load fast_unit.sage

fd=open("clean_cubic-1-4000-3-1.txt","r")
gd=open("fastprincipal-1-4000-3-1.txt","w")
hd=open("principalnonfast-1-4000-3-1.txt","w")
id=open("fastnonprincipal-1-4000-3-1.txt","w")


def gl_is_principal(f):
    K.<a> = NumberField(f)
    OK = K.ring_of_integers()
    m = K.disc().sqrt()
    answer = false
    for ell in m.prime_factors():
        gl = (ell*OK).factor()[0][0]
        if gl.is_principal():
            answer = true
            break
    return answer  


Qx.<x>=QQ[]
line=fd.readline()
total = 0
principalfast = 0
fastnonprincipal = 0
principalnonfast = 0
while line != "":
    if line[0] != "x":
        line=fd.readline()
        continue
    f=Qx(line)
    total += 1
    eps0,eps1=fast_units(f)
    fast_cond = eps0.is_unit() and (not eps0 in [1,-1])
    princ_cond =  gl_is_principal(f)
    if princ_cond and fast_cond:
        principalfast += 1 
        gd.write(line) 
    elif princ_cond and not fast_cond:
        principalnonfast += 1
        hd.write(line)
    elif fast_cond and not princ_cond:
        fastnonprincipal += 1
        id.write(line)
    line=fd.readline()
   

print total,principalnonfast,fastnonprincipal,principalfast