { t = v[i];}
+  }
+  return(t);
+}
+HelpAdd(["Max",
+["Max(v) returns the maximal element in v."]]);
+
+def Kernel(f) {
+  sm1(" [f] syz /FunctionValue set ");
+}
+def Syz(f) {
+  sm1(" [f] syz /FunctionValue set ");
+}
+HelpAdd(["Kernel",
+["Kernel(f) returns the syzygy of f.",
+ "Return value [b, c]: b is a set of generators of the syzygies of f",
+ "                   : c=[gb, backward transformation, syzygy without",
+ "                                                   dehomogenization",
+ "Example:  Weyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+ "          s=Kernel([x*Dx+1,Dx^2+x^5]); s[0]:"]]);
+/* cf. sm1_syz in cohom.k */
+def Gb(f) {
+  sm1(" [f] gb /FunctionValue set ");
+}
+HelpAdd(["Gb",
+["Gb(f) returns the Groebner basis of f.",
+ "cf. Kernel, Weyl."]]);
+
+
 /*  End of standard functions that should be moved to standard libraries. */
 def test0() {
   local f;
@@ -103,7 +199,6 @@ def test1() {
 }
 
   
-
 def Sweyl(v,w) {
   /* extern WeightOfSweyl ; */
   local ww,i,n;
@@ -193,8 +288,11 @@ def SresolutionFrameWithTower(g,opt) {
           }
         }
       }
-    }else{
+    } else if (IsNull(opt)){
+    } else {
       Println("Warning: option should be given by an array.");
+      Println(opt);
+      Println("--------------------------------------------");
     }
   }
 
@@ -229,7 +327,7 @@ def SresolutionFrameWithTower(g,opt) {
   /* -sugar is fine? */
   sm1(" setupEnvForResolution "); 
 
-  Println(g);
+  Sprintln(g);
   startingGB = g;
   /* ans = [ SzeroMap(g) ];  It has not been implemented. see resol1.withZeroMap */
   ans = [ ];
@@ -273,16 +371,22 @@ def NewPolynomialVector(size) {
 def  SturnOffHomogenization() {
   sm1("
     [(Homogenize)] system_variable 1 eq
-    { (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message
+    { Sverbose {
+      (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message } { } ifelse
       [(Homogenize) 0] system_variable
       [(ReduceLowerTerms) 0] system_variable
     } {  } ifelse
   ");
 }
+/* NOTE!!!  Be careful these changes of global environmental variables.
+   We should make a standard set of values and restore these values
+   after computation and interruption.  August 15, 2000.
+*/
 def  SturnOnHomogenization() {
   sm1("
     [(Homogenize)] system_variable 0 eq
-    { (Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.) message
+    { Sverbose {
+        (Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.) message } {  } ifelse
       [(Homogenize) 1] system_variable
       [(ReduceLowerTerms) 1] system_variable
     } {  } ifelse
@@ -330,7 +434,7 @@ def Sres0FrameWithSkelton(g) {
     si = pair[1,0];
     sj = pair[1,1];
     /* si g[i] + sj g[j] + \sum tmp[2][k] g[k] = 0 in res0 */
-    Print(".");
+    Sprint(".");
 
     t_syz = NewPolynomialVector(gLength);
     t_syz[i] = si;
@@ -338,7 +442,7 @@ def Sres0FrameWithSkelton(g) {
     syzAll[k] = t_syz;
   }
   t_syz = syzAll;
-  Print("Done. betti="); Println(betti);
+  Sprint("Done. betti="); Sprintln(betti);
   /* Println(g);  g is in a format such as 
     [e_*x^2 , e_*x*y , 2*x*Dx*h , ...]
     [e_*x^2 , e_*x*y , 2*x*Dx*h , ...]
@@ -358,6 +462,9 @@ def StotalDegree(f) {
   return(d0);
 }
 
+HelpAdd(["Sord_w",
+["Sord_w(f,w) returns the w-order of f",
+ "Example: Sord_w(x^2*Dx*Dy,[x,-1,Dx,1]):"]]);
 /* Sord_w(x^2*Dx*Dy,[x,-1,Dx,1]); */
 def Sord_w(f,w) {
   local neww,i,n;
@@ -391,8 +498,10 @@ def test_SinitOfArray() {
   f = [x^2+y^2+z^2, x*y+x*z+y*z, x*z^2+y*z^2, y^3-x^2*z - x*y*z+y*z^2,
        -y^2*z^2 + x*z^3 + y*z^3, -z^4];
   p=SresolutionFrameWithTower(f);
-  sm1_pmat(p); 
-  sm1_pmat(SgenerateTable(p[1]));
+  if (Sverbose) {
+    sm1_pmat(p); 
+    sm1_pmat(SgenerateTable(p[1]));
+  }
   return(p);
   frame = p[0];
   sm1_pmat(p[1]);
@@ -418,7 +527,7 @@ def SgenerateTable(tower) {
   local height, n,i,j, ans, ans_at_each_floor;
 
