OpenXM/src/k097/lib/minimal/minimal-test.k - diff

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Diff for /OpenXM/src/k097/lib/minimal/minimal-test.k between version 1.14 and 1.19

-version 1.14, 2000/08/02 04:26:36
+version 1.19, 2000/08/22 02:13:51
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- /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.13 2000/08/02 03:23:36 takayama Exp $ */
+ /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.18 2000/08/21 07:45:22 takayama Exp $ */
  load["minimal.k"];
  def sm1_resol1(p) {
    sm1(" p resol1 /FunctionValue set ");
 Line 334  def test21() {
 Line 334  def test21() {
 Line 334  def test21() {
     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));
+    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-maxR >= 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-maxR >= 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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