load PitounVarescon.sage

Qx.<x>=QQ[]
table3 = [ (x^4+x^3+x^2+x+1              ,CyclicPermutationGroup(4),[]),     \
           (x^4-23*x^3-6*x^2+23*x-1      ,CyclicPermutationGroup(4),[7]),    \
           (x^4-x^2+1                    ,KleinFourGroup(),[]),              \
           (x^4+10*x^2+1                 ,KleinFourGroup(),[7]),             \
           (x^4-3                        ,DihedralGroup(4),[]),              \
           (x^4-6                        ,DihedralGroup(4),[7]),             \
           (x^4+8*x+12                   ,AlternatingGroup(4),[]),           \
           (x^4 - x^3 - 16*x^2 - 7*x + 27,AlternatingGroup(4),[7]),          \
           (x^4+x+1                      ,SymmetricGroup(4),[]),             \
           (x^4+35*x+1                   ,SymmetricGroup(4),[7])             
          ]

for line in table3:
    f,G,qs = line
    ps = [ p for p in primes(5,70) if not is_p_rational(f,p)]
    print f,ps,qs
    #if (ps == [] and qs == []) or (7 in qs and ps == [7]):
    #    print str(f)+" is p-rational as indicated" 
    #else:
    #    print "Error for f="+str(f)