   /*
-  Print("SgenerateTable: tower=");Println(tower);  
+  Sprint("SgenerateTable: tower=");Sprintln(tower);  
   sm1(" print_switch_status "); */
   height = Length(tower);
   ans = NewArray(height);
@@ -503,17 +612,18 @@ def SlaScala(g,opt) {
         reductionTable_tmp;
   /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;
-  Print("WeightOfSweyl="); Println(WeightOfSweyl);
-  rf = SresolutionFrameWithTower(g,opt);
-  Print("rf="); sm1_pmat(rf);
+  Sprint("WeightOfSweyl="); Sprintln(WeightOfSweyl);
+  rf = SresolutionFrameWithTower(g,opt);  
+  Sprint("rf="); if (Sverbose) {sm1_pmat(rf);}
   redundant_seq = 1;   redundant_seq_ordinary = 1;
   tower = rf[1];
 
-  Println("Generating reduction table which gives an order of reduction.");
-  Print("WeghtOfSweyl="); Println(WeightOfSweyl);
-  Print("tower"); Println(tower);
+  Sprintln("Generating reduction table which gives an order of reduction.");
+  Sprint("WeghtOfSweyl="); Sprintln(WeightOfSweyl);
+  Sprint2("tower="); Sprintln2(tower);
   reductionTable = SgenerateTable(tower);
-  Print("reductionTable="); sm1_pmat(reductionTable);
+  Sprint2("reductionTable="); 
+  if (Sverbose || Sverbose2) {sm1_pmat(reductionTable);}
 
   skel = rf[2];
   redundantTable = SnewArrayOfFormat(rf[1]);
@@ -532,11 +642,12 @@ def SlaScala(g,opt) {
       while (SthereIs(reductionTable_tmp,strategy)) {
         i = SnextI(reductionTable_tmp,strategy,redundantTable,
                    skel,level,freeRes);
-        Println([level,i]);
+        Sprintln([level,i]);
         reductionTable_tmp[i] = -200000;
         if (reductionTable[level,i] == strategy) {
-           Print("Processing [level,i]= "); Print([level,i]);
-           Print("   Strategy = "); Println(strategy);
+           Sprint("Processing [level,i]= "); Sprint([level,i]);
+           Sprint("   Strategy = "); Sprintln(strategy);
+           Sprint2(strategy);
            if (level == 0) {
              if (IsNull(redundantTable[level,i])) {
                bases = freeRes[level];
@@ -562,9 +673,9 @@ if (Sordinary) {
 }else{
                   if (f[4] > f[5]) {
                     /* Zero in the gr-module */
-                    Print("v-degree of [org,remainder] = ");
-                    Println([f[4],f[5]]);
-                    Print("[level,i] = "); Println([level,i]);
+                    Sprint("v-degree of [org,remainder] = ");
+                    Sprintln([f[4],f[5]]);
+                    Sprint("[level,i] = "); Sprintln([level,i]);
                     redundantTable[level-1,place] = 0;
                   }else{
                     redundantTable[level-1,place] = redundant_seq;
@@ -596,6 +707,7 @@ if (Sordinary) {
     }
     strategy++;
   }
+  Sprintln2(" ");
   n = Length(freeRes);
   freeResV = SnewArrayOfFormat(freeRes);
   for (i=0; i<n; i++) {
@@ -643,9 +755,9 @@ def SnextI(reductionTable_tmp,strategy,redundantTable,
        }
      }
    }
-   Print("reductionTable_tmp=");
-   Println(reductionTable_tmp);
-   Println("See also reductionTable, strategy, level,i");
+   Sprint("reductionTable_tmp=");
+   Sprintln(reductionTable_tmp);
+   Sprintln("See also reductionTable, strategy, level,i");
    Error("SnextI: bases[i] or bases[j] is null for all combinations.");
 }
 
