(1/3,1/4) N=2 rel= None open germs: 0
   family: P=7 = 3+4+0  (m1,m2,v,n)=(3,4,2,4)  w=0.166667 meas1=0.500000 germs=[(1, 1), (1, -1), (2, 1), (2, -1)]
      float billiard: ('periodic', 7, 3, 4, 0)
   family: P=12 = 6+4+2  (m1,m2,v,n)=(3,2,1,3)  w=0.166667 meas1=0.500000 germs=[(1, -1), (1, 1)]
      float billiard: ('periodic', 12, 6, 4, 2)
   total G-measure of families: 1.0 exactly 1
   prediction: rational (None, 'no prediction')
(1/4,1/6) N=3 rel= None open germs: 0
   family: P=5 = 2+3+0  (m1,m2,v,n)=(2,3,1,2)  w=0.333333 meas1=0.666667 germs=[(1, 1), (1, -1), (2, 1), (2, -1)]
      float billiard: ('periodic', 5, 2, 3, 0)
   family: P=6 = 4+0+2  (m1,m2,v,n)=(2,0,0,1)  w=0.166667 meas1=0.333333 germs=[(1, -1), (1, 1)]
      float billiard: ('periodic', 6, 4, 0, 2)
   total G-measure of families: 1.0 exactly 1
   prediction: rational (None, 'no prediction')
(1/3,1/5) N=2 rel= None open germs: 0
   family: P=21 = 9+10+2  (m1,m2,v,n)=(9,10,4,10)  w=0.066667 meas1=0.600000 germs=[(1, 1), (1, -1), (2, 1), (2, -1)]
      float billiard: ('periodic', 21, 9, 10, 2)
   family: P=13 = 6+5+2  (m1,m2,v,n)=(6,5,2,6)  w=0.066667 meas1=0.400000 germs=[(1, -1), (1, 1)]
      float billiard: ('periodic', 13, 6, 5, 2)
   total G-measure of families: 1.0 exactly 1
   prediction: rational (None, 'no prediction')
(1/3,1/6) N=3 rel= None open germs: 0
   family: P=14 = 6+6+2  (m1,m2,v,n)=(3,3,1,3)  w=0.333333 meas1=1.000000 germs=[(1, 1), (1, -1), (1, 1), (1, -1), (2, 1), (2, -1)]
      float billiard: ('periodic', 14, 6, 6, 2)
   total G-measure of families: 1.0 exactly 1
   prediction: T5 (True, 'ok')
(1/4,1/sqrt30) N=2 rel= (2, 0, 1) open germs: 4
   family: P=6 = 4+0+2  (m1,m2,v,n)=(2,0,0,1)  w=0.134852 meas1=0.269703 germs=[(1, -1), (1, 1)]
      float billiard: ('periodic', 6, 4, 0, 2)
   total G-measure of families: 0.2697032566597785 
   prediction: 4b (True, 'ok')
   certificate on complement: (3, -6, -2, 7)
((5-sqrt5)/10, sqrt5/10) N=2 rel= (1, 1, 1) open germs: 0
   family: P=4 = 2+2+0  (m1,m2,v,n)=(2,2,1,2)  w=0.341641 meas1=0.683282 germs=[(1, 1), (2, -1)]
      float billiard: ('periodic', 4, 2, 2, 0)
   family: P=14 = 6+6+2  (m1,m2,v,n)=(3,3,1,3)  w=0.105573 meas1=0.316718 germs=[(1, -1), (1, 1), (1, -1), (2, 1)]
      float billiard: ('periodic', 14, 6, 6, 2)
   total G-measure of families: 1.0 exactly 1
   prediction: T5 (True, 'ok')
(5/11+sqrt2/100, 5/11-sqrt2/1000)  r1+10r2=5 N=1 rel= (1, 10, 10) open germs: 6
   total G-measure of families: 0.0 
   prediction: 4c (True, 'ok')
   certificate on complement: (3, 8, 30, 12)
