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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.2 and 1.4

version 1.2, 2000/06/08 08:37:53 version 1.4, 2000/06/14 07:44:05
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 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.1 2000/05/24 15:31:28 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.3 2000/06/09 08:04:54 takayama Exp $ */
 load["minimal.k"];  load["minimal.k"];
 def test5() {  def test5() {
   local a,b,c,cc,v;    local a,b,c,cc,v;
Line 139  def test8a() {
Line 139  def test8a() {
   
   v = [x,y,z];    v = [x,y,z];
   b = ans;    b = ans;
   Println("------ ker=im for Schreyer ?------------------");    Println("------ ker=im for Schreyer ?----- wrong method!!!-----------");
   c = Skernel(b[0],v);    c = Skernel(b[0],v);
   c = c[0];    c = c[0];
   sm1_pmat([c,b[1],v]);    sm1_pmat([c,b[1],v]);
Line 176  def test9() {
Line 176  def test9() {
   
 }  }
   
 /* Check if the complex is exact or not? */  /* Check if the complex by Sschreyer() is exact or not in our example? */
 def test10() {  def test10() {
   local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r;    local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r;
   f = "x^3-y^2*z^2";    f = "x^3-y^2*z^2";
Line 196  def test10() {
Line 196  def test10() {
   ans_all = Sschreyer(pp);  /* Schreyer by LaScala-Stillman */    ans_all = Sschreyer(pp);  /* Schreyer by LaScala-Stillman */
   ans2 = ans_all[0];    ans2 = ans_all[0];
   
   r= SisExact_h(ans2,[x,y,z]);    sm1(" /gb.verbose 1 def ");
   
     ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     Sweyl("x,y,z",ww2);
     ans2 = ReParse(ans2);
     r= IsExact_h(ans2,[x,y,z]);
   Print(r);    Print(r);
   
   return([r,[ans,ans2]]);    return([r,[ans,ans2]]);
   
 }  }
   
   def test11() {
     local  a;
     a = test_ann3("x^3-y^2*z^2");
     return(a);
   }
   /* f should be a string. */
   def test_ann3(f) {
     local a,v,ww2,ans2;
     a = Sannfs3_laScala2(f);
     ans2 = a[0];
     v = [x,y,z];
     ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     Sweyl("x,y,z",ww2);
     ans2 = ReParse(ans2);
     r= IsExact_h(ans2,[x,y,z]);
     Println(r);
     return([r,ans2]);
   }
   def test11a() {
     local a,v,ww2,ans2;
   /* constructed by test11.
     ans2 =
          [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
           [[3*Dx^2*h , 0 , Dy , -Dz] ,
            [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
            [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
            [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
            [0 , 0 , 0 , 0] ,
            [2*x*Dy*Dz , 0 , z , -y] ,
            [0 , 0 , 0 , 0] ,
            [0 , 0 , 0 , 0] ,
            [0 , 0 , 0 , 0]] ,
     [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy^2 , 3*Dy*Dz , -2*x*Dy , 2*x*Dz , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
      [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] ,
      [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
       [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
       [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]]
   */
     ans2 =
          [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
           [[3*Dx^2*h , 0 , Dy , -Dz] ,
            [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
            [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
            [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
            [2*x*Dy*Dz , 0 , z , -y]],
     [[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] ,
      [3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]];
   
     sm1_pmat( ans2[1]*ans2[0] );
     sm1_pmat( ans2[2]*ans2[1] );
     ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     Sweyl("x,y,z",ww2);
     ans2 = ReParse(ans2);
     r= IsExact_h(ans2,[x,y,z]);
     Println(r);
     return([r,ans2]);
   }
   
   def test12() {
     local a,v,ww2,ans2;
     a = Sannfs3("x^3-y^2*z^2");
     ans2 = a[0];
     v = [x,y,z];
     ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     Sweyl("x,y,z",ww2);
     ans2 = ReParse(ans2); /* DO NOT FORGET! */
     r= IsExact_h(ans2,[x,y,z]);
     Println(r);
     Println("It may stop by non-exact statement. The code of Sminimal_v (non-LaScala-Stillman contains bugs.");
     return([r,ans2]);
   }
   
   def test13() {
     Println("test13 try to construct a minimal free resolution");
     Println("of a GKZ system [[1,2]]. 6/12, 2000.");
     ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
     Sweyl("x1,x2",ww2);
     ans2 = GKZ([[1,2]],[0]);
     ans2 = ReParse(ans2[0]);
     return(Sminimal(ans2));
   }
   
   def test14() {
     Println("test14 try to construct a minimal free resolution");
     Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
     ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
     Sweyl("x1,x2,x3",ww2);
     ans2 = GKZ([[1,2,3]],[0]);  /* It stops by the strategy error. */
     ans2 = ReParse(ans2[0]);
     return(Sminimal(ans2));
   }
   def test14a() {
     Println("test14a try to construct a minimal free resolution");
     Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
     Println("Without automatic homogenization.");
     ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
     Sweyl("x1,x2,x3",ww2);
     ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,
             Dx2^2-Dx1*Dx3 ];
     ans2 = ReParse(ans2);
     return(Sminimal(ans2,"homogenized"));
   }
   
   def test15() {
     Println("test15 try to construct a minimal free resolution");
     Println("of a GKZ system [[1,2,3]] by the order filt. 6/12, 2000.");
     ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
     Sweyl("x1,x2,x3",ww2);
     ans2 = GKZ([[1,2,3]],[0]);
     ans2 = ReParse(ans2[0]);
     return(Sminimal(ans2));
   }
   
   def test15b() {
     Println("test15b try to construct a minimal free resolution");
     Println("of toric [[1,2,3]] by the order filt. 6/12, 2000.");
     ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
     Sweyl("x1,x2,x3",ww2);
     ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];
     ans2 = ReParse(ans2);
     return(Sminimal(ans2,"homogenized"));
   }
   
   def test16() {
     Println("test16 try to construct a minimal free resolution");
     Println("of a GKZ system [[1,2,3,5]] by the order filt. 6/12, 2000.");
     ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
     Sweyl("x1,x2,x3,x4",ww2);
     ans2 = GKZ([[1,2,3,5]],[0]);
     ans2 = ReParse(ans2[0]);
     return(Sminimal(ans2));
   }
   
   def test16b() {
     Println("test16b try to construct a minimal free resolution");
     Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000.");
     ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
     Sweyl("x1,x2,x3,x4",ww2);
     ans2 = GKZ([[1,2,3,5]],[0]);
     ans3 = Rest(ans2[0]);
     ans3 = ReParse(ans3);
     Println("Toric variety:");
     Println(ans3);
     return(Sminimal(ans3));
   }
   
   
   
   
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