"""
Given a totally real number field Q(d_1^(1/2), ...,d_t^(1/2)) this script searches for a which are p-rational. Final result is printed in file examples-<p>-<t>.txt where p and t are to be replaced by their value.
"""

import itertools
load Schirokauer.sage

p = 97     # replace 97 with any other prime > 3
ds = [2, 3, 5, 7, 11, 13, 19, 23, 43,73] # found by search_example_2_12.sage   

t = len(ds) + 1
print "searchind d_",t,"...",
gd=open("examples-"+str(p)+"-"+str(t)+".txt","w")
d = 0  
found = false
while not found:
    d -= 1
    if gcd(d,prod(ds+[1])*p) != 1 or not d.is_squarefree():
        continue  # we must guarantee that Gal(K/Q) = (Z/2Z)^t 
                  # and p is unramified
    prop_2_10 = true
    for sbset in itertools.product([0,1],repeat=t):
        D=prod([ds[i]^sbset[i] for i in range(t-1)])*d 
        D=D.squarefree_part()
        if  QuadraticField(D).class_number() % p == 0:
            print D        
            prop_2_10 = false
            break         
    if prop_2_10:
        ds.append(d)
        print d
        found = true
# at this point prop_2_10 == true so the Proposition 2.10 can be applied
# to prove that K is p-rational
gd.write(str(ds))
gd.close()