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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.18 and 1.23

version 1.18, 2000/07/30 02:26:25 version 1.23, 2000/08/01 08:51:03
Line 1 
Line 1 
 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.17 2000/07/26 12:56:36 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.22 2000/08/01 06:26:11 takayama Exp $ */
 #define DEBUG 1  #define DEBUG 1
 /* #define ORDINARY 1 */  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),
    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
Line 34  def load_tower() {
Line 34  def load_tower() {
   if (Boundp("k0-tower.sm1.loaded")) {    if (Boundp("k0-tower.sm1.loaded")) {
   }else{    }else{
     sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");      sm1(" [(parse) (k0-tower.sm1) pushfile ] extension ");
       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 49  def Reverse(f) {
Line 50  def Reverse(f) {
 def Sgroebner(f) {  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) {
     sm1(" s error ");
   }
   
   def IsNull(s) {
     if (Stag(s) == 0) return(true);
     else return(false);
   }
   
   def MonomialPart(f) {
     sm1(" [(lmonom) f] gbext /FunctionValue set ");
   }
   
   def Warning(s) {
     Print("Warning: ");
     Println(s);
   }
   def RingOf(f) {
     local r;
     if (IsPolynomial(f)) {
       if (f != Poly("0")) {
         sm1(f," (ring) dc /r set ");
       }else{
         sm1(" [(CurrentRingp)] system_variable /r set ");
       }
     }else{
       Warning("RingOf(f): the argument f must be a polynomial. Return the current ring.");
       sm1(" [(CurrentRingp)] system_variable /r set ");
     }
     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."]]);
   
   /*  End of standard functions that should be moved to standard libraries. */
 def test0() {  def test0() {
   local f;    local f;
   Sweyl("x,y,z");    Sweyl("x,y,z");
Line 136  sm1(" [(AvoidTheSameRing)] pushEnv 
Line 217  sm1(" [(AvoidTheSameRing)] pushEnv 
   
 def SresolutionFrameWithTower(g,opt) {  def SresolutionFrameWithTower(g,opt) {
   local gbTower, ans, ff, count, startingGB, opts, skelton,withSkel, autof,    local gbTower, ans, ff, count, startingGB, opts, skelton,withSkel, autof,
         gbasis, nohomog;          gbasis, nohomog,i,n;
     /* extern Sordinary */
   nohomog = false;    nohomog = false;
   count = -1;    count = -1;  Sordinary = false; /* default value for options. */
   if (Length(Arglist) >= 2) {    if (Length(Arglist) >= 2) {
     if (IsInteger(opt)) {      if (IsArray(opt)) {
       count = opt;        n = Length(opt);
     }else if (IsString(opt)) {        for (i=0; i<n; i++) {
       if (opt == "homogenized") {          if (IsInteger(opt[i])) {
          nohomog = true;            count = opt[i];
       }else{          }
          Println("Warning: unknown option");          if (IsString(opt[i])) {
          Println(opt);            if (opt[i] == "homogenized") {
               nohomog = true;
             }else if (opt[i] == "Sordinary") {
               Sordinary = true;
             }else{
               Println("Warning: unknown option");
               Println(opt);
             }
           }
       }        }
       } else if (IsNull(opt)){
       } else {
         Println("Warning: option should be given by an array.");
         Println(opt);
         Println("--------------------------------------------");
     }      }
   }else{  
     count = -1;  
   }    }
   
   sm1(" setupEnvForResolution ");    sm1(" setupEnvForResolution ");
Line 314  def StotalDegree(f) {
Line 407  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 512  def SlaScala(g,opt) {
Line 608  def SlaScala(g,opt) {
                   place = f[3];                    place = f[3];
                   /* (level-1, place) is the place for f[0],                    /* (level-1, place) is the place for f[0],
                      which is a newly obtained  GB. */                       which is a newly obtained  GB. */
 #ifdef ORDINARY  if (Sordinary) {
                   redundantTable[level-1,place] = redundant_seq;                    redundantTable[level-1,place] = redundant_seq;
                   redundant_seq++;                    redundant_seq++;
 #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] = ");                      Print("v-degree of [org,remainder] = ");
Line 526  def SlaScala(g,opt) {
Line 622  def SlaScala(g,opt) {
                     redundantTable[level-1,place] = redundant_seq;                      redundantTable[level-1,place] = redundant_seq;
                     redundant_seq++;                      redundant_seq++;
                   }                    }
 #endif  }
                   redundantTable_ordinary[level-1,place]                    redundantTable_ordinary[level-1,place]
                      =redundant_seq_ordinary;                       =redundant_seq_ordinary;
                   redundant_seq_ordinary++;                    redundant_seq_ordinary++;
Line 652  def SunitOfFormat(pos,forms) {
Line 748  def SunitOfFormat(pos,forms) {
   return(ans);    return(ans);
 }  }
   
