s608.py

from research import *
s=begin(608,'Derive covariance of anchored Keys','When does a translation commute with an anchored dilation?',{'anchor':14004,'point':1446,'translation':2,'Key':J},['General anchored-Key grammar; C572'])
D=lambda a,k,x:a+k*(x-a);a,x,t=F(14004),F(1446),F(2);lhs=D(a,J,x)+t;frame=D(a+t,J,x+t);point_only=D(a,J,x+t)
finish(s,{'translate_output':lhs,'move_anchor_and_point':frame,'move_point_only':point_only,'point_only_residual':point_only-lhs,'identity':'T_t D(a,k)=D(a+t,k) T_t'},'Translation commutes with dilation when the anchor moves with the frame. Holding the anchor while translating only the point leaves residual(k−1)t, here2/299. This formalizes why whole-pair and one-end changes behave differently.','Determine how allocation equivalence changes when interior junctions are retained.',{'covariance':lhs==frame==1406,'residual':point_only-lhs==(J-1)*t==F(2,299)})