from research import *
s=begin(1048,'Complete42-coordinate array rank','What is the information content of seven rows, two phases and three clutch positions?',{},['File61 §7','File62 §1'])
from algebra import Matrix
rows=[];labels=[]
for j in [0,1]:
 for k in [0,1,2]:
  for i in range(7):rows.append([int(a==i) for a in range(7)]+[j,-k]);labels.append([i,j,k])
M=Matrix(rows);a=artifact('model/clutch_array_matrix.json',json.dumps({'labels':labels,'matrix':rows,'rank':M.rank(),'form':'b_i+j·p−k·h'},indent=2)+'\n')
finish(s,{'array':a,'rank':M.rank(),'output_dependency_dimension':42-M.rank()},'The unrestricted array has nine parameters and33 linear output dependencies. Its42 coordinates therefore are not42 independent numerical observations.','Find a minimal observation set and test what missing states conceal.',{'complete_field':M.rows==42,'rank_nine':M.rank()==9,'dependencies':42-M.rank()==33})