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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.9 and 1.15

version 1.9, 2000/08/01 03:42:35 version 1.15, 2000/08/02 05:14:31
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 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.8 2000/07/31 01:21:41 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.14 2000/08/02 04:26:36 takayama Exp $ */
 load["minimal.k"];  load["minimal.k"];
 def sm1_resol1(p) {  def sm1_resol1(p) {
   sm1(" p resol1 /FunctionValue set ");    sm1(" p resol1 /FunctionValue set ");
Line 252  def test17() {
Line 252  def test17() {
    sm1_pmat(c);     sm1_pmat(c);
    Println(IsExact_h(c,"x,y,z"));     Println(IsExact_h(c,"x,y,z"));
 }  }
 def test17b() {  
    a=Sannfs3("x^3-y^2*z^2");  def test_if_v_strict(resmat,w,v) {
    b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];     local b,c,g;
    Sweyl("x,y,z",[w]); b = Reparse(b);     Sweyl(v,[w]); b = Reparse(resmat);
      Println("Degree shifts ");
      Println(SgetShifts(b,w));
    c=Sinit_w(b,w);     c=Sinit_w(b,w);
    Println("Resolution (b)----");     Println("Resolution (b)----");
    sm1_pmat(b);     sm1_pmat(b);
    Println("Initial (c)----");     Println("Initial (c)----");
    sm1_pmat(c);     sm1_pmat(c);
    Println(IsExact_h(c,"x,y,z"));     Println("Exactness of the resolution ---");
      Println(IsExact_h(b,v));
      Println("Exactness of the initial complex.---");
      Println(IsExact_h(c,v));
    g = Sinvolutive(b[0],w);     g = Sinvolutive(b[0],w);
    Println("Involutive basis ---");     /* Println("Involutive basis ---");
    sm1_pmat(g);        sm1_pmat(g);
         Println(Sinvolutive(c[0],w));
         sm1(" /gb.verbose 1 def "); */
    Println("Is same ideal?");     Println("Is same ideal?");
    Println(IsSameIdeal_h(g,c[0],"x,y"));     Println(IsSameIdeal_h(g,c[0],v));
   }
   def test17b() {
      a=Sannfs3("x^3-y^2*z^2");
      b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
      test_if_v_strict(b,w,"x,y,z");
      return(a);
 }  }
   
 def test18() {  def test18() {
    a=Sannfs2("x^3-y^2");     a=Sannfs2("x^3-y^2");
    b=a[0]; w = ["x",-1,"y",-1,"Dx",1,"Dy",1];     b=a[0]; w = ["x",-1,"y",-1,"Dx",1,"Dy",1];
    Sweyl("x,y",[w]); b = Reparse(b);     test_if_v_strict(b,w,"x,y");
    c=Sinit_w(b,w);     return(a);
    Println("Resolution (b)----");  }
    sm1_pmat(b);  
    Println("Initial (c)----");  def test19() {
    sm1_pmat(c);    Println("test19 try to construct a minimal free resolution and check if it is v-strict.");
    g = Sinvolutive(b[0],w);    Println("of a GKZ system [[1,2,3]] by -1,1");
    Println("Involutive basis ---");    ww2 = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1];
    sm1_pmat(g);    ans2 = GKZ([[1,2,3]],[0]);
    Println("Is same ideal?");    Sweyl("x1,x2,x3",[ww2]);
    Println(IsSameIdeal_h(g,c[0],"x,y"));    ans2 = ReParse(ans2[0]);
     a = Sminimal(ans2);
     Println("Minimal Resolution is "); sm1_pmat(a[0]);
     b = a[0];
     test_if_v_strict(b,ww2,"x1,x2,x3");
     return(a);
   }
   
   /* Need more than 100M memory. 291, 845, 1266, 1116, 592 : Schreyer frame.
      I've not yet tried to finish the computation. */
   def test20() {
     w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1];
     ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[0,0]);
     Sweyl("x1,x2,x3,x4",[w]);
     ans2 = ReParse(ans2[0]);
     a = Sminimal(ans2);
     Println("Minimal Resolution is "); sm1_pmat(a[0]);
     b = a[0];
     /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */
     return(a);
   }
   def test20b() {
     w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1];
     ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[1,2]);
     Sweyl("x1,x2,x3,x4",[w]);
     ans2 = ReParse(ans2[0]);
     a = Sminimal(ans2);
     Println("Minimal Resolution is "); sm1_pmat(a[0]);
     b = a[0];
     /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */
     return(a);
   }
   
   def test21() {
      a=Sannfs3("x^3-y^2*z^2+y^2+z^2");
      /* a=Sannfs3("x^3-y-z");  for debug */
      b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
      test_if_v_strict(b,w,"x,y,z");
      Println("Degree shifts of Schreyer resolution ----");
      Println(SgetShifts(Reparse(a[4,0]),w));
      return(a);
   }
   def test21b() {
     local i,j,n,sss, maxR, ttt,ans,p;
     Println("The dimensions of linear spaces -----");
     /* sss is the SgetShifts of the Schreyer resol. */
     sss=
     [[    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ,
      [ -1, -1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3 ] ,
      [ 0, 1, -1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 3, 2, 2, 1, 4, 3, 3, 2, 0, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 3, 2, 2, 3, 1, 3, 3, 3, 3, 4 ] ,
      [ 1, 0, 2, 3, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 0, 3, 1, 3, 2, 3, 4 ] ,
      [ 1, 1 ]  ] ;
      maxR = 2; /* Maximal root of the b-function. */
     n = Length(sss);
     for (i=0; i<n; i++) {
       ttt = sss[i];
       ans = 0;
       for (j=0; j<Length(ttt); j++) {
         p = ttt[j] + maxR + 3; /* degree */
         if (p >= 0) {
           ans = ans + CancelNumber(p*(p-1)*(p-2)/(3*2*1));
           /* Add the number of monomials */
         }
       }
       Print(ans); Print(", ");
     }
     Println(" ");
   }
   def test22() {
      a=Sannfs3("x^3+y^3+z^3");
      b=a[0]; w = ["x",-1,"y",-2,"z",-3,"Dx",1,"Dy",2,"Dz",3];
      test_if_v_strict(b,w,"x,y,z");
      return(a);
 }  }
   
   
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