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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.19 and 1.31

version 1.19, 2000/07/31 01:21:41 version 1.31, 2000/12/10 03:12:20
Line 1 
Line 1 
 /* $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  #define DEBUG 1
 Sordinary = false;  Sordinary = false;
 /* If you run this program on openxm version 1.1.2 (FreeBSD),  /* If you run this program on openxm version 1.1.2 (FreeBSD),
Line 7  Sordinary = false;
Line 7  Sordinary = false;
 */  */
 #define OFFSET 0  #define OFFSET 0
 /* #define OFFSET 20*/  /* #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.  /* Test sequences.
    Use load["minimal.k"];;     Use load["minimal.k"];;
   
Line 28  Sordinary = false;
Line 44  Sordinary = false;
   
 */  */
   
   /* We cannot use load command in the if statement. */
   load("lib/minimal/cohom.k");
   
 load("cohom.k");  
 def load_tower() {  def load_tower() {
     local ppp;
   if (Boundp("k0-tower.sm1.loaded")) {    if (Boundp("k0-tower.sm1.loaded")) {
   }else{    }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(" /k0-tower.sm1.loaded 1 def ");
   }    }
   sm1(" oxNoX ");    sm1(" oxNoX ");
Line 50  def Sgroebner(f) {
Line 79  def Sgroebner(f) {
    sm1(" [f] groebner /FunctionValue set");     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) {  def Error(s) {
   sm1(" s error ");    sm1(" s error ");
 }  }
Line 83  def RingOf(f) {
Line 125  def RingOf(f) {
   return(r);    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. */  /*  End of standard functions that should be moved to standard libraries. */
 def test0() {  def test0() {
   local f;    local f;
Line 103  def test1() {
Line 199  def test1() {
 }  }
   
   
   
 def Sweyl(v,w) {  def Sweyl(v,w) {
   /* extern WeightOfSweyl ; */    /* extern WeightOfSweyl ; */
   local ww,i,n;    local ww,i,n;
Line 193  def SresolutionFrameWithTower(g,opt) {
Line 288  def SresolutionFrameWithTower(g,opt) {
           }            }
         }          }
       }        }
     }else{      } else if (IsNull(opt)){
       } else {
       Println("Warning: option should be given by an array.");        Println("Warning: option should be given by an array.");
         Println(opt);
         Println("--------------------------------------------");
     }      }
   }    }
   
Line 229  def SresolutionFrameWithTower(g,opt) {
Line 327  def SresolutionFrameWithTower(g,opt) {
   /* -sugar is fine? */    /* -sugar is fine? */
   sm1(" setupEnvForResolution ");    sm1(" setupEnvForResolution ");
   
   Println(g);    Sprintln(g);
   startingGB = g;    startingGB = g;
   /* ans = [ SzeroMap(g) ];  It has not been implemented. see resol1.withZeroMap */    /* ans = [ SzeroMap(g) ];  It has not been implemented. see resol1.withZeroMap */
   ans = [ ];    ans = [ ];
Line 273  def NewPolynomialVector(size) {
Line 371  def NewPolynomialVector(size) {
 def  SturnOffHomogenization() {  def  SturnOffHomogenization() {
   sm1("    sm1("
     [(Homogenize)] system_variable 1 eq      [(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        [(Homogenize) 0] system_variable
       [(ReduceLowerTerms) 0] system_variable        [(ReduceLowerTerms) 0] system_variable
     } {  } ifelse      } {  } 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() {  def  SturnOnHomogenization() {
   sm1("    sm1("
     [(Homogenize)] system_variable 0 eq      [(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        [(Homogenize) 1] system_variable
       [(ReduceLowerTerms) 1] system_variable        [(ReduceLowerTerms) 1] system_variable
     } {  } ifelse      } {  } ifelse
Line 330  def Sres0FrameWithSkelton(g) {
Line 434  def Sres0FrameWithSkelton(g) {
     si = pair[1,0];      si = pair[1,0];
     sj = pair[1,1];      sj = pair[1,1];
     /* si g[i] + sj g[j] + \sum tmp[2][k] g[k] = 0 in res0 */      /* si g[i] + sj g[j] + \sum tmp[2][k] g[k] = 0 in res0 */
     Print(".");      Sprint(".");
   
