read(program):
_Env_LRE_tau := tau;
_Env_LRE_x := x;

L:=(x+8)*(x+7)^2+(56+7*x)*tau+(-1-x)*tau^2;
tausqsols(L);

L:=-(16*(x+2))*(x+1)+(-28-8*x)*tau+(x+6)*(x+5)*tau^2;
tausqsols(L);

L:=-4*x*(x^5-2*x^4-21*x^3-66*x^2-72*x-64)+(320-96*x-56*x^2+64*x^3+24*x^4)*tau+(x+8)*(x^5-7*x^4-3*x^3-25*x^2+10*x-40)*tau^2;
tausqsols(L);

L:=x*(x+1)*(2+3*x)-4*tau+(4-12*x)*tau^2;
tausqsols(L);

L:=-8*x*(x+3)-4*tau+(x+2)^2*tau^2;
tausqsols(L);

# This one requires a field extension
L:=tau^2-tau-x^2-1;
tausqsols(L);