//---[CLO, Using Algebraic Geometry, p. 432]
// 2-dimensional cyclic code [9,7]
// codifica di w |--> c
ring r = (2,a),(x,y),lp; minpoly = a^2+a+1;
ideal I = x^3-1, y^3-1;

qring q = std(I);
ideal J = x^2+a^2*x*y+a*y, y+1;
option(redSB);
ideal G = std(J);
poly w = x^2*y^2;
poly c = w - reduce(w,G);
c;
x2y2+(a+1)*x+(a)
reduce(c,G);
0
lead(J); 
_[1]=x2
_[2]=y
//posizioni di informazione: x^2,y, xy, x^2y,y^2,xy^2,x^2y^2
//--- posizioni di controllo: 1,x
division(w,G);
[1]:
   _[1,1]=x2y+x2
   _[2,1]=1
[2]:
   _[1]=(a+1)*x+(a)
[3]:
   _[1,1]=1
division(w,G)[2][1];
(a+1)*x+(a)
G;
G[1]=y+1
G[2]=x2+(a+1)*x+(a)
quit;