Converting linear combinations of symbols (with numbers) to linear combinations of list elements












3














I have a function that generates output that is a list of linear combinations of symbols with numbers, as an example:



{e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22}


What I want to be able to do is to take this output and then produce the exact same linear combinations of nested list elements. The way that it works is that the length of the number in the symbol indicates which "level" of the list it comes from, and the number itself states which position in that list. For example, if



list = {{1, 2}, {{3, 2}, {4, 5}}}


then the output should be



{1, 2, 6, -1., 6, 10}


i.e.



{1, 2, 2*3, (2-4)/2, 2+4, 2*5}


It is quite easy to do it without the linear combinations, but with those included, I am a bit stuck as to how to proceed!



symb2idx[list_,symb_]:=Extract[list, #[

 ToExpression@StringDrop[SymbolName[symb], 1]] & /@ {IntegerLength,

 IntegerDigits} // Flatten]





list-manipulation symbols







share|improve this question






















  • This looks like a clear example of an XY problem.
    – AccidentalFourierTransform
    Nov 10 at 19:51


















3














I have a function that generates output that is a list of linear combinations of symbols with numbers, as an example:



{e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22}


What I want to be able to do is to take this output and then produce the exact same linear combinations of nested list elements. The way that it works is that the length of the number in the symbol indicates which "level" of the list it comes from, and the number itself states which position in that list. For example, if



list = {{1, 2}, {{3, 2}, {4, 5}}}


then the output should be



{1, 2, 6, -1., 6, 10}


i.e.



{1, 2, 2*3, (2-4)/2, 2+4, 2*5}


It is quite easy to do it without the linear combinations, but with those included, I am a bit stuck as to how to proceed!



symb2idx[list_,symb_]:=Extract[list, #[

 ToExpression@StringDrop[SymbolName[symb], 1]] & /@ {IntegerLength,

 IntegerDigits} // Flatten]





list-manipulation symbols







share|improve this question






















  • This looks like a clear example of an XY problem.
    – AccidentalFourierTransform
    Nov 10 at 19:51
















3












3








3







I have a function that generates output that is a list of linear combinations of symbols with numbers, as an example:



{e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22}


What I want to be able to do is to take this output and then produce the exact same linear combinations of nested list elements. The way that it works is that the length of the number in the symbol indicates which "level" of the list it comes from, and the number itself states which position in that list. For example, if



list = {{1, 2}, {{3, 2}, {4, 5}}}


then the output should be



{1, 2, 6, -1., 6, 10}


i.e.



{1, 2, 2*3, (2-4)/2, 2+4, 2*5}


It is quite easy to do it without the linear combinations, but with those included, I am a bit stuck as to how to proceed!



symb2idx[list_,symb_]:=Extract[list, #[

 ToExpression@StringDrop[SymbolName[symb], 1]] & /@ {IntegerLength,

 IntegerDigits} // Flatten]





list-manipulation symbols







share|improve this question













I have a function that generates output that is a list of linear combinations of symbols with numbers, as an example:



{e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22}


What I want to be able to do is to take this output and then produce the exact same linear combinations of nested list elements. The way that it works is that the length of the number in the symbol indicates which "level" of the list it comes from, and the number itself states which position in that list. For example, if



list = {{1, 2}, {{3, 2}, {4, 5}}}


then the output should be



{1, 2, 6, -1., 6, 10}


i.e.



