import Diff,math


def circle(t,x):
# dx0/dt = x1, dx1/dt = -x0
  return [x[1],-x[0]]


N=100
x0=x1=x2=x3=[1,0]
dt = math.pi*2/N

for i in range(N*100):
  x0=Diff.runge(circle,x0,i*dt,(i+1)*dt,100) 
  x1=Diff.runge(circle,x1,i*dt,(i+1)*dt,1) 
  x2=Diff.second(circle,x2,i*dt,(i+1)*dt,1) 
  x3=Diff.euler(circle,x3,i*dt,(i+1)*dt,1) 
  print x0[0],x0[1],x1[1],x2[1],x3[1]