-- Initial analysis of the problem of 
-- 3 microphones and 3 speakers in the 
-- plane. This shows 32 solutions, however, 
-- removing symmetries gives the 8 solutions 
-- in the paper. 

KK = ZZ / 30097;
R = KK[a,b,c,x_1..x_6];
X1=transpose matrix {{0_R,0}};
X2=transpose matrix {{a,0}};
X3=transpose matrix {{b,c}};
Y1=transpose matrix {{x_1,x_2}};
Y2=transpose matrix {{x_3,x_4}};
Y3=transpose matrix {{x_5,x_6}};
fun=(X,Y,dum)->(m:=random(R^1,R^1); ideal (transpose(X-Y)*(X-Y)+m)); 
idfun=(X1,X2,X3,Y,m)->fun(X1,Y,m)+fun(X2,Y,m)+fun(X3,Y,m);
I=idfun(X1,X2,X3,Y1,1)+idfun(X1,X2,X3,Y2,1)+idfun(X1,X2,X3,Y3,1);
gbTrace 0
dim I,degree I