[✓] Entity throws a set:tag inactive in (....)[..] is protected, ...

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 Hi, Entity throws a set:tag inactive in (....)[..] is protected, but ReleaseHold[WolframAlpha[...] is not. I am wondering why. I am following Michael Trott blog at: http://blog.wolfram.com/data/uploads/2013/08/MusingMagnets.cdf He is getting curated data into the notebook by using WolframAlpha: \[Psi]BarMagnetHeld = WolframAlpha[ "magnetic potential rectangular bar magnet", {{"Result", 1}, "Input"}]; (* magnetic potential *) \[Psi]BarMagnet[{x_, y_, z_}, {a_, b_, c_}] = ReleaseHold[\[Psi]BarMagnetHeld]/Subscript[M, 0]; His output from the second input looks like this: -(1/(4 \[Pi]))(((-(a/2) - x) (-(b/2) - y))/ Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] - ((a/2 - x) (-(b/2) - y))/ Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] - ((-(a/2) - x) (b/2 - y))/ Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + ((a/2 - x) (b/2 - y))/ Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] - ((-(a/2) - x) ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - y)^3)/(2 ((-(b/2) - y)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^( 3/2) + (-(a/2) - x)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) - ((-(a/2) - x)^3 ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - y))/(2 ((-(a/2) - x)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^( 3/2) + (-(b/2) - y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) + ((a/2 - x) ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - y)^3)/(2 ((-(b/2) - y)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^( 3/ 2) + (a/2 - x)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) + ((a/2 - x)^3 ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - y))/(2 ((a/2 - x)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^( 3/2) + (-(b/2) - y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) + ((-(a/2) - x) ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - y)^3)/(2 ((b/2 - y)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) + (-(a/2) - x)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) + ((-(a/2) - x)^3 ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - y))/(2 ((-(a/2) - x)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) + (b/2 - y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - z)^2)) - ((a/2 - x) ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - y)^3)/(2 ((b/2 - y)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) + (a/2 - x)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/ 2) - z)^2)) - ((a/2 - x)^3 ((a/2 - x)^2 + (b/2 - y)^2) (b/ 2 - y))/(2 ((a/2 - x)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) + (b/2 - y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/ 2) - z)^2)) - ((-(a/2) - x) (-(b/2) - y))/ Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((a/2 - x) (-(b/2) - y))/ Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((-(a/2) - x) (b/2 - y))/ Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] - ((a/2 - x) (b/ 2 - y))/Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + ((-(a/2) - x) ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - y)^3)/(2 ((-(b/2) - y)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) + (-(a/2) - x)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - z)^2)) + ((-(a/2) - x)^3 ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - y))/(2 ((-(a/2) - x)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) + (-(b/2) - y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - z)^2)) - ((a/2 - x) ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - y)^3)/(2 ((-(b/2) - y)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) + (a/2 - x)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/ 2 - z)^2)) - ((a/2 - x)^3 ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - y))/(2 ((a/2 - x)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) + (-(b/2) - y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/ 2 - z)^2)) - ((-(a/2) - x) ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - y)^3)/(2 ((b/2 - y)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) + (-(a/2) - x)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/ 2 - z)^2)) - ((-(a/2) - x)^3 ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - y))/(2 ((-(a/2) - x)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) + (b/2 - y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/ 2 - z)^2)) + ((a/2 - x) ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - y)^3)/(2 ((b/2 - y)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) + (a/2 - x)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - z)^2)) + ((a/2 - x)^3 ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - y))/(2 ((a/2 - x)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) + (b/2 - y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - z)^2)) + ((-(b/2) - y) (-(c/2) - z)^2)/((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(a/2) - x) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-( c/2) - z)^2) + ((-(a/2) - x) (-(c/2) - z)^2)/((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(b/2) - y) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-( c/2) - z)^2) - ((-(b/2) - y) (-(c/2) - z)^2)/((a/2 - x)^2 + (-(b/2) - y)^2 + (a/2 - x) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(c/ 2) - z)^2) - ((a/2 - x) (-(c/2) - z)^2)/((a/2 - x)^2 + (-(b/2) - y)^2 + (-(b/2) - y) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(c/ 2) - z)^2) - ((b/2 - y) (-(c/2) - z)^2)/((-(a/2) - x)^2 + (b/ 2 - y)^2 + (-(a/2) - x) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/ 2) - z)^2) - ((-(a/2) - x) (-(c/2) - z)^2)/((-(a/2) - x)^2 + (b/2 - y)^2 + (b/2 - y) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/ 2) - z)^2) + ((b/2 - y) (-(c/2) - z)^2)/((a/2 - x)^2 + (b/2 - y)^2 + (a/2 - x) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/2) - z)^2) + ((a/2 - x) (-(c/2) - z)^2)/((a/2 - x)^2 + (b/2 - y)^2 + (b/2 - y) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/2) - z)^2) + ((-(a/2) - x) (-(b/2) - y) ((-(a/2) - x)^2 + (-(b/2) - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) - z)^2)/(2 ((-(a/2) - x)^2 (-(b/2) - y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(3/2) (-(c/2) - z)^2)) - ((a/2 - x) (-(b/2) - y) ((a/2 - x)^2 + (-(b/2) - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) - z)^2)/(2 ((a/2 - x)^2 (-(b/2) - y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^( 3/2) (-(c/2) - z)^2)) - ((-(a/2) - x) (b/2 - y) ((-(a/2) - x)^2 + (b/2 - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) - z)^2)/(2 ((-(a/2) - x)^2 (b/2 - y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) (-(c/2) - z)^2)) + ((a/2 - x) (b/2 - y) ((a/2 - x)^2 + (b/2 - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) - z)^2)/(2 ((a/2 - x)^2 (b/2 - y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^( 3/2) (-(c/2) - z)^2)) - ((-(b/2) - y) (c/2 - z)^2)/((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(a/2) - x) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) - ((-(a/2) - x) (c/2 - z)^2)/((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(b/2) - y) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) + ((-(b/2) - y) (c/2 - z)^2)/((a/2 - x)^2 + (-(b/2) - y)^2 + (a/2 - x) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) + ((a/2 - x) (c/2 - z)^2)/((a/2 - x)^2 + (-(b/2) - y)^2 + (-(b/2) - y) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) + ((b/2 - y) (c/2 - z)^2)/((-(a/2) - x)^2 + (b/2 - y)^2 + (-(a/2) - x) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) + ((-(a/2) - x) (c/2 - z)^2)/((-(a/2) - x)^2 + (b/2 - y)^2 + (b/2 - y) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) - ((b/2 - y) (c/2 - z)^2)/((a/2 - x)^2 + (b/2 - y)^2 + (a/2 - x) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) - ((a/2 - x) (c/2 - z)^2)/((a/2 - x)^2 + (b/2 - y)^2 + (b/2 - y) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - z)^2) - ((-(a/2) - x) (-(b/2) - y) ((-(a/2) - x)^2 + (-(b/2) - y)^2 + 2 (c/2 - z)^2) (c/2 - z)^2)/(2 ((-(a/2) - x)^2 (-(b/2) - y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) (c/2 - z)^2)) + ((a/2 - x) (-(b/2) - y) ((a/2 - x)^2 + (-(b/2) - y)^2 + 2 (c/2 - z)^2) (c/2 - z)^2)/(2 ((a/2 - x)^2 (-(b/2) - y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^( 3/2) (c/2 - z)^2)) + ((-(a/2) - x) (b/2 - y) ((-(a/2) - x)^2 + (b/2 - y)^2 + 2 (c/2 - z)^2) (c/2 - z)^2)/(2 ((-(a/2) - x)^2 (b/2 - y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) (c/2 - z)^2)) - ((a/2 - x) (b/2 - y) ((a/2 - x)^2 + (b/2 - y)^2 + 2 (c/2 - z)^2) (c/2 - z)^2)/(2 ((a/2 - x)^2 (b/2 - y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^( 3/2) (c/2 - z)^2)) - (-(c/2) - z) ArcTan[((-(a/2) - x) (-(b/2) - y))/( Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z))] + (-(c/2) - z) ArcTan[((a/2 - x) (-(b/2) - y))/( Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - z))] + (-(c/2) - z) ArcTan[((-(a/2) - x) (b/2 - y))/( Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - z))] - (-(c/2) - z) ArcTan[((a/2 - x) (b/2 - y))/( Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - z))] + (c/2 - z) ArcTan[((-(a/2) - x) (-(b/2) - y))/( Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - z))] - (c/2 - z) ArcTan[((a/2 - x) (-(b/2) - y))/( Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - z))] - (c/2 - z) ArcTan[((-(a/2) - x) (b/2 - y))/( Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - z))] + (c/2 - z) ArcTan[((a/2 - x) (b/2 - y))/( Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - z))] + (-(b/ 2) - y) Log[-(a/2) - x + Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] + (-(a/ 2) - x) Log[-(b/2) - y + Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (-(b/ 2) - y) Log[ a/2 - x + Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (a/2 - x) Log[-(b/2) - y + Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (b/2 - y) Log[-(a/2) - x + Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] - (-(a/2) - x) Log[b/2 - y + Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] + (b/2 - y) Log[a/2 - x + Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] + (a/2 - x) Log[b/2 - y + Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] - (-(b/2) - y) Log[-(a/2) - x + Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] - (-(a/2) - x) Log[-(b/2) - y + Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (-(b/2) - y) Log[a/2 - x + Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (a/2 - x) Log[-(b/2) - y + Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (b/2 - y) Log[-(a/2) - x + Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] + (-(a/2) - x) Log[ b/2 - y + Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] - (b/ 2 - y) Log[ a/2 - x + Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] - (a/2 - x) Log[b/2 - y + Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]]) without any warnings. I am trying to do the same but without WolframAlpha. In[65]:= rbmmsp[{x_, y_, z_}, {a_, b_, c_}] = Entity["PhysicalSystem", "RectangularBarMagnet"][ "MagneticScalarPotential"]/Subscript[M, 0] During evaluation of In[65]:= Set::write: Tag Inactive in (-((Subscript[M, 0] (Log[Subscript[y, m]+Subscript[r, 1,1,1]] Subscript[x, m]-Log[Subscript[y, m]+Subscript[r, 1,1,2]] Subscript[x, m]-Log[Subscript[y, p]+Subscript[r, <<1>>]] Subscript[x, m]+<<71>>+<<22>>))/(4 \[Pi]))//.