     t_syz = NewPolynomialVector(gLength);      t_syz = NewPolynomialVector(gLength);
     t_syz[i] = si;      t_syz[i] = si;
Line 338  def Sres0FrameWithSkelton(g) {
Line 442  def Sres0FrameWithSkelton(g) {
     syzAll[k] = t_syz;      syzAll[k] = t_syz;
   }    }
   t_syz = syzAll;    t_syz = syzAll;
   Print("Done. betti="); Println(betti);    Sprint("Done. betti="); Sprintln(betti);
   /* Println(g);  g is in a format such as    /* 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 , ...]
     [e_*x^2 , e_*x*y , 2*x*Dx*h , ...]      [e_*x^2 , e_*x*y , 2*x*Dx*h , ...]
Line 358  def StotalDegree(f) {
Line 462  def StotalDegree(f) {
   return(d0);    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]); */  /* Sord_w(x^2*Dx*Dy,[x,-1,Dx,1]); */
 def Sord_w(f,w) {  def Sord_w(f,w) {
   local neww,i,n;    local neww,i,n;
Line 391  def test_SinitOfArray() {
Line 498  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,    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];         -y^2*z^2 + x*z^3 + y*z^3, -z^4];
   p=SresolutionFrameWithTower(f);    p=SresolutionFrameWithTower(f);
   sm1_pmat(p);    if (Sverbose) {
   sm1_pmat(SgenerateTable(p[1]));      sm1_pmat(p);
       sm1_pmat(SgenerateTable(p[1]));
     }
   return(p);    return(p);
   frame = p[0];    frame = p[0];
   sm1_pmat(p[1]);    sm1_pmat(p[1]);
Line 418  def SgenerateTable(tower) {
Line 527  def SgenerateTable(tower) {
   local height, n,i,j, ans, ans_at_each_floor;    local height, n,i,j, ans, ans_at_each_floor;
   
   /*    /*
   Print("SgenerateTable: tower=");Println(tower);    Sprint("SgenerateTable: tower=");Sprintln(tower);
   sm1(" print_switch_status "); */    sm1(" print_switch_status "); */
   height = Length(tower);    height = Length(tower);
   ans = NewArray(height);    ans = NewArray(height);
Line 503  def SlaScala(g,opt) {
Line 612  def SlaScala(g,opt) {
         reductionTable_tmp;          reductionTable_tmp;
   /* extern WeightOfSweyl; */    /* extern WeightOfSweyl; */
   ww = WeightOfSweyl;    ww = WeightOfSweyl;
   Print("WeightOfSweyl="); Println(WeightOfSweyl);    Sprint("WeightOfSweyl="); Sprintln(WeightOfSweyl);
   rf = SresolutionFrameWithTower(g,opt);    rf = SresolutionFrameWithTower(g,opt);
   Print("rf="); sm1_pmat(rf);    Sprint("rf="); if (Sverbose) {sm1_pmat(rf);}
   redundant_seq = 1;   redundant_seq_ordinary = 1;    redundant_seq = 1;   redundant_seq_ordinary = 1;
   tower = rf[1];    tower = rf[1];
   
   Println("Generating reduction table which gives an order of reduction.");    Sprintln("Generating reduction table which gives an order of reduction.");
   Print("WeghtOfSweyl="); Println(WeightOfSweyl);    Sprint("WeghtOfSweyl="); Sprintln(WeightOfSweyl);
   Print("tower"); Println(tower);    Sprint2("tower="); Sprintln2(tower);
   reductionTable = SgenerateTable(tower);    reductionTable = SgenerateTable(tower);
   Print("reductionTable="); sm1_pmat(reductionTable);    Sprint2("reductionTable=");
     if (Sverbose || Sverbose2) {sm1_pmat(reductionTable);}
   