@@ -679,7 +791,7 @@ def SwhereInGB(f,tower) {
     q = MonomialPart(f);
     if (p == q) return(i);
   }
-  Println([f,tower]);
+  Sprintln([f,tower]);
   Error("whereInGB : [f,myset]: f could not be found in the myset.");      
 }
 def SunitOfFormat(pos,forms) {
@@ -733,7 +845,7 @@ def SwhereInTower(f,tower) {
     q = MonomialPart(f);
     if (p == q) return(i);
   }
-  Println([f,tower]);
+  Sprintln([f,tower]);
   Error("[f,tower]: f could not be found in the tower.");      
 }
 
@@ -745,23 +857,23 @@ def SpairAndReduction(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;
-  Println("SpairAndReduction:");
+  Sprintln("SpairAndReduction:");
 
   if (level < 1) Error("level should be >= 1 in SpairAndReduction.");
   p = skel[level,ii];
   myindex = p[0];  
   i = myindex[0]; j = myindex[1];
   bases = freeRes[level-1];
-  Println(["p and bases ",p,bases]);
+  Sprintln(["p and bases ",p,bases]);
   if (IsNull(bases[i]) || IsNull(bases[j])) {
-    Println([level,i,j,bases[i],bases[j]]);
+    Sprintln([level,i,j,bases[i],bases[j]]);
     Error("level, i, j : bases[i], bases[j]  must not be NULL.");
   }
 
   tower2 = StowerOf(tower,level-1);
   SsetTower(tower2);  
-  Println(["level=",level]);
-  Println(["tower2=",tower2]);
+  Sprintln(["level=",level]);
+  Sprintln(["tower2=",tower2]);
   /** sm1(" show_ring ");   */
 
   gi = Stoes_vec(bases[i]);
@@ -772,23 +884,23 @@ def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   sj = ssp[0,1];
   syzHead = si*es^i;
   /* This will be the head term, I think. But, double check. */
-  Println([si*es^i,sj*es^j]);
+  Sprintln([si*es^i,sj*es^j]);
 
-  Print("[gi, gj] = "); Println([gi,gj]);
-  sm1(" [(Homogenize)] system_variable message ");
-  Print("Reduce the element "); Println(si*gi+sj*gj);
-  Print("by  "); Println(bases);
+  Sprint("[gi, gj] = "); Sprintln([gi,gj]);
+  sm1(" [(Homogenize)] system_variable  ");
+  Sprint("Reduce the element "); Sprintln(si*gi+sj*gj);
+  Sprint("by  "); Sprintln(bases);
 
   tmp = Sreduction(si*gi+sj*gj, bases);
 
-  Print("result is "); Println(tmp);
+  Sprint("result is "); Sprintln(tmp);
 
   /* This is essential part for V-minimal resolution. */
   /* vdeg = SvDegree(si*gi+sj*gj,tower,level-1,ww); */
   vdeg = SvDegree(si*gi,tower,level-1,ww); 
   vdeg_reduced = SvDegree(tmp[0],tower,level-1,ww);  
-  Print("vdegree of the original = "); Println(vdeg);
-  Print("vdegree of the remainder = "); Println(vdeg_reduced);
+  Sprint("vdegree of the original = "); Sprintln(vdeg);
+  Sprint("vdegree of the remainder = "); Sprintln(vdeg_reduced);
 
   t_syz = tmp[2];
   si = si*tmp[1]+t_syz[i];
@@ -804,7 +916,7 @@ def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced];
   /* pos is the place to put syzygy at level. */
   /* pos2 is the place to put a new GB at level-1. */   
-  Println(ans);
+  Sprintln(ans);
   return(ans);
 }
 
