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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.5 and 1.6

version 1.5, 2000/05/05 08:13:49 version 1.6, 2000/05/06 07:58:37
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Line 1 
 /* $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 1.5 2000/05/05 08:13:49 takayama Exp $ */
 #define DEBUG 1  #define DEBUG 1
 /* #define ORDINARY 1 */  /* #define ORDINARY 1 */
 /* If you run this program on openxm version 1.1.2 (FreeBSD),  /* If you run this program on openxm version 1.1.2 (FreeBSD),
    make a symbolic link by the command     make a symbolic link by the command
    ln -s /usr/bin/cpp /lib/cpp     ln -s /usr/bin/cpp /lib/cpp
 */  */
   #define OFFSET 0
   #define TOTAL_STRATEGY
   /* #define OFFSET 20*/
 /* Test sequences.  /* Test sequences.
    Use load["minimal.k"];;     Use load["minimal.k"];;
   
Line 336  def test_SinitOfArray() {
Line 339  def test_SinitOfArray() {
   
 /* f is assumed to be a monomial with toes. */  /* f is assumed to be a monomial with toes. */
 def Sdegree(f,tower,level) {  def Sdegree(f,tower,level) {
   local i;    local i,ww, wd;
     /* extern WeightOfSweyl; */
     ww = WeightOfSweyl;
   f = Init(f);    f = Init(f);
   if (level <= 1) return(StotalDegree(f));    if (level <= 1) return(StotalDegree(f));
   i = Degree(f,es);    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) {  def SgenerateTable(tower) {
Line 351  def SgenerateTable(tower) {
Line 364  def SgenerateTable(tower) {
     n = Length(tower[i]);      n = Length(tower[i]);
     ans_at_each_floor=NewArray(n);      ans_at_each_floor=NewArray(n);
     for (j=0; j<n; j++) {      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]]); */        /* Println([i,j,ans_at_each_floor[j]]); */
     }      }
     ans[i] = ans_at_each_floor;      ans[i] = ans_at_each_floor;
Line 427  def SlaScala(g) {
Line 441  def SlaScala(g) {
         reductionTable_tmp;          reductionTable_tmp;
   /* extern WeightOfSweyl; */    /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;    ww = WeightOfSweyl;
   Print("WeghtOfSweyl="); Println(WeightOfSweyl);    Print("WeightOfSweyl="); Println(WeightOfSweyl);
   rf = SresolutionFrameWithTower(g);    rf = SresolutionFrameWithTower(g);
   redundant_seq = 1;   redundant_seq_ordinary = 1;    redundant_seq = 1;   redundant_seq_ordinary = 1;
   tower = rf[1];    tower = rf[1];
Line 1024  def Sannfs(f,v) {
Line 1038  def Sannfs(f,v) {
 def Sannfs2(f) {  def Sannfs2(f) {
   local p,pp;    local p,pp;
   p = Sannfs(f,"x,y");    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],    Sweyl("x,y",[["x",1,"y",1,"Dx",1,"Dy",1,"h",1],
                ["x",-1,"y",-1,"Dx",1,"Dy",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)); */
   }
   
   /* 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");    pp = Map(p[0],"Spoly");
   return(Sminimal(pp));    return(Sminimal(pp));
 }  }
Line 1035  def Sannfs2(f) {
Line 1065  def Sannfs2(f) {
 def Sannfs3(f) {  def Sannfs3(f) {
   local p,pp;    local p,pp;
   p = Sannfs(f,"x,y,z");    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]]);    Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
   pp = Map(p[0],"Spoly");    pp = Map(p,"Spoly");
   return(Sminimal(pp));    return(Sminimal_v(pp));
 }  }
   
 /*  /*
Line 1050  def Sannfs3(f) {
Line 1081  def Sannfs3(f) {
   
   
   
 /*  The below is under construction. */  /*  The below does not use LaScala-Stillman's algorithm. */
 def Sschreyer(g) {  def Sschreyer(g) {
   local rf, tower, reductionTable, skel, redundantTable, bases,    local rf, tower, reductionTable, skel, redundantTable, bases,
         strategy, maxOfStrategy, height, level, n, i,          strategy, maxOfStrategy, height, level, n, i,
         freeRes,place, f, reducer,pos, redundant_seq,bettiTable,freeResV,ww,          freeRes,place, f, reducer,pos, redundant_seq,bettiTable,freeResV,ww,
         redundantTable_ordinary, redundant_seq_ordinary,          redundantTable_ordinary, redundant_seq_ordinary,
         reductionTable_tmp,c2,ii,nn;          reductionTable_tmp,c2,ii,nn, m,ii, jj, reducerBase;
   /* extern WeightOfSweyl; */    /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;    ww = WeightOfSweyl;
   Print("WeghtOfSweyl="); Println(WeightOfSweyl);    Print("WeghtOfSweyl="); Println(WeightOfSweyl);
Line 1121  def Sschreyer(g) {
Line 1152  def Sschreyer(g) {
                   /* i must be equal to f[2], I think. Double check. */                    /* i must be equal to f[2], I think. Double check. */
   
