s964.py

from research import *
s=begin(964,'Late begetting constraint rank','What do the three capped lives determine about four late begetting intervals?',{'matrix':[[1,1,1,1],[0,0,1,1],[0,0,0,1]],'rhs':[246,119,52]},['C961','File18 §3.1'])
M=s['inputs']['matrix']; kernel=[1,-1,0,0]; dots=[sum(a*b for a,b in zip(row,kernel)) for row in M]; recovered={'Lamech_completed':52,'Methuselah':119-52,'Jared_plus_Enoch':246-119}
finish(s,{'rank':3,'kernel':kernel,'recoverable':recovered},'The cap equations recover Lamech52, Methuselah67, and Jared+Enoch127; they do not separate Jared from Enoch.','Add the independently retained Enoch65 row and test the complete late reconstruction.',{'kernel':dots==[0,0,0],'rank_three':M[0][0]*M[1][2]*M[2][3]==1,'recovered':recovered=={'Lamech_completed':52,'Methuselah':67,'Jared_plus_Enoch':127}})