s752.py

from research import *
s=begin(752,'Derive the finite rounding defect law','Can one residue table explain every parts-versus-total defect?',{},['C749–750; File51a rounding rules'])
q=lambda n:5*((n+2)//5)
table=[[q(b)+q(r)-q(b+r) for r in range(5)] for b in range(5)]
finish(s,{'table_b_rows_r_columns':table,'formula':'K(b,r)=Q(b)+Q(r)-Q(b+r)','periodicity':'Q(x+5k)=Q(x)+5k'},'Every compatible integer row belongs to one of 25 residue classes; defects are only −5,0,+5. Methuselah and Reu share class(2,2).','Check whether the three traditions add new defect classes within the admitted domains.',{'values':sorted(set(sum(table,[])))==[-5,0,5],'periodic_exhaustion':all(q(b)+q(r)-q(b+r)==table[b%5][r%5] for b in range(100) for r in range(100))})