def __init__(self, pgl: PGL):
self._pgl = pgl
self._pf = pgl.get_pf()
from projective_sets.pxl2_subsets import psl2_a4_copies
from group_actions import PGLGroupAction
from projective_sets.pgl import PGL
qs = [3, 5, 7, 11, 23, 31, 47]
for q in qs:
pgl = PGL(2, q)
action = PGLGroupAction(pgl)
field = pgl.get_pf().get_field()
a4_copies = psl2_a4_copies(field)
good_a4 = [a4_copies[0]]
a4_copies.pop(0)
if q % 8 in [1, 7]:
while len(a4_copies) > 0 or len(good_a4) < 2:
a4 = a4_copies[0]
unique_a4 = True
for element in pgl.get_all_elements():
if element.det().legendre() != 1:
continue
a4_conjugated = set([element*x*element.inverse() for x in a4])
if a4_conjugated in good_a4:
unique_a4 = False
break
if unique_a4:
good_a4.append(a4)
a4_copies.pop(0)
for copy in good_a4:
print(q, copy)