 def Error(s) {  
   sm1(" s error ");  
 }  
   
 def IsNull(s) {  
   if (Stag(s) == 0) return(true);  
   else return(false);  
 }  
   
 def StowerOf(tower,level) {  def StowerOf(tower,level) {
   local ans,i;    local ans,i;
   ans = [ ];    ans = [ ];
Line 681  def Sspolynomial(f,g) {
Line 769  def Sspolynomial(f,g) {
   sm1("f g spol /FunctionValue set");    sm1("f g spol /FunctionValue set");
 }  }
   
 def MonomialPart(f) {  
   sm1(" [(lmonom) f] gbext /FunctionValue set ");  
 }  
   
 /* WARNING:  /* WARNING:
   When you use SwhereInTower, you have to change gbList    When you use SwhereInTower, you have to change gbList
Line 804  def Sreduction(f,myset) {
Line 889  def Sreduction(f,myset) {
   return([tmp[0],tmp[1],t_syz]);    return([tmp[0],tmp[1],t_syz]);
 }  }
   
 def Warning(s) {  
   Print("Warning: ");  
   Println(s);  
 }  
 def RingOf(f) {  
   local r;  
   if (IsPolynomial(f)) {  
     if (f != Poly("0")) {  
       sm1(f," (ring) dc /r set ");  
     }else{  
       sm1(" [(CurrentRingp)] system_variable /r set ");  
     }  
   }else{  
     Warning("RingOf(f): the argument f must be a polynomial. Return the current ring.");  
     sm1(" [(CurrentRingp)] system_variable /r set ");  
   }  
   return(r);  
 }  
   
 def Sfrom_es(f,size) {  def Sfrom_es(f,size) {
   local c,ans, i, d, myes, myee, j,n,r,ans2;    local c,ans, i, d, myes, myee, j,n,r,ans2;
Line 882  def Sbases_to_vec(bases,size) {
Line 949  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)",
    "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]]);",
  "          v=[[2*x*Dx + 3*y*Dy+6, 0],",   "          v=[[2*x*Dx + 3*y*Dy+6, 0],",
  "             [3*x^2*Dy + 2*y*Dx, 0],",   "             [3*x^2*Dy + 2*y*Dx, 0],",
Line 896  HelpAdd(["Sminimal",
Line 965  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;
   if (Length(Arglist) < 2) {    if (Length(Arglist) < 2) {
      opt = null;       opt = null;
   }    }
     /* Sordinary is set in SlaScala(g,opt) --> SresolutionFrameWithTower */
   
   ScheckIfSchreyer("Sminimal:0");    ScheckIfSchreyer("Sminimal:0");
   r = SlaScala(g,opt);    r = SlaScala(g,opt);
   /* Should I turn off the tower?? */    /* Should I turn off the tower?? */
Line 907  def Sminimal(g,opt) {
Line 978  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);
     Println("Betti numbers are ------");
     sm1_pmat(bettiTable);
   minRes = SnewArrayOfFormat(freeRes);    minRes = SnewArrayOfFormat(freeRes);
   seq = 0;    seq = 0;
   maxSeq = SgetMaxSeq(redundantTable);    maxSeq = SgetMaxSeq(redundantTable);
Line 1323  HelpAdd(["IsExact_h",
Line 1397  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 1362  def ScheckIfSchreyer(s) {
Line 1448  def ScheckIfSchreyer(s) {
   }    }
   /* 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);
     m0 = NewArray(Length(resmat[0,0]));
     ans[0] = m0;
     for (i=0; i<n-1; 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);
 }  }
   
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  Added in v.1.23
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