File: [local] / OpenXM / src / k097 / lib / minimal / minimal-test.k (download)
Revision 1.23, Sun Dec 10 03:12:20 2000 UTC (23 years, 8 months ago) by takayama
Branch: MAIN
CVS Tags: R_1_3_1-2, RELEASE_1_3_1_13b, RELEASE_1_2_3_12, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, KNOPPIX_2006, HEAD, DEB_REL_1_2_3-9 Changes since 1.22: +2 -2
lines
Boundp(s) checks if the symbol s is bounded to a value or not.
GetPathName(s) checks if the file s exists in the current direcotry or
in LOAD_K_PATH. If there exists, it returns the path name.
Loading method for minimal.k is rewritten with these functions.
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/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.23 2000/12/10 03:12:20 takayama Exp $ */
load["lib/minimal/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;
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[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",-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);
test_if_v_strict(aa,w,"x1,x2,x3");
/* 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);
}