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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.1 and 1.6

version 1.1, 2000/05/24 15:31:28 version 1.6, 2000/07/26 02:21:31
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 /* $OpenXM$ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.5 2000/06/15 07:38:35 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 175  def test9() {
Line 175  def test9() {
   return([ans,ans2]);    return([ans,ans2]);
   
 }  }
   
   /* Check if the complex by Sschreyer() is exact or not in our example? */
   def test10() {
     local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r;
     f = "x^3-y^2*z^2";
     p = Sannfs(f,"x,y,z");
     ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
     Sweyl("x,y,z",ww2);
     pp = Map(p,"Spoly");
     ans = sm1_resol1([pp,"x,y,z",ww2]);
   
     f = "x^3-y^2*z^2";
     p = Sannfs(f,"x,y,z");
     sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
     ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
     Sweyl("x,y,z",ww);
     pp = Map(p,"Spoly");
     ans_all = Sschreyer(pp);  /* Schreyer by LaScala-Stillman */
     ans2 = ans_all[0];
   
     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);
   
     return([r,[ans,ans2]]);
   
   }
   
   def test11() {
     local  a;
     a = test_ann3("x^3-y^2*z^2");
     return(a);
   }
   /* f should be a string. */
   /* a=test_ann3("x^3+y^3+z^3");
   It returns the following resolution in 1.5 hours.  June 14, 2000.
    [
     [
       [    x*Dx+y*Dy+z*Dz-3*h^2 ]
       [    -z*Dy^2+y*Dz^2 ]
       [    -z*Dx^2+x*Dz^2 ]
       [    -y*Dx^2+x*Dy^2 ]
     ]
     [
       [    0 , -x , y , -z ]
       [    z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ]
       [    y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ]
       [    0 , Dx^2 , -Dy^2 , Dz^2 ]
       [    z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ]
     ]
     [
       [    -x*Dx+3*h^2 , y , -z , 0 , -x ]
       [    Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ]
     ]
    ]
   */
   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.");
     ans2 = GKZ([[1,2]],[0]);
      /* Be careful!! It resets the grade to module1, not module1v */
     ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
     Sweyl("x1,x2",ww2);
     ans2 = ReParse(ans2[0]);
     Println(ans2);
     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.");
     ans2 = GKZ([[1,2,3]],[0]);
        /* It stops by the strategy error.
           July 26, 2000. It works fine after fixing a bug in resol.c */
     ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
     Sweyl("x1,x2,x3",ww2);
     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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  Added in v.1.6
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