                   /* Correction Of Constant */                    /* Correction Of Constant */
                   c2 = f[6];                    c2 = -f[6];  /* or f[6]?  Double check. */
                   nn = Length(bases);                    nn = Length(bases);
                   for (ii=0; ii<nn;ii++) {                    for (ii=0; ii<nn;ii++) {
                      if (ii != place) {                       if ((ii != place) && (! IsNull(bases[ii]))) {
                        bases[ii] = bases[ii]*c2;                         bases[ii] = bases[ii]*c2;
                      }                       }
                   }                    }
   
                   freeRes[level] = bases;                    freeRes[level] = bases;
                   /* bases = freeRes[level-1];  
                      bases[place] = f[0];                   /* Update the freeRes[level-1] */
                      freeRes[level-1] = bases;  It is already set. */                    bases = freeRes[level-1];
                     bases[place] = f[0];
                     freeRes[level-1] = bases;
   
                   reducer[level-1,place] = f[1];                    reducer[level-1,place] = f[1];
                }else{                 }else{
                   /* redundantTable[level,i] = 0; */                    /* redundantTable[level,i] = 0; */
Line 1143  def Sschreyer(g) {
Line 1177  def Sschreyer(g) {
              }  /* end of level >= 1 */               }  /* end of level >= 1 */
           }            }
     } /* i loop */      } /* i loop */
   
       /* Triangulate reducer */
       if (level >= 1) {
         Println(" ");
         Print("Triangulating reducer at level "); Println(level-1);
         reducerBase = reducer[level-1];
         Print("reducerBase=");  Println(reducerBase);
         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];
                 }
                }
              }
            }
          }
          Println("New reducer");
          sm1_pmat(reducerBase);
          reducer[level-1] = reducerBase;
       }
   
   } /* level loop */    } /* level loop */
   n = Length(freeRes);    n = Length(freeRes);
   freeResV = SnewArrayOfFormat(freeRes);    freeResV = SnewArrayOfFormat(freeRes);
Line 1151  def Sschreyer(g) {
Line 1209  def Sschreyer(g) {
     bases = Sbases_to_vec(bases,bettiTable[i]);      bases = Sbases_to_vec(bases,bettiTable[i]);
     freeResV[i] = bases;      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]);    return([freeResV, redundantTable,reducer,bettiTable,redundantTable_ordinary]);
 }  }
   
Line 1158  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1228  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   local i, j, myindex, p, bases, tower2, gi, gj,    local i, j, myindex, p, bases, tower2, gi, gj,
        si, sj, tmp, t_syz, pos, ans, ssp, syzHead,pos2,         si, sj, tmp, t_syz, pos, ans, ssp, syzHead,pos2,
        vdeg,vdeg_reduced,n,c2;         vdeg,vdeg_reduced,n,c2;
   Println("SpairAndReduction2:");    Println("SpairAndReduction2 : -------------------------");
   
   if (level < 1) Error("level should be >= 1 in SpairAndReduction.");    if (level < 1) Error("level should be >= 1 in SpairAndReduction.");
   p = skel[level,ii];    p = skel[level,ii];
Line 1193  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1263  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   tmp = Sreduction(si*gi+sj*gj, bases);    tmp = Sreduction(si*gi+sj*gj, bases);
   
   Print("result is "); Println(tmp);    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];    t_syz = tmp[2];
   si = si*tmp[1]+t_syz[i];    si = si*tmp[1]+t_syz[i];
   sj = sj*tmp[1]+t_syz[j];    sj = sj*tmp[1]+t_syz[j];
Line 1203  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1278  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   /* tmp[0] must be zero */    /* tmp[0] must be zero */
   n = Length(t_syz);    n = Length(t_syz);
   for (i=0; i<n; i++) {    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])) {         if (IsNull(redundantTable[level-1,i])) {
          /* i must equal to pos2 below. */           /* i must equal to pos2 below. */
          c2 = -t_syz[i];           c2 = -t_syz[i];
          tmp[0] = freeRes[level-1,i];           tmp[0] = c2*Stoes_vec(freeRes[level-1,i]);
          t_syz[i] = 0;           t_syz[i] = 0;
            /* tmp[0] = t_syz . g */
          /* break; does not work. Use */           /* break; does not work. Use */
          i = n;           i = n;
        }         }
         }
      }       }
   }    }
   
Line 1228  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1306  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   /* pos is the place to put syzygy at level. */    /* pos is the place to put syzygy at level. */
   /* pos2 is the place to put a new GB at level-1. */    /* pos2 is the place to put a new GB at level-1. */
   Println(ans);    Println(ans);
     Println("  ");
   return(ans);    return(ans);
 }  }
   
   def Sminimal_v(g) {
     local r, freeRes, redundantTable, reducer, maxLevel,
           minRes, seq, maxSeq, level, betti, q, bases, dr,
           betti_levelplus, newbases, i, j,qq;
     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;
               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;
               }
               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
   /*  Do it later.
               for (qq=0; qq<betti; qq++) {
                   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]);
                       Error("Stop in Sminimal for debugging.");
                     }
                   }
               }
   */
   #endif
             }
           }
         }
      }
      return([Stetris(minRes,redundantTable),
             [ 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 */
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