Pensieve header: Verifying the $PR^4$ relation.

Startup

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\SL2Portfolio2"];
<<"../Profile/Profile.m";
<<"Engine-Speedy.m";
<<"Objects.m";
HL[ℰ_] := Style[ℰ, Background -> If[TrueQ@ℰ,,]];
BeginProfile[];
PopupWindow[Button["Show Profile Monitor"],Dynamic[PrintProfile[], UpdateInterval->3, TrackedSymbols->{}]]

$k=1; (*ℏ=γ=1;*)

rhs=((Subscript[R, o1,u1])(Subscript[R, o3,u2])(Subscript[R, o2,u3])(Subscript[R, o4,u4]))//((Subscript[bm, o1,o3->o1])(Subscript[bm, o2,o4->o2])(Subscript[am, u1,u3->u1])(Subscript[am, u2,u4->u2]))

lhs=((Subscript[R, oa,u1])(Subscript[R, ob,u2])//(Subscript[bm, oa,ob->o]))((Subscript[R, o1,ua])(Subscript[R, o2,ub])//(Subscript[am, ua,ub->u]))//(Subscript[P, o,u]);

lhs≡rhs

(The above was tested to $k=4).

(Subscript[am, 1,2->3])

(Subscript[bm, 1,2->3])

?*Values

Cases[DownValues[Subscript], (a_:>_)/;!FreeQ[a,R]]//Column

Cases[DownValues[Subscript], (_[(Subscript[a_, __])]:>_)/;a===R]//Column

Cases[DownValues[Subscript], _[_[(Subscript[_, _List,_Integer])],_]] // Column

DownValues[Subscript]=Cases[DownValues[Subscript], Except[((_[(Subscript[a_, __])]:>_)/;a===R)|(_[_[(Subscript[_, _List,_Integer])],_])]]

Cases[DownValues[Subscript], (_[(Subscript[a_, __])]:>_)/;a===R]//Column

Cases[DownValues[Subscript], _[_[(Subscript[_, _List,_Integer])],_]] // Column

Define[(Subscript[R, i,j])=i+j]

Cases[DownValues[Subscript], (_[(Subscript[a_, __])]:>_)/;a===R]//Column

Cases[DownValues[Subscript], _[_[(Subscript[_, _List,_Integer])],_]] // Column