   skel = rf[2];    skel = rf[2];
   redundantTable = SnewArrayOfFormat(rf[1]);    redundantTable = SnewArrayOfFormat(rf[1]);
Line 532  def SlaScala(g,opt) {
Line 642  def SlaScala(g,opt) {
       while (SthereIs(reductionTable_tmp,strategy)) {        while (SthereIs(reductionTable_tmp,strategy)) {
         i = SnextI(reductionTable_tmp,strategy,redundantTable,          i = SnextI(reductionTable_tmp,strategy,redundantTable,
                    skel,level,freeRes);                     skel,level,freeRes);
         Println([level,i]);          Sprintln([level,i]);
         reductionTable_tmp[i] = -200000;          reductionTable_tmp[i] = -200000;
         if (reductionTable[level,i] == strategy) {          if (reductionTable[level,i] == strategy) {
            Print("Processing [level,i]= "); Print([level,i]);             Sprint("Processing [level,i]= "); Sprint([level,i]);
            Print("   Strategy = "); Println(strategy);             Sprint("   Strategy = "); Sprintln(strategy);
              Sprint2(strategy);
            if (level == 0) {             if (level == 0) {
              if (IsNull(redundantTable[level,i])) {               if (IsNull(redundantTable[level,i])) {
                bases = freeRes[level];                 bases = freeRes[level];
Line 562  if (Sordinary) {
Line 673  if (Sordinary) {
 }else{  }else{
                   if (f[4] > f[5]) {                    if (f[4] > f[5]) {
                     /* Zero in the gr-module */                      /* Zero in the gr-module */
                     Print("v-degree of [org,remainder] = ");                      Sprint("v-degree of [org,remainder] = ");
                     Println([f[4],f[5]]);                      Sprintln([f[4],f[5]]);
                     Print("[level,i] = "); Println([level,i]);                      Sprint("[level,i] = "); Sprintln([level,i]);
                     redundantTable[level-1,place] = 0;                      redundantTable[level-1,place] = 0;
                   }else{                    }else{
                     redundantTable[level-1,place] = redundant_seq;                      redundantTable[level-1,place] = redundant_seq;
Line 596  if (Sordinary) {
Line 707  if (Sordinary) {
     }      }
     strategy++;      strategy++;
   }    }
     Sprintln2(" ");
   n = Length(freeRes);    n = Length(freeRes);
   freeResV = SnewArrayOfFormat(freeRes);    freeResV = SnewArrayOfFormat(freeRes);
   for (i=0; i<n; i++) {    for (i=0; i<n; i++) {
Line 643  def SnextI(reductionTable_tmp,strategy,redundantTable,
Line 755  def SnextI(reductionTable_tmp,strategy,redundantTable,
        }         }
      }       }
    }     }
    Print("reductionTable_tmp=");     Sprint("reductionTable_tmp=");
    Println(reductionTable_tmp);     Sprintln(reductionTable_tmp);
    Println("See also reductionTable, strategy, level,i");     Sprintln("See also reductionTable, strategy, level,i");
    Error("SnextI: bases[i] or bases[j] is null for all combinations.");     Error("SnextI: bases[i] or bases[j] is null for all combinations.");
 }  }
   
Line 679  def SwhereInGB(f,tower) {
Line 791  def SwhereInGB(f,tower) {
     q = MonomialPart(f);      q = MonomialPart(f);
     if (p == q) return(i);      if (p == q) return(i);
   }    }
   Println([f,tower]);    Sprintln([f,tower]);
   Error("whereInGB : [f,myset]: f could not be found in the myset.");    Error("whereInGB : [f,myset]: f could not be found in the myset.");
 }  }
 def SunitOfFormat(pos,forms) {  def SunitOfFormat(pos,forms) {
Line 733  def SwhereInTower(f,tower) {
Line 845  def SwhereInTower(f,tower) {
     q = MonomialPart(f);      q = MonomialPart(f);
     if (p == q) return(i);      if (p == q) return(i);
   }    }
   Println([f,tower]);    Sprintln([f,tower]);
   Error("[f,tower]: f could not be found in the tower.");    Error("[f,tower]: f could not be found in the tower.");
 }  }
   
Line 745  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
Line 857  def SpairAndReduction(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;         vdeg,vdeg_reduced;
   Println("SpairAndReduction:");    Sprintln("SpairAndReduction:");
   
