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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.19 and 1.25

version 1.19, 2000/07/31 01:21:41 version 1.25, 2000/08/02 05:14:31
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 1.24 2000/08/02 03:23:36 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 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 50  def Sgroebner(f) {
Line 51  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 97  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."]]);
   
 /*  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 193  def SresolutionFrameWithTower(g,opt) {
Line 239  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 358  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 913  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, ansSminimal;
   if (Length(Arglist) < 2) {    if (Length(Arglist) < 2) {
      opt = null;       opt = null;
   }    }
Line 926  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 979  def Sminimal(g,opt) {
Line 1034  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]];
      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(Map(ansSminimal[0],"Length"));
      Print("Betti numbers of the Schreyer frame: ");
      Println(Map(ansSminimal[3],"Length"));
      Println("-----------------------------------------------");
   
      sm1(" restoreEnvAfterResolution ");
   
      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 1342  HelpAdd(["IsExact_h",
Line 1411  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 1381  def ScheckIfSchreyer(s) {
Line 1462  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.1.25
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