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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.11 and 1.16

version 1.11, 2000/08/01 06:26:10 version 1.16, 2000/08/09 03:45:27
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Line 1 
 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.10 2000/08/01 05:16:02 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.15 2000/08/02 05:14:31 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 254  def test17() {
Line 254  def test17() {
 }  }
   
 def test_if_v_strict(resmat,w,v) {  def test_if_v_strict(resmat,w,v) {
    local b,c,g,cc;     local b,c,g;
    Sweyl(v,[w]); b = Reparse(resmat);     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); cc=c;     sm1_pmat(c);
    Println("Exactness of the resolution ---");     Println("Exactness of the resolution ---");
    Println(IsExact_h(b,v));  /* IsExact_h breaks the variable c.     Println(IsExact_h(b,v));
                                 THIS BUG SHOULD BE FIXED. */  
    Println("Why is the initial c rewritten by b? (buggy) ");sm1_pmat(c[0]);  
    Println("Exactness of the initial complex.---");     Println("Exactness of the initial complex.---");
    Println(IsExact_h(cc,v));     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(cc[0],w));        Println(Sinvolutive(c[0],w));
       sm1(" /gb.verbose 1 def "); */        sm1(" /gb.verbose 1 def "); */
    Println("Is same ideal?");     Println("Is same ideal?");
    Println(IsSameIdeal_h(g,cc[0],v));     Println(IsSameIdeal_h(g,c[0],v));
 }  }
 def test17b() {  def test17b() {
    a=Sannfs3("x^3-y^2*z^2");     a=Sannfs3("x^3-y^2*z^2");
Line 303  def test19() {
Line 303  def test19() {
   return(a);    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() {  def test20() {
   w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1];    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]);    ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[0,0]);
Line 325  def test20b() {
Line 327  def test20b() {
   /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */    /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */
   return(a);    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);
   }
   
   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);
   }
   
   
   
   
   
   
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