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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.7 and 1.10

version 1.7, 2000/07/30 02:26:25 version 1.10, 2000/08/01 05:16:02
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 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.6 2000/07/26 02:21:31 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.9 2000/08/01 03:42:35 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 41  def test8() {
Line 41  def test8() {
    SisComplex(a):     SisComplex(a):
 */  */
   
 def test8a() {  
   local p,pp,ans,b,c,cc,ww, ans_all;  
   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]];  
   /* Removed "x",1, ... ===> It causes an error. I do not know the reason.*/  
   Sweyl("x,y,z",ww);  
   pp = Map(p,"Spoly");  
   /* return(pp); */  
   /* pp =  
      [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 ,  
       2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ]  
   */  
   ans_all = Sschreyer(pp);  
   ans = ans_all[0];  
   /* ans = sm1_resol1([pp,"x,y,z",ww]); */  
   /* Schreyer is in ans. */  
   
   v = [x,y,z];  
   b = ans;  
   Println("------ ker=im for Schreyer ?----- wrong method!!!-----------");  
   c = Skernel(b[0],v);  
   c = c[0];  
   sm1_pmat([c,b[1],v]);  
   cc = sm1_res_div(c,b[1],v);  
   sm1_pmat(sm1_gb(cc,v));  
   c = Skernel(b[1],v);  
   c = c[0];  
   cc = sm1_res_div(c,b[2],v);  
   sm1_pmat(sm1_gb(cc,v));  
   return(ans);  
 }  
   
 /* Comparing two constructions */  
 def test9() {  
   local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2;  
   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);  
   ans2 = ans_all[0];  
   
   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() {  def test11() {
   local  a;    local  a;
   a = test_ann3("x^3-y^2*z^2");    a = test_ann3("x^3-y^2*z^2");
Line 169  def test_ann3(f) {
Line 79  def test_ann3(f) {
   ans2 = ReParse(ans2);    ans2 = ReParse(ans2);
   r= IsExact_h(ans2,[x,y,z]);    r= IsExact_h(ans2,[x,y,z]);
   Println(r);    Println(r);
   return([r,ans2]);    return([r,ans2,a]);
 }  }
 def test11a() {  def test11a() {
   local a,v,ww2,ans2;    local a,v,ww2,ans2;
Line 263  def test14a() {
Line 173  def test14a() {
   ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,    ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,
           Dx2^2-Dx1*Dx3 ];            Dx2^2-Dx1*Dx3 ];
   ans2 = ReParse(ans2);    ans2 = ReParse(ans2);
   return(Sminimal(ans2,"homogenized"));    return(Sminimal(ans2,["homogenized"]));
 }  }
   
 def test15() {  def test15() {
Line 289  def test15b() {
Line 199  def test15b() {
   Sweyl("x1,x2,x3",ww2);    Sweyl("x1,x2,x3",ww2);
   ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];    ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];
   ans2 = ReParse(ans2);    ans2 = ReParse(ans2);
   return(Sminimal(ans2,"homogenized"));    return(Sminimal(ans2,["homogenized"]));
 }  }
   
 def test15c() {  def test15c() {
Line 330  def test16b() {
Line 240  def test16b() {
   return(Sminimal(ans3));    return(Sminimal(ans3));
 }  }
   
   
   
   def test17() {
      a=Sannfs3("x^3-y^2*z^2");
      b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
      Sweyl("x,y,z",[w]); b = Reparse(b);
      c=Sinit_w(b,w);
      Println("Resolution (b)----");
      sm1_pmat(b);
      Println("Initial (c)----");
      sm1_pmat(c);
      Println(IsExact_h(c,"x,y,z"));
   }
   
   def test_if_v_strict(resmat,w,v) {
      local b,c;
      Sweyl(v,[w]); b = Reparse(resmat);
      c=Sinit_w(b,w);
      Println("Resolution (b)----");
      sm1_pmat(b);
      Println("Initial (c)----");
      sm1_pmat(c);
      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);
      /* Println("Involutive basis ---");
        sm1_pmat(g); */
      Println("Is same ideal?");
      Println(IsSameIdeal_h(g,c[0],"x,y"));
   }
   def test17b() {
      a=Sannfs3("x^3-y^2*z^2");
      b=a[0]; w = ["x",-1,"y",-1,"z",-5,"Dx",1,"Dy",1,"Dz",5];
      test_if_v_strict(b,w,"x,y,z");
      return(a);
   }
   
   def test18() {
      a=Sannfs2("x^3-y^2");
      b=a[0]; w = ["x",-1,"y",-1,"Dx",1,"Dy",1];
      test_if_v_strict(b,w,"x,y");
      return(a);
   }
   
   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);
   }
   
   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);
   }
   
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