from research import *
s=begin(1047,'Eliminate the generated common point','How many source constraints are added by two routes to one landing?',{},['C1040','C1041'])
from algebra import Matrix
M=Matrix([[1,-J,0,-1],[1,0,-E,-1]])
finish(s,{'unknowns':['Q','Levi_radius','Joseph_radius','common_point'],'two_route_rank':M.rank(),'eliminated_relation':'J·Levi_radius=E·Joseph_radius, equivalently13w=12u','interpretation':'one equation defines the point; one tests agreement'},'Adding a common-point coordinate introduces one generated quantity and one agreement condition. The two displayed landings should not be counted as two independent source constraints.','Model the complete phase/clutch field before imposing its numerical source equalities.',{'two_equations':M.rank()==2,'primitive_ratio':J/E==F(12,13)})