// make run by:
// execute(read("robot3.txt"));

ring r=(0,l2,a,b,c,s),(c1,s1,l3),lp;
option(redSB);
ideal id=l3*c+l2*c1-a,
l3*s+l2*s1-b,
c1^2+s1^2-1;
ideal j=std(id);
dim(j);
j;
ring t=0,(c1,s1,l3,l2,a,b,c,s),lp;
ideal id=imap(r,id);
ring re=(real,6),(c1,s1,l3,l2,a,b,c,s),lp;
ideal id=imap(t,id);
//ideal ids=subst(id,l2,3,a,4,b,3,c,1,s,0);
//ideal ids=subst(id,l2,3,a,5,b,2,c,1,s,0);
ideal ids=subst(id,l2,3,a,2.51,b,2.96,c,1,s,0);
ring re2=(real,15),(c1,s1,l3),lp;
ideal id=imap(re,ids);
ideal ids=std(id);
LIB "solve.lib";
list l=solve(ids,6,0);
l;