   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];
   myindex = p[0];    myindex = p[0];
   i = myindex[0]; j = myindex[1];    i = myindex[0]; j = myindex[1];
   bases = freeRes[level-1];    bases = freeRes[level-1];
   Println(["p and bases ",p,bases]);    Sprintln(["p and bases ",p,bases]);
   if (IsNull(bases[i]) || IsNull(bases[j])) {    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.");      Error("level, i, j : bases[i], bases[j]  must not be NULL.");
   }    }
   
   tower2 = StowerOf(tower,level-1);    tower2 = StowerOf(tower,level-1);
   SsetTower(tower2);    SsetTower(tower2);
   Println(["level=",level]);    Sprintln(["level=",level]);
   Println(["tower2=",tower2]);    Sprintln(["tower2=",tower2]);
   /** sm1(" show_ring ");   */    /** sm1(" show_ring ");   */
   
   gi = Stoes_vec(bases[i]);    gi = Stoes_vec(bases[i]);
Line 772  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
Line 884  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   sj = ssp[0,1];    sj = ssp[0,1];
   syzHead = si*es^i;    syzHead = si*es^i;
   /* This will be the head term, I think. But, double check. */    /* 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]);    Sprint("[gi, gj] = "); Sprintln([gi,gj]);
   sm1(" [(Homogenize)] system_variable message ");    sm1(" [(Homogenize)] system_variable  ");
   Print("Reduce the element "); Println(si*gi+sj*gj);    Sprint("Reduce the element "); Sprintln(si*gi+sj*gj);
   Print("by  "); Println(bases);    Sprint("by  "); Sprintln(bases);
   
   tmp = Sreduction(si*gi+sj*gj, 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. */    /* This is essential part for V-minimal resolution. */
   /* vdeg = SvDegree(si*gi+sj*gj,tower,level-1,ww); */    /* vdeg = SvDegree(si*gi+sj*gj,tower,level-1,ww); */
   vdeg = SvDegree(si*gi,tower,level-1,ww);    vdeg = SvDegree(si*gi,tower,level-1,ww);
   vdeg_reduced = SvDegree(tmp[0],tower,level-1,ww);    vdeg_reduced = SvDegree(tmp[0],tower,level-1,ww);
   Print("vdegree of the original = "); Println(vdeg);    Sprint("vdegree of the original = "); Sprintln(vdeg);
   Print("vdegree of the remainder = "); Println(vdeg_reduced);    Sprint("vdegree of the remainder = "); Sprintln(vdeg_reduced);
   
   t_syz = tmp[2];    t_syz = tmp[2];
   si = si*tmp[1]+t_syz[i];    si = si*tmp[1]+t_syz[i];
Line 804  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
Line 916  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced];    ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced];
   /* 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);    Sprintln(ans);
   return(ans);    return(ans);
 }  }
   
Line 896  def Sbases_to_vec(bases,size) {
Line 1008  def Sbases_to_vec(bases,size) {
   