{Subscript[x, m]:>-(a/2)-x,Subscript[x, p]:>a/2-x,Subscript[y, m]:>-(b/2)-y,Subscript[y, p]:>b/2-y,<<7>>,Subscript[r, 2,1,2]:>Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)],Subscript[r, 2,2,1]:>Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\)],Subscript[r, 2,2,2]:>Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)]})[{x_,y_,z_},{a_,b_,c_}] is Protected. Out[65]= 1/Subscript[M, 0] (-(1/(4 \[Pi])) QuantityVariable[Subscript["M", 0],"Magnetization"] (Log[ \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) + Subscript["r", 1, 1, 1]] \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) + Subscript["r", 1, 1, 2]] \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Subscript["r", 1, 2, 1]] \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) + Log[ \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Subscript["r", 1, 2, 2]] \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) + Subscript["r", 2, 1, 1]] \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Log[ \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) + Subscript["r", 2, 1, 2]] \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Log[ \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Subscript["r", 2, 2, 1]] \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) - Log[ \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Subscript["r", 2, 2, 2]] \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Log[ \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) + Subscript["r", 1, 1, 1]] \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) + Subscript["r", 1, 1, 2]] \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Subscript["r", 2, 1, 1]] \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) + Log[ \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Subscript["r", 2, 1, 2]] \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) - Log[ \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) + Subscript["r", 1, 2, 1]] \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Log[ \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) + Subscript["r", 1, 2, 2]] \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) + Log[ \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Subscript["r", 2, 2, 1]] \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) - Log[ \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) + Subscript["r", 2, 2, 2]] \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) - ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) Subscript["r", 1, 1, 1])] \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) + ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) Subscript["r", 1, 2, 1])] \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) + ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) Subscript["r", 2, 1, 1])] \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) - ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) Subscript["r", 2, 2, 1])] \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) + ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) Subscript["r", 1, 1, 2])] \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) - ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) Subscript["r", 1, 2, 2])] \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) - ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) Subscript["r", 2, 1, 2])] \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) + ArcTan[( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/( \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) Subscript["r", 2, 2, 2])] \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/Subscript["r", 1, 1, 1] + ( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) Subscript["r", 1, 1, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 1$$, $$2$$]\)) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) Subscript["r", 1, 1, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 1$$, $$2$$]\)) - (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"m"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$1, 1, 1$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$1, 1, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/Subscript["r", 1, 1, 2] - ( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) Subscript["r", 1, 1, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 2$$, $$2$$]\)) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) Subscript["r", 1, 1, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 2$$, $$2$$]\)) + (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"m"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$1, 1, 2$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 2$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 1, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$1, 1, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 1, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/Subscript["r", 1, 2, 1] - ( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) Subscript["r", 1, 2, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 1$$, $$2$$]\)) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) Subscript["r", 1, 2, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 1$$, $$2$$]\)) + (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"p"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$1, 2, 1$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$1, 2, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/Subscript["r", 1, 2, 2] + ( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) Subscript["r", 1, 2, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 2$$, $$2$$]\)) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) Subscript["r", 1, 2, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 2$$, $$2$$]\)) - (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"p"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$1, 2, 2$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$1, 2, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 2$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$1, 2, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$1, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$1, 2, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/Subscript["r", 2, 1, 1] - ( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) Subscript["r", 2, 1, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 1$$, $$2$$]\)) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) Subscript["r", 2, 1, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 1$$, $$2$$]\)) + (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"m"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$2, 