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 1.8 and 1.15

-version 1.8, 2000/07/31 01:21:41
+version 1.15, 2000/08/02 05:14:31
 Line 1
 Line 1
 Line 1
- /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.7 2000/07/30 02:26:25 takayama Exp $ */
+ /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.14 2000/08/02 04:26:36 takayama Exp $ */
  load["minimal.k"];
  def sm1_resol1(p) {
    sm1(" p resol1 /FunctionValue set ");
 Line 79  def test_ann3(f) {
 Line 79  def test_ann3(f) {
 Line 79  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;
 Line 240  def test16b() {
 Line 240  def test16b() {
 Line 240  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);
+ }

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