s1034.py

from research import *
s=begin(1034,'Covenant relative-coordinate dimension','How much information disappears when absolute placement is removed?',{},['C1033'])
from covenant_model import *
from algebra import Matrix
def rel(v):
 r=regular(v);return [x-r['Q'] for k,x in r.items() if k!='Q']
M=Matrix(coefficient_matrix(rel,KEYS[:12]));v={k:F(x) for k,x in json.loads((ROOT/'model/covenant_source_inputs.json').read_text()).items()};w=v.copy();w['Q']+=215;w['T']+=215
finish(s,{'relative_rank':M.rank(),'absolute_rank':12,'shared_translation':[regular(w)[k]-regular(v)[k] for k in regular(v)]},'Removing one common placement leaves eleven relative parameters. The admitted whole-frame translation changes all coordinates equally and preserves the relational field.','Identify the two actual conditions behind the three147 rails.',{'one_dimension_removed':M.rank()==11,'translation_covariant':all(regular(w)[k]-regular(v)[k]==215 for k in regular(v))})