s988.py

from research import *
s=begin(988,'Calibration leaves one scale','What does common calendar volume determine without an allocation relation?',{},['C987','File12'])
from algebra import Matrix
M=Matrix([[336,-360,0],[336,0,-364]]);v=[F(1,336),F(1,360),F(1,364)];K=336*E
finish(s,{'rank':M.rank(),'free_family':'K·(1/336,1/360,1/364)','selected_common_volume':K},'Calendar calibration determines relative factors but leaves a common scale K. A completion relation fixes that scale; the other allocation becomes a compatibility check.','Derive the second allocation from the first pair and its calendar measure.',{'one_free_dimension':3-M.rank()==1,'calibrated_vector':list(M*Matrix(v))==[0,0],'common_volume':K==360*P==364*J})