File: [local] / OpenXM / src / k097 / lib / minimal / minimal-test.k (download)
Revision 1.11, Tue Aug 1 06:26:10 2000 UTC (23 years, 11 months ago) by takayama
Branch: MAIN
Changes since 1.10: +12 -8
lines
A bug appeared in test_if_v_strict and IsExact_h.
It has not yet fixed.
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/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.11 2000/08/01 06:26:10 takayama Exp $ */
load["minimal.k"];
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";
p = Sannfs(f,"x,y,z");
ww = [["x",1,"y",1,"z",1,"Dx",1,"Dy",1,"Dz",1,"h",1],
["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
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",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 = sm1_resol1([pp,"x,y,z",ww]);
/* Schreyer is in ans. */
v = [x,y,z];
b = ans;
Println("------ ker=im for Schreyer ?------------------");
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);
}
/*
a = test8();
SisComplex(a):
*/
def test11() {
local a;
a = test_ann3("x^3-y^2*z^2");
return(a);
}
/* f should be a string. */
/* a=test_ann3("x^3+y^3+z^3");
It returns the following resolution in 1.5 hours. June 14, 2000.
[
[
[ x*Dx+y*Dy+z*Dz-3*h^2 ]
[ -z*Dy^2+y*Dz^2 ]
[ -z*Dx^2+x*Dz^2 ]
[ -y*Dx^2+x*Dy^2 ]
]
[
[ 0 , -x , y , -z ]
[ z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ]
[ y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ]
[ 0 , Dx^2 , -Dy^2 , Dz^2 ]
[ z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ]
]
[
[ -x*Dx+3*h^2 , y , -z , 0 , -x ]
[ Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ]
]
]
*/
def test_ann3(f) {
local a,v,ww2,ans2;
a = Sannfs3(f);
ans2 = a[0];
v = [x,y,z];
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]);
Println(r);
return([r,ans2,a]);
}
def test11a() {
local a,v,ww2,ans2;
/* constructed by test11.
ans2 =
[[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
[[3*Dx^2*h , 0 , Dy , -Dz] ,
[6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
[0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
[2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
[0 , 0 , 0 , 0] ,
[2*x*Dy*Dz , 0 , z , -y] ,
[0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0]] ,
[[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy^2 , 3*Dy*Dz , -2*x*Dy , 2*x*Dz , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] ,
[[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]]
*/
ans2 =
[[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
[[3*Dx^2*h , 0 , Dy , -Dz] ,
[6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
[0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
[2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
[2*x*Dy*Dz , 0 , z , -y]],
[[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] ,
[3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]];
sm1_pmat( ans2[1]*ans2[0] );
sm1_pmat( ans2[2]*ans2[1] );
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]);
Println(r);
return([r,ans2]);
}
def test12() {
local a,v,ww2,ans2;
a = Sannfs3("x^3-y^2*z^2");
ans2 = a[0];
v = [x,y,z];
ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
Sweyl("x,y,z",ww2);
ans2 = ReParse(ans2); /* DO NOT FORGET! */
r= IsExact_h(ans2,[x,y,z]);
Println(r);
return([r,ans2]);
}
def test13() {
Println("test13 try to construct a minimal free resolution");
Println("of a GKZ system [[1,2]]. 6/12, 2000.");
ans2 = GKZ([[1,2]],[0]);
/* Be careful!! It resets the grade to module1, not module1v */
ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
Sweyl("x1,x2",ww2);
ans2 = ReParse(ans2[0]);
Println(ans2);
return(Sminimal(ans2));
}
def test14() {
Println("test14 try to construct a minimal free resolution");
Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
ans2 = GKZ([[1,2,3]],[0]);
/* It stops by the strategy error.
July 26, 2000. It works fine after fixing a bug in resol.c */
ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
Sweyl("x1,x2,x3",ww2);
ans2 = ReParse(ans2[0]);
return(Sminimal(ans2));
}
def test14a() {
Println("test14a try to construct a minimal free resolution");
Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
Println("Without automatic homogenization.");
ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
Sweyl("x1,x2,x3",ww2);
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"]));
}
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]];
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 test15b() {
Println("test15b try to construct a minimal free resolution");
Println("of toric [[1,2,3]] by the order filt. 6/12, 2000.");
ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
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"]));
}
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.");
ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
Sweyl("x1,x2,x3,x4",ww2);
ans2 = GKZ([[1,2,3,5]],[0]);
ans2 = ReParse(ans2[0]);
return(Sminimal(ans2));
}
def test16b() {
Println("test16b try to construct a minimal free resolution");
Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000.");
ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
Sweyl("x1,x2,x3,x4",ww2);
ans2 = GKZ([[1,2,3,5]],[0]);
ans3 = Rest(ans2[0]);
ans3 = ReParse(ans3);
Println("Toric variety:");
Println(ans3);
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,cc;
Sweyl(v,[w]); b = Reparse(resmat);
c=Sinit_w(b,w);
Println("Resolution (b)----");
sm1_pmat(b);
Println("Initial (c)----");
sm1_pmat(c); cc=c;
Println("Exactness of the resolution ---");
Println(IsExact_h(b,v)); /* IsExact_h breaks the variable c.
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(IsExact_h(cc,v));
g = Sinvolutive(b[0],w);
/* Println("Involutive basis ---");
sm1_pmat(g);
Println(Sinvolutive(cc[0],w));
sm1(" /gb.verbose 1 def "); */
Println("Is same ideal?");
Println(IsSameIdeal_h(g,cc[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);
}
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);
}