===================================================================
RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal-test.k,v
retrieving revision 1.6
retrieving revision 1.17
diff -u -p -r1.6 -r1.17
--- OpenXM/src/k097/lib/minimal/minimal-test.k	2000/07/26 02:21:31	1.6
+++ OpenXM/src/k097/lib/minimal/minimal-test.k	2000/08/10 02:59:08	1.17
@@ -1,86 +1,9 @@
-/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.5 2000/06/15 07:38:35 takayama Exp $ */
+/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.16 2000/08/09 03:45:27 takayama Exp $ */
 load["minimal.k"];
-def test5() {
-  local a,b,c,cc,v;
-  a = Sannfs3_laScala2("x^3-y^2*z^2");
-  b = a[0];
-  v = [x,y,z];
-  c = Skernel(b[0],v);
-  c = c[0];
-  sm1_pmat([c,b[1],v]);
-  Println("-----------------------------------");
-  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(a);
-}
-def test6() {
-  local a,b,c,cc,v;
-  a = Sannfs3("x^3-y^2*z^2");
-  b = a[0];
-  v = [x,y,z];
-  c = Skernel(b[0],v);
-  c = c[0];
-  sm1_pmat([c,b[1],v]);
-  Println("-------ker = im for minimal ?---------------------");
-  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));
-  Println("------ ker=im for Schreyer ?------------------");
-  b = a[3];
-  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(a);
-}
-
-/* May 23, Tue */
-def test7() {
-  local a,b,c,cc,v;
-  a = Sannfs3_laScala2("x^3-y^2*z^2");
-  b = a[0];
-  v = [x,y,z];
-  c = Skernel(b[0],v);
-  c = c[0];
-  sm1_pmat([c,b[1],v]);
-  Println("-------ker = im for minimal ?---------------------");
-  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));
-  Println("------ ker=im for Schreyer ?------------------");
-  b = a[3];
-  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(a);
-}
-
 def sm1_resol1(p) {
   sm1(" p resol1 /FunctionValue set ");
 }
 
-
 def test8() {
   local p,pp,ans,b,c,cc,ww,ww2;
   f = "x^3-y^2*z^2";
@@ -118,96 +41,6 @@ def test8() {
    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() {
   local  a;
   a = test_ann3("x^3-y^2*z^2");
@@ -238,7 +71,7 @@ It returns the following resolution in 1.5 hours.  Jun
 */
 def test_ann3(f) {
   local a,v,ww2,ans2;
-  a = Sannfs3_laScala2(f);
+  a = Sannfs3(f);
   ans2 = a[0];
   v = [x,y,z];
   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
@@ -246,7 +79,7 @@ def test_ann3(f) {
   ans2 = ReParse(ans2);
   r= IsExact_h(ans2,[x,y,z]);
   Println(r);
-  return([r,ans2]);
+  return([r,ans2,a]);
 }
 def test11a() {
   local a,v,ww2,ans2;
@@ -305,7 +138,6 @@ def test12() {
   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]);
 }
 
@@ -341,17 +173,23 @@ def test14a() {
   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"));
+  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]);  
+  Sweyl("x1,x2,x3",ww2);
   ans2 = ReParse(ans2[0]);
-  return(Sminimal(ans2));
+  a = Sminimal(ans2);
+  Println("Minimal Resolution is "); sm1_pmat(a[0]);
+  Sweyl("x1,x2,x3");
+  ans3 = ReParse(a[0]);
+  r= IsExact_h(ans3,[x1,x2,x3]);
+  Println(r);
+  return(a);
 }
 
 def test15b() {
@@ -361,9 +199,24 @@ def test15b() {
   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"));
+  return(Sminimal(ans2,["homogenized"]));
 }
 
+def test15c() {
+  Println("test15c try to construct a minimal free resolution ");
+  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]);
+  Sweyl("x1,x2,x3");
+  ans3 = ReParse(a[0]);
+  r= IsExact_h(ans3,[x1,x2,x3]);
+  Println(r);
+  return(a);
+}
 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.");
@@ -387,6 +240,227 @@ def test16b() {
   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,g;
+   Sweyl(v,[w]); b = Reparse(resmat);
+   Println("Degree shifts ");
+   Println(SgetShifts(b,w));
+   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(Sinvolutive(c[0],w));
+      sm1(" /gb.verbose 1 def "); */
+   Println("Is same ideal?");
+   Println(IsSameIdeal_h(g,c[0],v));
+}
+def test17b() {
+   a=Sannfs3("x^3-y^2*z^2");
+   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");
+   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);
+}
+
+/* Need more than 100M memory. 291, 845, 1266, 1116, 592 : Schreyer frame.
+   I've not yet tried to finish the computation. */
+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);
+}
+
+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);
+}
+
+
+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);
+}
+
+