 HelpAdd(["Sminimal",  HelpAdd(["Sminimal",
 ["It constructs the V-minimal free resolution by LaScala's algorithm",  ["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)",   "      : \"Sordinary\"   (no (u,v)-minimal resolution)",
  "Options should be given as an array.",   "Options should be given as an array.",
  "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",   "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",
Line 913  HelpAdd(["Sminimal",
Line 1025  HelpAdd(["Sminimal",
 def Sminimal(g,opt) {  def Sminimal(g,opt) {
   local r, freeRes, redundantTable, reducer, maxLevel,    local r, freeRes, redundantTable, reducer, maxLevel,
         minRes, seq, maxSeq, level, betti, q, bases, dr,          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) {    if (Length(Arglist) < 2) {
      opt = null;       opt = null;
   }    }
Line 926  def Sminimal(g,opt) {
Line 1038  def Sminimal(g,opt) {
   freeRes = r[0];    freeRes = r[0];
   redundantTable = r[1];    redundantTable = r[1];
   reducer = r[2];    reducer = r[2];
     bettiTable = SbettiTable(redundantTable);
     Sprintln2("BettiTable ------");
     if (Sverbose || Sverbose2) {sm1_pmat(bettiTable);}
   minRes = SnewArrayOfFormat(freeRes);    minRes = SnewArrayOfFormat(freeRes);
   seq = 0;    seq = 0;
   maxSeq = SgetMaxSeq(redundantTable);    maxSeq = SgetMaxSeq(redundantTable);
Line 935  def Sminimal(g,opt) {
Line 1050  def Sminimal(g,opt) {
   }    }
   seq=maxSeq+1;    seq=maxSeq+1;
   while (seq > 1) {    while (seq > 1) {
     seq--;      seq--;  Sprint2(seq);
     for (level = 0; level < maxLevel; level++) {      for (level = 0; level < maxLevel; level++) {
       betti = Length(freeRes[level]);        betti = Length(freeRes[level]);
       for (q = 0; q<betti; q++) {        for (q = 0; q<betti; q++) {
         if (redundantTable[level,q] == seq) {          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) {            if (level < maxLevel-1) {
             bases = freeRes[level+1];              bases = freeRes[level+1];
             dr = reducer[level,q];              dr = reducer[level,q];
Line 953  def Sminimal(g,opt) {
Line 1068  def Sminimal(g,opt) {
             for (i=0; i<betti_levelplus; i++) {              for (i=0; i<betti_levelplus; i++) {
               newbases[i] = bases[i] + bases[i,q]*dr;                newbases[i] = bases[i] + bases[i,q]*dr;
             }              }
             Println(["level, q =", level,q]);              Sprintln(["level, q =", level,q]);
             Println("bases="); sm1_pmat(bases);              Sprintln("bases="); if (Sverbose) {sm1_pmat(bases); }
             Println("dr="); sm1_pmat(dr);              Sprintln("dr="); if (Sverbose) {sm1_pmat(dr);}
             Println("newbases="); sm1_pmat(newbases);              Sprintln("newbases="); if (Sverbose) {sm1_pmat(newbases);}
             minRes[level+1] = newbases;              minRes[level+1] = newbases;
             freeRes = minRes;              freeRes = minRes;
 #ifdef DEBUG  #ifdef DEBUG
Line 966  def Sminimal(g,opt) {
Line 1081  def Sminimal(g,opt) {
                 for (i=0; i<betti_levelplus; i++) {                  for (i=0; i<betti_levelplus; i++) {
                   if (!IsZero(newbases[i,qq])) {                    if (!IsZero(newbases[i,qq])) {
                     Println(["[i,qq]=",[i,qq]," is not zero in newbases."]);                      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.");                      Error("Stop in Sminimal for debugging.");
                   }                    }
                 }                  }
Line 979  def Sminimal(g,opt) {
Line 1094  def Sminimal(g,opt) {
     }      }
    }     }
    tminRes = Stetris(minRes,redundantTable);     tminRes = Stetris(minRes,redundantTable);
    return([SpruneZeroRow(tminRes), tminRes,     ansSminimal = [SpruneZeroRow(tminRes), tminRes,
           [ minRes, redundantTable, reducer,r[3],r[4]],r[0],r[5]]);                    [ 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[4] is the redundantTable_ordinary */
   /* r[0] is the freeResolution */    /* r[0] is the freeResolution */
   /* r[5] is the skelton */    /* r[5] is the skelton */
Line 1052  def Stetris(freeRes,redundantTable) {
Line 1183  def Stetris(freeRes,redundantTable) {
     }else{      }else{
       newbases = bases;        newbases = bases;
     }      }
     Println(["level=", level]);      Sprintln(["level=", level]);
     sm1_pmat(bases);      if (Sverbose){
     sm1_pmat(newbases);        sm1_pmat(bases);
         sm1_pmat(newbases);
       }
   
     minRes[level] = newbases;      minRes[level] = newbases;
   }    }
Line 1342  HelpAdd(["IsExact_h",
Line 1475  HelpAdd(["IsExact_h",
  "cf. ReParse"   "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) {  def ReParse(a) {
   local c;    local c;
   if (IsArray(a)) {    if (IsArray(a)) {
Line 1376  def ScheckIfSchreyer(s) {
Line 1521  def ScheckIfSchreyer(s) {
   */    */
   sm1(" [(Schreyer)] system_variable (universalNumber) dc /ss set ");    sm1(" [(Schreyer)] system_variable (universalNumber) dc /ss set ");
   if (ss != 1) {    if (ss != 1) {
      Print("ScheckIfSchreyer: from "); Println(s);       Print("ScheckIfSchreyer: from "); Printl(s);
      Error("Schreyer order is not set.");       Error("Schreyer order is not set.");
   }    }
   /* More check will be necessary. */    /* More check will be necessary. */
   return(true);    return(true);
 }  
   
   }
   
   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]);"
   ]]);
   
   
   
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  Added in v.1.31
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