s991.py

from research import *
s=begin(991,'Allocation triangle','Do the three relative Key gains form one nested-selection law?',{},['C985–C990'])
fEP=(P-1)/(E-1);fPJ=(J-1)/(P-1);fEJ=(J-1)/(E-1);A=lambda f,k:1+f*(k-1)
finish(s,{'E_to_P':fEP,'P_to_J':fPJ,'E_to_J':fEJ,'nested_factor':A(fPJ,A(fEP,E))},'The fractions1/6,3/13 and1/26 satisfy the nested-selection product law. The derived3/13 alone supplies no source-appointed chronological cut.','Separate this selection composition from sequential application of Keys.',{'product':fEP*fPJ==fEJ,'fractions':[fEP,fPJ,fEJ]==[F(1,6),F(3,13),F(1,26)],'nested':A(fPJ,A(fEP,E))==J})