@@ -896,7 +1008,7 @@ def Sbases_to_vec(bases,size) {
 
 HelpAdd(["Sminimal",
 ["It constructs the V-minimal free resolution by LaScala's algorithm",
- "option: \"homogenized\" (no automatic homogenization ",
+ "option: \"homogenized\" (no automatic homogenization)",
  "      : \"Sordinary\"   (no (u,v)-minimal resolution)",
  "Options should be given as an array.",
  "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);", 
@@ -913,7 +1025,7 @@ HelpAdd(["Sminimal",
 def Sminimal(g,opt) {
   local r, freeRes, redundantTable, reducer, maxLevel,
         minRes, seq, maxSeq, level, betti, q, bases, dr,
-        betti_levelplus, newbases, i, j,qq, tminRes;
+        betti_levelplus, newbases, i, j,qq, tminRes,bettiTable, ansSminimal;
   if (Length(Arglist) < 2) {
      opt = null;
   }
@@ -926,6 +1038,9 @@ def Sminimal(g,opt) {
   freeRes = r[0];
   redundantTable = r[1];
   reducer = r[2];
+  bettiTable = SbettiTable(redundantTable);
+  Sprintln2("BettiTable ------");
+  if (Sverbose || Sverbose2) {sm1_pmat(bettiTable);}
   minRes = SnewArrayOfFormat(freeRes);
   seq = 0;
   maxSeq = SgetMaxSeq(redundantTable);
@@ -935,12 +1050,12 @@ def Sminimal(g,opt) {
   }
   seq=maxSeq+1;
   while (seq > 1) {
-    seq--;
+    seq--;  Sprint2(seq);
     for (level = 0; level < maxLevel; level++) {
       betti = Length(freeRes[level]);
       for (q = 0; q<betti; q++) {
         if (redundantTable[level,q] == seq) {
-          Print("[seq,level,q]="); Println([seq,level,q]);
+          Sprint("[seq,level,q]="); Sprintln([seq,level,q]);
           if (level < maxLevel-1) {
             bases = freeRes[level+1];
             dr = reducer[level,q];
@@ -953,10 +1068,10 @@ def Sminimal(g,opt) {
             for (i=0; i<betti_levelplus; i++) {
               newbases[i] = 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);
+            Sprintln(["level, q =", level,q]);
+            Sprintln("bases="); if (Sverbose) {sm1_pmat(bases); }
+            Sprintln("dr="); if (Sverbose) {sm1_pmat(dr);}
+            Sprintln("newbases="); if (Sverbose) {sm1_pmat(newbases);}
             minRes[level+1] = newbases;
             freeRes = minRes;
 #ifdef DEBUG
@@ -966,7 +1081,7 @@ def Sminimal(g,opt) {
                 for (i=0; i<betti_levelplus; i++) {
                   if (!IsZero(newbases[i,qq])) {
                     Println(["[i,qq]=",[i,qq]," is not zero in newbases."]);
-                    Print("redundantTable ="); sm1_pmat(redundantTable[level]);
+                    Sprint("redundantTable ="); sm1_pmat(redundantTable[level]);
                     Error("Stop in Sminimal for debugging.");
                   }
                 }
@@ -979,8 +1094,24 @@ def Sminimal(g,opt) {
     }
    }
    tminRes = Stetris(minRes,redundantTable);
-   return([SpruneZeroRow(tminRes), tminRes,
-          [ minRes, redundantTable, reducer,r[3],r[4]],r[0],r[5]]);
+   ansSminimal = [SpruneZeroRow(tminRes), tminRes,
+                  [ minRes, redundantTable, reducer,r[3],r[4]],r[0],r[5]];
+   Sprintln2(" ");
+   Println("------------ Note -----------------------------");
+   Println("To get shift vectors, use Reparse and SgetShifts(resmat,w)");
+   Println("To get initial of the complex, use Reparse and Sinit_w(resmat,w)");
+   Println("0: minimal resolution, 3: Schreyer resolution ");
+   Println("------------ Resolution Summary  --------------");
+   Print("Betti numbers : "); 
+   Println(Join([Length(ansSminimal[0,0,0])],Map(ansSminimal[0],"Length")));
+   Print("Betti numbers of the Schreyer frame: ");
+   Println(Join([Length(ansSminimal[3,0,0])],Map(ansSminimal[3],"Length")));
+   Println("-----------------------------------------------");
+
+   sm1(" restoreEnvAfterResolution ");
+   Sordinary = false;
+
+   return(ansSminimal);
   /* r[4] is the redundantTable_ordinary */
   /* r[0] is the freeResolution */
   /* r[5] is the skelton */
@@ -1052,9 +1183,11 @@ def Stetris(freeRes,redundantTable) {
     }else{
       newbases = bases;
     }
-    Println(["level=", level]);
-    sm1_pmat(bases);
-    sm1_pmat(newbases);
+    Sprintln(["level=", level]);
+    if (Sverbose){
+      sm1_pmat(bases);
+      sm1_pmat(newbases);
+    }
 
     minRes[level] = newbases;
   }
@@ -1342,6 +1475,18 @@ HelpAdd(["IsExact_h",
  "cf. ReParse"
 ]]);
 
