from research import *
s=begin(995,'Retained-part measurement rank','How many independent totals describe a converted part and retained part?',{},['SupplementA690/30 table','File52c retained-lower family','C993'])
from algebra import Matrix
M=Matrix([[1,1],[P,1],[E,1]]);left=Matrix([[5,-6,1]]);det=Matrix([[1,1],[P,1]]).det()
a=artifact('model/retained_part_measurement.json',json.dumps(clean({'matrix':M.tolist(),'rank':M.rank(),'left_constraint':[5,-6,1],'inverse':'u=69(TP−T0); v=T0−u'}),indent=2)+'\n')
finish(s,{'basis':a,'rank':M.rank(),'two_measurement_determinant':det},'The native, P and E totals form a rank-two measurement system. Its dependent relation is5T0−6TP+TE=0.','Apply that basis to the complete supplied flank and macro fields.',{'rank_two':M.rank()==2,'left_kernel':list(left*M)==[0,0],'invertible_pair':det==-F(1,69)})