s985.py

from research import *
s=begin(985,'First calibration and allocation pair','What factors satisfy the336/360 calibration and last-sixth completion identity?',{},['C984','File63 §1.3'])
from algebra import Matrix
M=Matrix([[336,-360],[1,-6]]);rhs=Matrix([0,-5]);sol=M.gauss_jordan_solve(rhs)[0]
finish(s,{'solution':list(sol),'determinant':M.det()},'These two retained relations uniquely recover E=25/23 and P=70/69. This is a backward constraint basis for already established relations.','Check whether the second calendar/partition pair demands the same E.',{'unique':M.det()!=0,'ratios':list(sol)==[E,P]})