+def IsSameIdeal_h(ii,jj,v) {
+  local a;
+  v = ToString_array(v);
+  a = [ii,jj,v];
+  sm1(a," isSameIdeal_h /FunctionValue set ");
+}
+HelpAdd(["IsSameIdeal_h",
+["IsSameIdeal_h(ii,jj,var): bool",
+ "It checks the given ideals are the same or not in D<h> (homogenized Weyl algebra)",
+ "cf. ReParse"
+]]);
+
 def ReParse(a) {
   local c;
   if (IsArray(a)) {
@@ -1376,9 +1521,108 @@ def ScheckIfSchreyer(s) {
   */
   sm1(" [(Schreyer)] system_variable (universalNumber) dc /ss set ");
   if (ss != 1) {
-     Print("ScheckIfSchreyer: from "); Println(s);
+     Print("ScheckIfSchreyer: from "); Printl(s);
      Error("Schreyer order is not set.");
   }
   /* More check will be necessary. */
   return(true);
-}
\ No newline at end of file
+}
+
+def SgetShift(mat,w,m) {
+  local omat;
+  sm1(" mat { w m ord_w<m> {(universalNumber) dc}map } map /omat set");
+  return(Map(omat,"Max")); 
+}
+HelpAdd(["SgetShift",
+["SgetShift(mat,w,m) returns the shift vector of mat with respect to w with the shift m.",
+ "Note that the order of the ring and the weight w must be the same.",
+ "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ",
+ "          SgetShift([[x*Dx+1,Dx^2+x^5],[Poly(\"0\"),x],[x,x]],[\"x\",-1,\"Dx\",1],[2,0]):"]]);
+
+def SgetShifts(resmat,w) {
+  local i,n,ans,m0;
+  n = Length(resmat);
+  ans = NewArray(n+1);
+  m0 = NewArray(Length(resmat[0,0]));
+  ans[0] = m0;
+  for (i=0; i<n; i++) {
+    ans[i+1] = SgetShift(resmat[i],w,m0);
+    m0 = ans[i+1];
+  }
+  return(ans);
+}
+HelpAdd(["SgetShifts",
+["SgetShifts(resmat,w) returns the shift vectors of the resolution resmat",
+ " with respect to w with the shift m.",
+ "Note that the order of the ring and the weight w must be the same.",
+ "Zero row is not allowed.",
+ "Example:   a=Sannfs2(\"x^3-y^2\");",
+ "           b=a[0]; w = [\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1];",
+ "           Sweyl(\"x,y\",[w]); b = Reparse(b);",
+ "           SgetShifts(b,w):"]]);
+
+def Sinit_w(resmat,w) {
+  local shifts,ans,n,i,m,mat,j;
+  shifts = SgetShifts(resmat,w);
+  n = Length(resmat);
+  ans = NewArray(n);
+  for (i=0; i<n; i++) {
+    m = shifts[i];
+    mat = ScopyArray(resmat[i]);
+    for (j=0; j<Length(mat); j++) {
+      mat[j] = Init_w_m(mat[j],w,m);
+    }
+    ans[i] = mat;
+  }
+  return(ans);
+}
+HelpAdd(["Sinit_w",
+["Sinit_w(resmat,w) returns the initial of the complex resmat with respect to the weight w.",
+ "Example:   a=Sannfs2(\"x^3-y^2\");",
+ "           b=a[0]; w = [\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1];",
+ "           Sweyl(\"x,y\",[w]); b = Reparse(b);",
+ "           c=Sinit_w(b,w); c:"
+]]);
+
+/* This method does not work, because we have zero rows. 
+   Think about it later. */
+def SbettiTable(rtable) {
+  local ans,i,j,pp;
+  ans = SnewArrayOfFormat(rtable);
+  for (i=0; i<Length(rtable); i++) {
+    pp = 0;
+    for (j=0; j<Length(rtable[i]); j++) {
+       if (rtable[i,j] != 0) {pp = pp+1;}
+    }
+    ans[i] = pp;
+  }
+  return(ans);
+}
+
+def BfRoots1(G,V) {
+   local bb,ans;
+   sm1(" /BFparlist [ ] def ");
+   if (IsString(V)) {
+      sm1(" [ V to_records pop ] /V set ");
+   }else {
+     sm1(" V { toString } map /V set ");  
+   }
+   sm1(" /BFvarlist V def ");
+  
+   sm1(" G flatten { toString } map  /G set ");
+   sm1(" G V bfm /bb set ");
+   if (IsSm1Integer(bb)) {
+     return([ ]);
+   }
+   sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
+   return([ans, bb]);
+}
+
+HelpAdd(["BfRoots1",
+["BfRoots1(g,v) returns the integral roots of g with respect to the weight",
+ "vector (1,1,...,1) and the b-function itself",
+ "Example:  BfRoots1([x*Dx-2, y*Dy-3],[x,y]);"
+]]);
+
+
+