"""
This script reads a file which contains on each line a cyclic cubic field and, for a given list of primes p, tries to certify that the p-adic regulator is not divisible by p. It is Algorithm 3.
"""

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

E1=1                       # we treat all cyclic cubic fields with conductor 
E2=10000                   # in the interval [E1,E2]
ell=3                      # the script can be easily modified to deal with  
r=1                        # other abelian Galois groups
                           # so we specify ell=3 for "cubic"
                           # r=1 for Galois group = (Z/3^Z)^r
ps=[5,7,11,13,17,19]       # list of primes for which we certify that
                           # p doesn't divide the p-adic regulator
input_file="cubic-"+str(E1)+"-"+str(E2)+"-"+str(ell)+"-"+str(r)+".txt"
# the list of cyclic cubic fields is read from file input_file, created by
# the script ListCyclicCubic.sage
result_file="pRegulator-"+str(E1)+"-"+str(E2)+"-"+str(ell)+"-"+str(r)+"-"+str(ps)+".txt"
fd=open(input_file,"r")
gd=open(result_file,"ab+")

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

load algorithm2.sage
load Schirokauer.sage

# END OF TOOLS #############################################################

# Main enumeration.
Qx.<x>=QQ['x']
line=fd.readline()                      # line = next line of file fd
cond=0                                  # cond = conductor of previous field
while line != "":                       # until end f file    
    if not line[0] == "x":              # skip comment lines
        cond=int(line)
    else:
        f=Qx(line.strip())              # f = polynomial read in file
        K.<a>=NumberField(f)            # K=Q(a) is the number field of f
        OK=K.ring_of_integers()         # ring of integers
        m = K.disc().sqrt()             # since K is cyclic cubic, m=cond(K)
        if m < cond:                    # skip f if its conductor is smaller
            line=fd.readline()          # thanprevious conductor because
            continue                    # it has been already treated 
        for p in ps:
            bool = criterium_p_not_divides_pRegulator(f,p) 
            if bool == "True":
                bools = bools + ",False"
            else:
                bools = bools + ",Maybe"
        gd.write(str(f)+":"+bools+"\n")
        gd.flush()
    line=fd.readline()