Skip to main content

factorization - Lists of coefficients of derivatives


I want to extract two separate lists of coefficients of derivatives. If I have, for example,


cl= A1*D[P[x, y], {x, 1}] + A2*D[P[x, y], {x, 2}] + 
    A3*D[Q[x, y], {y, 3}] + A4*D[Q[x, y], {y, 1}];


I want to extract the lists {A1, A2} and {A3, A4} but do not want to type all the derivative expressions into command CoefficientList. I want to extract these lists programmatically because of I have a very long list of derivatives in my actual problem, which I thought was too long to post here.


The following seems to work, but how can I do it without typing in the list of derivatives?


Coefficient[cl, {D[P[x, y], {x, 1}], D[P[x, y], {x, 2}]}]
Coefficient[cl, {D[Q[x, y], {y, 3}], D[Q[x, y], {y, 1}]}]

Longer example


 cl2=B1*Derivative[0, 1, 0][R][x, y, z] + 
 B2*Derivative[2, 0, 0][R][x, y, z] + 
 B4*Derivative[2, 1, 3][V][x, y, z] + 
 B3*Derivative[3, 2, 1][R][x, y, z] + B5*Derivative[4, 1, 5][V][x, y, z] + B0*V[x, y, z]  + B00*R[x, y, z];


I need list of coefficients and list of derivatives parallel to know for which derivative is appropriate coefficient. But if I have zero derivatives, they don't appear in the list?



Answer



Also borrowing from Daniel's comment, perhaps you would like:


cl = A1*D[P[x, y], {x, 1}] + A2*D[P[x, y], {x, 2}] + 
     A3*D[Q[x, y], {y, 3}] + A4*D[Q[x, y], {y, 1}];

Cases[cl, coef_ * Derivative[__][x_][__] :> {x, coef}, 1];

{#[[1, 1]], #[[All, 2]]} & /@ GatherBy[%, First]



{{Q, {A4, A3}}, {P, {A1, A2}}}

Or somewhat less transparently as a one-liner:


Reap[Cases[cl, coef_*Derivative[__][x_][__] :> Sow[coef, x], 1], _, List][[2]]


{{Q, {A4, A3}}, {P, {A1, A2}}}



Based on the comments below I believe you may use:


Reap[Cases[cl2, coef_ * d : Derivative[__][_][__] :> Sow[coef, d], 1], _, List][[2]]

Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more