"""
This script decides p-rationality of a list of cyclic cubic fields as in Algorithm 4.
"""

# DATA ################################################################

E1=1
E2=2
ell=3
r=1
p=[5,7,11,13,17,19]

fd=open("cubic-"+str(E1)+"-"+str(E2)+"-"+str(ell)+"-"+str(r)+".txt","r")
gd=open("result-"+str(E1)+"-"+str(E2)+"-"+str(ell)+"-"+str(r)+"-"+str(p)+".txt","w")

# TOOL SCRIPTS #######################################################

load algorithm1.sage
load algorithm2.sage
load PitounVarescon.sage

######################################################################


# Main enumeration.
Qx.<x>=QQ['x']
line=fd.readline()
while line != "":
    if line[0] == "x":
        f=Qx(line.strip())
        # read f in the file produced by ListCyclicCubic.sage                           if f.change_ring(GF(p)).discriminant() != 0:  # if p is not ramified
            c_cl = criterion_p_not_divides_h(f,p)
            c_unit = criterium_p_not_divides_pRegulator(f,p)
            if c_cl == "True" and c_unit == "True":
                gd.write(str(f)+":True,True,True\n")
                # If both the class number and the p-adic regulator are
                # non-divisible by p then by Lemma 2.1 
                # we conclude that K is p-rational.
                gd.flush()
                continue
        prational = is_p_rational(f,p)             
        gd.write(str(f)+":"+str(prational)+","+str(c_cl)+","+str(c_unit)+"\n")
        gd.flush()
    line=fd.readline()