File: [local] / OpenXM / src / k097 / lib / minimal / minimal-test.k (download)
Revision 1.3, Fri Jun 9 08:04:54 2000 UTC (24 years ago) by takayama
Branch: MAIN
Changes since 1.2: +89 -4
lines
Bug fix of Sminimal().
test_ann3(f) computes the V-minimal free resolution for
the laplace transform of the annihilating ideal 1/f.
It also checks if the obtained one is exact or not by using
IsExact_h().
Sminimal() still contains troubles.
For example, it does not work for [x^2+y^2, x*y] with
(-1,-1,1,1) weight vector.
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/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.3 2000/06/09 08:04:54 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";
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 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");
return(a);
}
/* f should be a string. */
def test_ann3(f) {
local a,v,ww2,ans2;
a = Sannfs3_laScala2(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]);
}
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);
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]);
}