1, 1$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$2, 1, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 1$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\))/Subscript["r", 2, 1, 2] + ( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) Subscript["r", 2, 1, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 2$$, $$2$$]\)) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) Subscript["r", 2, 1, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 2$$, $$2$$]\)) - (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"m"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$2, 1, 2$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 1, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 2$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$2, 1, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 1, 2$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 1, 2$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/Subscript["r", 2, 2, 1] + ( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) Subscript["r", 2, 2, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 1$$, $$2$$]\)) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) Subscript["r", 2, 2, 1] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 1$$, $$2$$]\)) - (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"p"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$2, 2, 1$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 1$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$2, 2, 1$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 1$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"m"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 1$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\))/Subscript["r", 2, 2, 2] - ( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) Subscript["r", 2, 2, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 2$$, $$2$$]\)) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\))/( \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) Subscript["r", 2, 2, 2] + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 2$$, $$2$$]\)) + (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$3$$]\ \*SubscriptBox[$$"y"$$, $$"p"$$]\ $$(\(- \*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \*SubsuperscriptBox[$$"r"$$, $$2, 2, 2$$, $$2$$])\)\))/(2 (\!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 2$$, $$3$$]\))) + ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$3$$]\) (- \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) + \!$$\*SubsuperscriptBox[\("r"$$, $$2, 2, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("y"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 2$$, $$3$$]\))) - ( \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\) (\!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"r"$$, $$2, 2, 2$$, $$2$$]\)))/(2 (\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$]\ \*SubscriptBox[$$"r"$$, $$2, 2, 2$$]\) + \!$$\*SubsuperscriptBox[\("z"$$, $$"p"$$, $$2$$]\ \*SubsuperscriptBox[$$"r"$$, $$2, 2, 2$$, $$3$$]\)))) \!$$\* TagBox["//.", "InactiveToken", BaseStyle->"Inactive", SyntaxForm->"//."]$$ { \!$$\*SubscriptBox[\("x"$$, $$"m"$$]\) :> -(QuantityVariable[ "a","Length"]/2) - QuantityVariable["x","Length"], \!$$\*SubscriptBox[\("x"$$, $$"p"$$]\) :> QuantityVariable["a","Length"]/2 - QuantityVariable[ "x","Length"], \!$$\*SubscriptBox[\("y"$$, $$"m"$$]\) :> -(QuantityVariable[ "b","Length"]/2) - QuantityVariable["y","Length"], \!$$\*SubscriptBox[\("y"$$, $$"p"$$]\) :> QuantityVariable["b","Length"]/2 - QuantityVariable[ "y","Length"], \!$$\*SubscriptBox[\("z"$$, $$"m"$$]\) :> -(QuantityVariable[ "c","Length"]/2) - QuantityVariable["z","Length"], \!$$\*SubscriptBox[\("z"$$, $$"p"$$]\) :> QuantityVariable["c","Length"]/2 - QuantityVariable[ "z","Length"], Subscript["r", 1, 1, 1] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\)], Subscript["r", 1, 1, 2] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)], Subscript["r", 1, 2, 1] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\)], Subscript["r", 2, 1, 1] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\)], Subscript["r", 1, 2, 2] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)], Subscript["r", 2, 1, 2] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"m"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)], Subscript["r", 2, 2, 1] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"m"$$, $$2$$]\)], Subscript["r", 2, 2, 2] :> Sqrt[\!$$\*SubsuperscriptBox[\("x"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"y"$$, $$"p"$$, $$2$$] + \*SubsuperscriptBox[$$"z"$$, $$"p"$$, $$2$$]\)]}) and I am getting the warning.How can I avoid it? Thanks ahead, János
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Posted 1 year ago
 Let's look at the output of Entity["PhysicalSystem", "RectangularBarMagnet"]["MagneticScalarPotential"] The output will look fairly normal, but if you inspect it closely, you'll notice two things. (1) "Subscript[M, 0]" is not actually a simple variable. Mouse over it. It's a "QuantityVariable". More specifically it's actually: QuantityVariable[Subscript["M", 0], "Magnetization"] You need to divide by that and not Subscript[M, 0].(2) The expression contains Inactivate. Inactivate is a more modern way of stoping something from evaluating than using Hold. Use Activate to remove the Inactivations. Activate[Entity["PhysicalSystem", "RectangularBarMagnet"]["MagneticScalarPotential"]/QuantityVariable[Subscript["M", 0],"Magnetization"]] 
 Hi Sean,I saw the HoldComplete[ReleaseHold[Hold[... ] construct and the ReleaseHold[...] on the result when executed Michael's code in Mathematica, so I also tried ReleaseHold[...] on the Entity[...] line, but it did not worked. Of course now Activate[...] with the QuantityVariable[Subscript["M", 0],"Magnetization"]] is working and the two outputs are the same, so I can continue with me study of his blog. Thanks a lot, János