from research import *
s=begin(713,'Derive whole-total effects from a retained partition','Why does partialP produce the364/360 ratio in the new macro family?',{'upper':9660,'lower':2940,'total':12600},['C690; Supplement A §10.3'])
fraction=F(9660,12600); effects=[1+(k-1)*fraction for k in [P,E]]
finish(s,{'converted_fraction':fraction,'retained_fraction':F(2940,12600),'effective_total_ratios':effects,'calendar_ratios':[F(364,360),F(40*336,35*360)]},'The converted upper arm is23/30 of12600. Therefore partialP has total ratio1+(P−1)23/30=91/90, and partialE has ratio16/15. These are consequences of this retained partition, explaining its calendar-body outputs without adding universal Keys.','Compare the new partial-conversion mechanism with the earlier one-sixth and one-twenty-sixth bridges.',{'fractions':fraction==F(23,30) and F(2940,12600)==F(7,30),'effects':effects==[F(91,90),F(16,15)],'outputs':[12600*x for x in effects]==[12740,13440]})