===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal-test.k,v
retrieving revision 1.13
retrieving revision 1.21
diff -u -p -r1.13 -r1.21
--- OpenXM/src/k097/lib/minimal/minimal-test.k	2000/08/02 03:23:36	1.13
+++ OpenXM/src/k097/lib/minimal/minimal-test.k	2000/08/24 00:48:58	1.21
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.12 2000/08/01 08:51:02 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.20 2000/08/22 05:34:06 takayama Exp $ */
 load["minimal.k"];
 def sm1_resol1(p) {
   sm1(" p resol1 /FunctionValue set ");
@@ -334,14 +334,181 @@ 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 = 3; /* 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 = 3; /* 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",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
+   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);
+}
+
+def test25b() {
+  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 = ans2[0];
+  sm1(" ans2 rest rest rest rest /ans2 set ");
+  Println(ans2);  /* Generators of the toric ideal */
+  ans2 = ReParse(ans2);
+  a = Sminimal(ans2);
+}
+