load PitounVarescon.sage

table1 = [
          [5 , 7,[2,3,11,47,97,4691,-178290313]],\
          [7 , 7,[2,5,11,17,41,619,-816371]],\
          [11 ,8,[2,3,5,7,37,101,5501,-1193167]],\
          [13 ,8,[3,5,7,11,19,73,1097,-85279]],\
          [17 ,8,[2,3,5,11,13,37,277,-203]],\
          [19 ,9,[2,3,5,7,29,31,59,12461, -7663849]],\
          [23 ,9,[2,3,5,11,13,19,59,2803,-194377]],\
          [29 ,9,[2,3,5,7,13,17,59,293,-11]],\
          [31 ,9,[3,5,7,11,13,17,53,326,-8137]],\
          [37 ,9,[2,3,5,19,23,31,43,569,-523]],\
          [41 ,9,[2,3,5,11,13,17,19,241,-1]],\
          [43,10,[2,3,5,13,17,29,31,127,511,-2465249]],\
          [47,10,[2,3,5,7,11,13,17,113,349,-1777]],\
          [53,10,[2,3,5,7,11,13,17,73,181,-1213]],\
          [59,10,[2,3,5,11,13,17,31,257,1392,-185401]],\
          [61,10,[2,3,5,7,13,17,29,83,137, -24383]],\
          [67,11,[2,3,5,7,11,13,17,31,47,5011,-2131]],\
          [71,10,[2,3,5,11,13,17,19,59, 79,-943]],\
          [73,10,[2,3,5,7,13,17,23,37,61,-1]],\
          [79,10,[2,3,5,7,11,23,29,103,107,-1]],\
          [83,10,[2,3,5,7,11,13,17,43,97,-1]],\
          [89,11,[2,3,5,7,11,23,31,41,97,401,-425791]],\
          [97,11,[2,3,5,7,11,13,19,23,43,73,-1]]
          ]

from itertools import product
Qx.<x>=QQ[]
for line in table1:
    p,t,ds = line
    print "-------------------------------------------"
    print "Check for p=",p," t=",t," ds=",ds
    for sbset in product([0,1],repeat=len(ds)):
        # enumerate characteristic functions of the subsets of the list ds 
        D=prod([ds[i]^sbset[i] for i in range(len(ds))])
        # product of the subset sbset
        D=D.squarefree_part()
        # replace D by its squarefree part
        classOK=True
        if D==1:
           continue
           # if D == 1 then the corresponding field are the rationals (skip)
        print "D=",D
        if (not is_p_rational(x^2-D,p)):
            # and (QuadraticField(D).class_number(proof=false) % p == 0 ):
            if QuadraticField(D).class_number() % p != 0:
                continue
            print "Failure for line\n"+str(line)+"\n"+"Q(sqrt("+str(D)+\
                 ")) is not "+str(p)+"-rational."
            print 
            break
            # If one cyclic subfield is not p-rational we don't test the others
            # because we cannot apply Proposition 2.9
    # When we reach this point all cyclic subfields have been tested
    # and we can apply Proposition 2.9 to conclude that 
    # the compositum number field is p-rational.
    print "The compositum is p-rational"