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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.9 and 1.10

version 1.9, 2000/05/06 13:41:12 version 1.10, 2000/05/07 02:10:44
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 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.8 2000/05/06 10:45:43 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.9 2000/05/06 13:41:12 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),
Line 1044  def Sannfs2(f) {
Line 1044  def Sannfs2(f) {
   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,"h",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]]);    Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
   pp = Map(p,"Spoly");    pp = Map(p,"Spoly");
   return(Sminimal_v(pp));    return(Sminimal_v(pp));
   /* return(Sminimal(pp)); */    /* return(Sminimal(pp)); */
 }  }
   
   HelpAdd(["Sannfs2",
   ["Sannfs2(f) constructs the V-minimal free resolution for the weight (-1,1)",
    "of the Laplace transform of the annihilating ideal of the polynomial f in x,y.",
    "See also Sminimal_v, Sannfs3.",
    "Example: a=Sannfs2(\"x^3-y^2\");",
    "         b=a[0]; sm1_pmat(b);",
    "         b[1]*b[0]:",
    "Example: a=Sannfs2(\"x*y*(x-y)*(x+y)\");",
    "         b=a[0]; sm1_pmat(b);",
    "         b[1]*b[0]:"
   ]]);
   
 /* Do not forget to turn on TOTAL_STRATEGY */  /* Do not forget to turn on TOTAL_STRATEGY */
 def Sannfs2_laScala(f) {  def Sannfs2_laScala(f) {
   local p,pp;    local p,pp;
Line 1072  def Sannfs3(f) {
Line 1085  def Sannfs3(f) {
   return(Sminimal_v(pp));    return(Sminimal_v(pp));
 }  }
   
   HelpAdd(["Sannfs3",
   ["Sannfs3(f) constructs the V-minimal free resolution for the weight (-1,1)",
    "of the Laplace transform of the annihilating ideal of the polynomial f in x,y,z.",
    "See also Sminimal_v, Sannfs2.",
    "Example: a=Sannfs3(\"x^3-y^2*z^2\");",
    "         b=a[0]; sm1_pmat(b);",
    "         b[1]*b[0]: b[2]*b[1]:"]]);
   
 /*  /*
   The betti numbers of most examples are 2,1. (0-th and 1-th).    The betti numbers of most examples are 2,1. (0-th and 1-th).
   a=Sannfs2("x*y*(x+y-1)"); ==> The betti numbers are 3, 2.    a=Sannfs2("x*y*(x+y-1)"); ==> The betti numbers are 3, 2.
Line 1341  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1362  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   return(ans);    return(ans);
 }  }
   
   HelpAdd(["Sminimal_v",
   ["It constructs the V-minimal free resolution from the Schreyer resolution",
    "step by step.",
    "Example:   Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",
    "          v=[[2*x*Dx + 3*y*Dy+6, 0],",
    "             [3*x^2*Dy + 2*y*Dx, 0],",
    "             [0,  x^2+y^2],",
    "             [0,  x*y]];",
    "         a=Sminimal_v(v);",
    "         sm1_pmat(a[0]); b=a[0]; b[1]*b[0]:",
    "Note:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution."]]);
   
   
 def Sminimal_v(g) {  def Sminimal_v(g) {
   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;          betti_levelplus, newbases, i, j,qq,tminRes;
   r = Sschreyer(g);    r = Sschreyer(g);
   sm1_pmat(r);    sm1_pmat(r);
   Debug_Sminimal_v = r;    Debug_Sminimal_v = r;
Line 1399  def Sminimal_v(g) {
Line 1433  def Sminimal_v(g) {
         }          }
       }        }
    }     }
    return([Stetris(minRes,redundantTable),     tminRes = Stetris(minRes,redundantTable);
      return([SpruneZeroRow(tminRes), tminRes,
           [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]);            [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]);
   /* r[4] is the redundantTable_ordinary */    /* r[4] is the redundantTable_ordinary */
   /* r[0] is the freeResolution */    /* r[0] is the freeResolution */
 }  }
   
 /* Sannfs2("x*y*(x-y)*(x+y)"); is a test problem */  /* Sannfs2("x*y*(x-y)*(x+y)"); is a test problem */
   /* x y (x+y-1)(x-2),  x^3-y^2, x^3 - y^2 z^2,
      x y z (x+y+z-1) seems to be interesting, because the first syzygy
     contains 1.
   */
   
   def CopyArray(m) {
     local ans,i,n;
     if (IsArray(m)) {
        n = Length(m);
        ans = NewArray(n);
        for (i=0; i<n; i++) {
          ans[i] = CopyArray(m[i]);
        }
        return(ans);
     }else{
        return(m);
     }
   }
   HelpAdd(["CopyArray",
   ["It duplicates the argument array recursively.",
    "Example: m=[1,[2,3]];",
    "         a=CopyArray(m); a[1] = \"Hello\";",
    "         Println(m); Println(a);"]]);
   
   def IsZeroVector(m) {
     local n,i;
     n = Length(m);
     for (i=0; i<n; i++) {
       if (!IsZero(m[i])) {
         return(false);
       }
     }
     return(true);
   }
   
   def SpruneZeroRow(res) {
     local minRes, n,i,j,m, base,base2,newbase,newbase2, newMinRes;
   
     minRes = CopyArray(res);
     n = Length(minRes);
     for (i=0; i<n; i++) {
       base = minRes[i];
       m = Length(base);
       if (i != n-1) {
         base2 = minRes[i+1];
         base2 = Transpose(base2);
       }
       newbase = [ ];
       newbase2 = [ ];
       for (j=0; j<m; j++) {
         if (!IsZeroVector(base[j])) {
           newbase = Append(newbase,base[j]);
           if (i != n-1) {
             newbase2 = Append(newbase2,base2[j]);
           }
         }
       }
       minRes[i] = newbase;
       if (i != n-1) {
         if (newbase2 == [ ]) {
           minRes[i+1] = [ ];
         }else{
           minRes[i+1] = Transpose(newbase2);
         }
       }
     }
   
     newMinRes = [ ];
     n = Length(minRes);
     i = 0;
     while (i < n ) {
       base = minRes[i];
       if (base == [ ]) {
         i = n; /* break; */
       }else{
         newMinRes = Append(newMinRes,base);
       }
       i++;
     }
     return(newMinRes);
   }
   
   def testAnnfs2(f) {
     local a,i,n;
     a = Sannfs2(f);
     b=a[0];
     n = Length(b);
     Println("------ V-minimal free resolution -----");
     sm1_pmat(b);
     Println("----- Is it complex?  ---------------");
     for (i=0; i<n-1; i++) {
       Println(b[i+1]*b[i]);
     }
     return(a);
   }
   def testAnnfs3(f) {
     local a,i,n;
     a = Sannfs3(f);
     b=a[0];
     n = Length(b);
     Println("------ V-minimal free resolution -----");
     sm1_pmat(b);
     Println("----- Is it complex?  ---------------");
     for (i=0; i<n-1; i++) {
       Println(b[i+1]*b[i]);
     }
     return(a);
   }
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