from research import *
s=begin(705,'Verify the whole-set affine mirror','Does the declared5842 translation match the mirror for every fixed node?',{'center':-2921,'template_coefficients':[15,2,F(1,4)],'translation':5842},['Supplement A §13.2; C704'])
X=set(-2921+15*r+2*g+F(p,4) for r in [-1,1] for g in [-1,0,1] for p in [-1,1]); R=lambda x:-5842-x
pairs=sorted((x,R(x)) for x in X if x<R(x))
finish(s,{'transpositions':pairs,'fixed_points':sum(R(x)==x for x in X),'translated_equals_mirrored':{x+5842 for x in X}=={-x for x in X}},'The5842 translation sends the entire fixed field onto its mirror; the associated reflection permutes it in six pairs with no fixed node. This is affine reflection of phase coordinates, distinct from decimal digit reversal and from File52c’s rounded mirror chart.','Compare all four source-listed cycle totals against the same fixed set.',{'set_reflection':{R(x) for x in X}==X,'double_reflection':all(R(R(x))==x for x in X),'translation':{x+5842 for x in X}=={-x for x in X},'six_pairs':len(pairs)==6})