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expression manipulation - Group symbols by a given partition of the occuring symbols


I have following expression


−3bσd−3bσv−b−b2+2j−2j2−2j3+2j6+12



Mathematica input


12-b+2 j-Subscript[b, 2]-3 Subscript[b, Subscript[\[Sigma], d]]-3 Subscript[b, Subscript[\[Sigma], v]]-2 Subscript[j, 2]-2 Subscript[j, 3]+2 Subscript[j, 6]

I want to reorder this expression by partitioning the occuring symbols. Additionally, common factors of the partitions should be factored out:


Partition (given by user): {{j,j2,j3,j6},{b,b2,bσd,bσv}}


The order should also be respected. The end result would look like 2(j−j2−j3+j6)−(b+b2+3bσd+3bσv)+12


I have considered FactorTerms[poly,{x_1,x_2,...] and Collect[expr,{x_1,x_2,...}] but was not successful to achieve this.



Answer



expr = 12 - b + 2 j - Subscript[b, 2] - 
 3 Subscript[b, Subscript[σ, d]] - 

 3 Subscript[b, Subscript[σ, v]] - 2 Subscript[j, 2] - 
 2 Subscript[j, 3] + 2 Subscript[j, 6]

Inactive[Plus] @@ 
  (Total /@ Join @@ 
     GatherBy[List @@ expr, MatchQ[_ (# | Subscript[#, _])] & /@ {j, b}])

TeXForm @ %



12+(−3bσd−3bσv−b−b2)+(2j−2j2−2j3+2j6)



Update:


ClearAll[f]
f[e_] := Row @ Flatten @ Append[Reverse @ Values @ 
   GroupBy[Transpose[{Coefficient[e, #], #}& @ Variables[e]] /.
      {a_, b_Symbol} :> {a, Subscript[b, 0]}, #[[2,1]]&, 
     Row[{# /. { 1 -> " + ", -1 -> " - "}, "(", HoldForm @ #2, ")"}]& @@ 
     FactorList[ Dot @@ Transpose[#]][[All, 1]]&],
      If[# < 0, {" - ", -#}, {" + ", #}]&[e /.

       (Alternatives@@Variables[e] -> 0)] /. {_, 0} -> Nothing] /.
    Subscript[a_, 0] -> a

Examples:


f @ expr

enter image description here


System`Convert`CommonDump`templateBoxToDisplay = BoxForm`TemplateBoxToDisplayBoxes;

TeXForm @ f @ expr



2(j−j2−j3+j6) - (b+b2+3bσd+3bσv) + 12



f[- expr - 20] // TeXForm


−2(j−j2−j3+j6) + (b+b2+3bσd+3bσv) - 32



Note: I used Carl's answer from this q/a to make TeXForm process Rows properly.



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