s641.py

from research import *
from math import lcm
s=begin(641,'Identify the calendar compatibility period','Why is the full congruence period32760, and how does it meet the earlier common-volume family?',{'half_calendars':[168,180,182],'full_calendars':[336,360,364]},['C640; File12 calendar definitions; C575'])
half=lcm(168,180,182);full=lcm(336,360,364);old=900*364
finish(s,{'half_calendar_lcm':half,'full_calendar_lcm':full,'previous_volume_coefficient':old,'ratios':[F(full,half),F(old,half)]},'The period32760 is the least common multiple of the three half-calendars. Doubling gives65520 for full calendars; the earlier327600 common-volume coefficient is ten half-periods. The numerical link comes from the same calendar denominators, with units retained.','Execute the no-Cainan rail companion and locate which calendar divisibilities it preserves.',{'period':half==32760 and full==65520,'previous_volume':old==327600==10*half,'counts_increment':[half//x for x in [182,168,180]]==[180,195,182]})