lindep([sqrt(2), sqrt(3), sqrt(2)+sqrt(3)])
lindep([1, 2 + 3 + 3^2 + 3^3 + 3^4 + O(3^5)])
lindep([1,2,3;4,5,6;7,8,9])
lindep([x*y, x^2 + y, x^2*y + x*y^2, 1])
lindep([0*x])
z = sqrt(1+5*y+y^2+y^3);
seralgdep(z, 2,3)
seralgdep(z, 2,2)
seralgdep(1/(1-y+O(y^5)), 1,1)
seralgdep(1+5*y+O(y^3), 1,10)
seralgdep(Ser([0,1,0,u]*Mod(1,(u^2+u+1)*Mod(1,2)),y),2,2)
S=sum(i=0,50,binomial(3*i,i)*T^i)+O(T^51);
seralgdep(S, 3, 3)
serdiffdep(S, 3, 3)
serdiffdep(exp(T^2)+T^2,3,3)
lindep([])
lindep([0])
lindep([1])
lindep([1,I])
algdep(1,0)
algdep(1,-1)
z=sqrt(2+O(7^4)); algdep(z,2)
z=Mod(-85995*a-52515,a^2-a-1);
algdep(z,1)
algdep(z,2)
lindep(Mod([E*x, E*x + E, E^2*x^2 + E*x + 2*E], E^3))
lindep([[1,0,0],[0,1,0],[1,1,0]])
lindep([[1,0,0]~,[0,1,0]~,[1,1,0]~])
lindep([[1,0,0]~,[0,1,0]~,[1,1,1]~])
lindep([[1,0,0]~,[0,1,0],[1,1,0]])
lindep([[1,0,0]~,[0,1,0]~,[1,1,0]~])

T=polcyclo(5,'t); zT = polroots(T)[1];
bestapprnf(sqrt(5), T)
bestapprnf(x*zT+sqrt(5), T, zT)
bestapprnf([exp(2*I*Pi/5)+2], T, zT)
z=sqrt(2);
bestapprnf(z+1, x^2-2)
bestapprnf(z+1, 4*x^2-2)
T=x^3-2; vT=polroots(T); z=3*2^(1/3)+1;
bestapprnf(z, T, vT[1])
type(bestapprnf(z, T, vT[2]))
