
(off gc)
(clearall)
(rabbit 2 2 15)
vars a,b,c,d;a*a-a,b*b-b,c*c-c,d*d-d,
a*b*a-a*b, b*a*b-a*b,a*c*a-a*c,c*a*c-a*c,a*d*a-a*d,d*a*d-a*d,b*c*b-b*c,c*b*c-b*c,b*d*b-b*d,d*b*d-b*d,c*d*c-c*d,d*c*d-c*d;

(clearall)
(ncpbh "in1" "r1" "p1")

(off gc)
(clearall)
(rabbit 2 3 24)
vars a,b,c,d,e;a*a-a,b*b-b,c*c-c,d*d-d,e*e-e,
a*b*a-a*b, b*a*b-a*b,a*c*a-a*c,c*a*c-a*c,a*d*a-a*d,d*a*d-a*d,
a*e*a-a*e, e*a*e-a*e,
b*c*b-b*c,c*b*c-b*c,b*d*b-b*d,d*b*d-b*d, b*e*b-b*e,e*b*e-b*e,
c*d*c-c*d,d*c*d-c*d, c*e*c-c*e,e*c*e-e*c,
e*d*e-d*e,d*e*d-d*e;

(off gc)
(clearring)

(setweights 1 1 1)
(minr)
12
1
vars x,y,a;x*x;
a*x,a*y;

(off gc)
(clearring)

(setweights 1 1 1)
(minr)
12
1
vars x,y,a;x*x+x*y+y*x+y*y;
a*x,a*y;

(off gc)
(clearring)

(setweights 1 1 1 1)
(minr)
12
1
vars x,y,z,a;x*y,y*x-z*z,x*x*z;
a*x,a*y,a*z;

Calculated Poincare-Betti series is
1t+3t^2z+2t^3z^2+1t^4z^2+1t^5z^3+1t^7z^4
+1t^8z^4+1t^9z^5+1t^11z^6+1t^12z^6


(off gc)
(clearring)
(modulebettinumbers)
12
1
vars x,y,z,a;x*y,y*x-z*z,x*x*z,
a*x,a*y,a*z;B(0,0)=1
B(1,1)=3
B(2,2)=2
B(2,3)=1
B(3,4)=1
B(3,5)=2
B(3,6)=1
B(4,6)=4
B(4,7)=3
B(5,7)=2
B(5,8)=4
B(5,9)=1
B(6,9)=2
B(5,10)=1
B(6,10)=4
B(6,11)=5
B(7,11)=5
    0   1   2   3   4   5   6   7   8   9   10  11  12
  +--------------------------------------------------
0 | 1   3   2   -   -   -   -   -   -   -   -   -
1 | -   -   1   1   -   -   -   -   -   -   -
2 | -   -   -   2   4   2   -   -   -   -
3 | -   -   -   1   3   4   2   -   -
4 | -   -   -   -   -   1   4   5
5 | -   -   -   -   -   1   5
6 | -   -   -   -   -   -
7 | -   -   -   -   -
8 | -   -   -   -
9 | -   -   -
10| -   -
11| -

(off gc)
(clearring)
(setweights 1 1 1 1)
(minr)
12
1
vars  z,x,y,a;x*y,y*x-z*z;
a*x,a*y,a*z;

(off gc)
(clearring)
(setweights 1 1 1 1)
(minr)
12
1
vars  x,y,z,a;x*y,y*x-z*z;
a*x,a*y,a*z;

(off gc)
(clearring)
(setweights 1 1 1 1)
(noncommify)
(simple)
vars  x,y,z,a;x*y,y*x-z*z;

(noncommify)
(setweights 1 1 1 1)
(modulebettinumbers)
12
1
vars  x,y,z,a;x*y,y*x-z*z,
a*x,a*y,a*z;

(setweights 1 1 1 1)
(modulebettinumbers)
12
1
vars  z,x,y,a;x*y,y*x-z*z,
a*x,a*y,a*z;


Calculated Poincare-Betti series is
1t+3t^2z+2t^3z^2


(off gc)
(clearring)
(modulebettinumbers)
12
1
vars x,y,z,a;x*y,y*x-z*z,a*x,a*y,a*z;

B(0,0)=1
B(1,1)=3
B(2,2)=2
B(3,5)=2
B(4,6)=3
B(5,7)=2
B(6,10)=2
B(7,11)=3
    0   1   2   3   4   5   6   7   8   9   10  11  12
  +--------------------------------------------------
0 | 1   3   2   -   -   -   -   -   -   -   -   -
1 | -   -   -   -   -   -   -   -   -   -   -
2 | -   -   -   2   3   2   -   -   -   -
3 | -   -   -   -   -   -   -   -   -
4 | -   -   -   -   -   -   2   3
5 | -   -   -   -   -   -   -
6 | -   -   -   -   -   -
7 | -   -   -   -   -
8 | -   -   -   -
9 | -   -   -
10| -   -
11| -
end of Calculations.
nil
