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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.9 and 1.18

version 1.9, 2000/08/01 03:42:35 version 1.18, 2000/08/21 07:45:22
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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 1.17 2000/08/10 02:59:08 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)----");  
    sm1_pmat(c);  
    g = Sinvolutive(b[0],w);  
    Println("Involutive basis ---");  
    sm1_pmat(g);  
    Println("Is same ideal?");  
    Println(IsSameIdeal_h(g,c[0],"x,y"));  
   
 }  }
   
   def test19() {
     Println("test19 try to construct a minimal free resolution and check if it is v-strict.");
     Println("of a GKZ system [[1,2,3]] by -1,1");
     ww2 = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1];
     ans2 = GKZ([[1,2,3]],[0]);
     Sweyl("x1,x2,x3",[ww2]);
     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[3]),w));
      return(a);
   }
   def test21b() {
     local i,j,n,sss, maxR, ttt,ans,p, euler;
     Println("The dimensions of linear spaces -----");
     /* sss is the SgetShifts of the Schreyer resol. */
     sss=[    [    0 ]  , [    2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 2 , 1 , 3 , 2 ]  , [    1 , 1 , 1 , 2 , 3 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 2 , 2 , 2 , 3 , 2 , 3 , 3 , 3 , 4 , 3 , 3 , 4 , 3 , 3 , 4 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 5 , 4 , 4 , 3 , 5 , 5 , 5 , 5 , 4 ]  , [    1 , 3 , 1 , 3 , 3 , 1 , 2 , 2 , 3 , 2 , 3 , 2 , 3 , 5 , 4 , 4 , 3 , 6 , 5 , 4 , 3 , 2 , 3 , 3 , 5 , 4 , 3 , 2 , 4 , 4 , 4 , 4 , 5 , 3 , 2 , 3 , 3 , 4 , 4 , 4 , 5 , 4 , 4 , 5 , 3 , 5 , 4 , 5 , 5 , 6 ]  , [    3 , 1 , 4 , 5 , 4 , 5 , 2 , 3 , 2 , 4 , 3 , 4 , 3 , 3 , 2 , 4 , 3 , 5 , 4 , 5 , 6 ]  , [    2 , 3 ]  ] ;
     maxR = 2; /* Maximal root of the b-function. */
     n = Length(sss);
     euler = 0;
     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(", ");
       euler = euler+(-1)^i*ans;
     }
     Println(" ");
     Print("Euler number is : "); Println(euler);
   }
   def test21c() {
     local i,j,n,sss, maxR, ttt,ans,p, euler;
     Println("The dimensions of linear spaces -----");
     /* sss is the SgetShifts of the minimal resol. */
     sss= [    [    0 ]  , [    2 , 2 , 2 , 2 , 2 , 2 , 2 ]  , [    1 , 2 , 2 , 2 , 2 , 3 , 4 , 4 , 4 , 4 ]  , [    1 , 3 , 4 , 6 ]  ];
     maxR = 2; /* Maximal root of the b-function. */
     n = Length(sss);
     euler = 0;
     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(", ");
       euler = euler+(-1)^i*ans;
     }
     Println(" ");
     Print("Euler number is : "); Println(euler);
   }
   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);
   }
   
   def FillFromLeft(mat,p,z) {
     local m,n,i,j,aa;
     m = Length(mat); n = Length(mat[0]);
     aa = NewMatrix(m,n+p);
     for (i=0; i<m; i++) {
       for (j=0; j<p; j++) {
         aa[i,j] = z; /* zero */
       }
       for (j=0; j<n; j++) {
         aa[i,j+p] = mat[i,j];
       }
     }
     return(aa);
   }
   
   def FillFromRight(mat,p,z) {
     local m,n,i,j,aa;
     m = Length(mat); n = Length(mat[0]);
     aa = NewMatrix(m,n+p);
     for (i=0; i<m; i++) {
       for (j=n; j<n+p; j++) {
         aa[i,j] = z; /* zero */
       }
       for (j=0; j<n; j++) {
         aa[i,j] = mat[i,j];
       }
     }
     return(aa);
   }
   
   def test23() {
     w = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1];
     Sweyl("x1,x2,x3",[w]);
     d2 = [[Dx1^2-Dx2*h] , [-Dx1*Dx2+Dx3*h] , [Dx2^2-Dx1*Dx3] ];
     d1 = [[-Dx2, -Dx1, -h],[Dx3,Dx2,Dx1]];
     LL = x1*Dx1 + 2*x2*Dx2+3*x3*Dx3;
     /* It is exact for LL = Dx1 + 2*Dx2+3*Dx3;  */
     u1 = [[LL+4*h^2,Poly("0")],[Poly("0"),LL+5*h^2]];
     u2 = [[LL+2*h^2,Poly("0"),Poly("0")],
           [Poly("0"),LL+3*h^2,Poly("0")],
           [Poly("0"),Poly("0"),LL+4*h^2]];
     u3 = [[LL]];
     Println("Checking if it is a double complex. ");
     Println("u^2 d^2 - d^2 u^3");
     sm1_pmat(u2*d2 - d2*u3);
     Println("u^1 d^1 - d^1 u^2");
     sm1_pmat(u1*d1 - d1*u2);
     aa = [
            Join(u3,d2),
            Join(FillFromLeft(u2,1,Poly("0"))-FillFromRight(d2,3,Poly("0")),
                 FillFromLeft(d1,1,Poly("0"))),
            FillFromLeft(u1,3,Poly("0"))-FillFromRight(d1,2,Poly("0"))
          ];
     Println([ aa[1]*aa[0], aa[2]*aa[1] ]);
     r= IsExact_h(aa,[x1,x2,x3]);
     Println(r);
     /* sm1_pmat(aa); */
     return(aa);
   }
   
   
   def test24() {
     local Res, Eqs, ww,a;
     ww = ["x",-1,"y",-1,"Dx",1,"Dy",1];
     Println("Example of V-minimal <> minimal ");
     Sweyl("x,y", [ww]);
     Eqs = [Dx-(x*Dx+y*Dy),
            Dy-(x*Dx+y*Dy)];
     sm1(" Eqs dehomogenize /Eqs set");
     Res = Sminimal(Eqs);
     Sweyl("x,y", [ww]);
     a = Reparse(Res[0]);
     sm1_pmat(a);
     Println("Initial of the complex is ");
     sm1_pmat( Sinit_w(a,ww) );
     return(Res);
   }
   
   def test24b() {
     local Res, Eqs, ww ;
     ww = ["x",-1,"y",-1,"Dx",1,"Dy",1];
     Println("Construction of minimal ");
     Sweyl("x,y", [ww]);
     Eqs = [Dx-(x*Dx+y*Dy),
            Dy-(x*Dx+y*Dy)];
     sm1(" Eqs dehomogenize /Eqs set");
     Res = Sminimal(Eqs,["Sordinary"]);
     sm1_pmat(Res[0]);
     return(Res);
   }
   
   def test25() {
     w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"Dx5",1,"Dx6",1,
          "x1",-1,"x2",-1,"x3",-1,"x4",-1,"x5",-1,"x6",-1];
     ans2 = GKZ([[1,1,1,1,1,1],
                 [0,0,0,1,1,1],
                 [0,1,0,0,1,0],
                 [0,0,1,0,0,1]],[0,0,0,0]);;
     Sweyl("x1,x2,x3,x4,x5,x6",[w]);
     ans2 = ReParse(ans2[0]);
     a = Sminimal(ans2);
   }
   
   
   
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