{1, 2, 2*3, (2-4)/2, 2+4, 2*5}


It is quite easy to do it without the linear combinations, but with those included, I am a bit stuck as to how to proceed!



symb2idx[list_,symb_]:=Extract[list, #[

 ToExpression@StringDrop[SymbolName[symb], 1]] & /@ {IntegerLength,

 IntegerDigits} // Flatten]





list-manipulation symbols




list-manipulation symbols






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Nov 10 at 12:31









wilsnunn

465210




465210












  • This looks like a clear example of an XY problem.
    – AccidentalFourierTransform
    Nov 10 at 19:51




















  • This looks like a clear example of an XY problem.
    – AccidentalFourierTransform
    Nov 10 at 19:51


















This looks like a clear example of an XY problem.
– AccidentalFourierTransform
Nov 10 at 19:51






This looks like a clear example of an XY problem.
– AccidentalFourierTransform
Nov 10 at 19:51












1 Answer
1






active

oldest

votes


















4














Try the following:



symbol = {e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22};

list = {{1, 2}, {{3, 2}, {4, 5}}};



makeitconvenient = 

  a_Symbol /; StringTake[ToString@a, 1] === "e" :> 

   With[{str = Characters@ToString@a}, str[[1]]@ToExpression@Rest@str];



extract = "e"[{num__}] :> list[[Length@{num}, num]];



symbol /. makeitconvenient /. extract

(* {1, 2, 6, -1, 6, 10} *)


Notice if you can make the input be something like



symbol2 = {e[1], e[2], 2 e[1, 1], (e[1, 2] - e[2, 1])/2, e[1, 2] + e[2, 1], 2 e[2, 2]};


Then the solution can be simplified to:



symbol2 /. e[num__] :> list[[Length@{num}, num]]





share|improve this answer





















  • Thanks for this, I am not entirely sure that I follow exactly how it works though!
    – wilsnunn
    Nov 10 at 13:28











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4














Try the following:



symbol = {e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22};

list = {{1, 2}, {{3, 2}, {4, 5}}};



makeitconvenient = 

  a_Symbol /; StringTake[ToString@a, 1] === "e" :> 

   With[{str = Characters@ToString@a}, str[[1]]@ToExpression@Rest@str];



extract = "e"[{num__}] :> list[[Length@{num}, num]];



symbol /. makeitconvenient /. extract

(* {1, 2, 6, -1, 6, 10} *)


Notice if you can make the input be something like



symbol2 = {e[1], e[2], 2 e[1, 1], (e[1, 2] - e[2, 1])/2, e[1, 2] + e[2, 1], 2 e[2, 2]};


Then the solution can be simplified to:



symbol2 /. e[num__] :> list[[Length@{num}, num]]





share|improve this answer





















  • Thanks for this, I am not entirely sure that I follow exactly how it works though!
    – wilsnunn
    Nov 10 at 13:28
















4














Try the following:



symbol = {e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22};

list = {{1, 2}, {{3, 2}, {4, 5}}};



makeitconvenient = 

  a_Symbol /; StringTake[ToString@a, 1] === "e" :> 

   With[{str = Characters@ToString@a}, str[[1]]@ToExpression@Rest@str];



extract = "e"[{num__}] :> list[[Length@{num}, num]];



symbol /. makeitconvenient /. extract

(* {1, 2, 6, -1, 6, 10} *)


Notice if you can make the input be something like



symbol2 = {e[1], e[2], 2 e[1, 1], (e[1, 2] - e[2, 1])/2, e[1, 2] + e[2, 1], 2 e[2, 2]};


Then the solution can be simplified to:



symbol2 /. e[num__] :> list[[Length@{num}, num]]





share|improve this answer





















  • Thanks for this, I am not entirely sure that I follow exactly how it works though!
    – wilsnunn
    Nov 10 at 13:28














4












4








4






Try the following:



symbol = {e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22};

list = {{1, 2}, {{3, 2}, {4, 5}}};



makeitconvenient = 

  a_Symbol /; StringTake[ToString@a, 1] === "e" :> 

   With[{str = Characters@ToString@a}, str[[1]]@ToExpression@Rest@str];



extract = "e"[{num__}] :> list[[Length@{num}, num]];



symbol /. makeitconvenient /. extract

(* {1, 2, 6, -1, 6, 10} *)


Notice if you can make the input be something like



symbol2 = {e[1], e[2], 2 e[1, 1], (e[1, 2] - e[2, 1])/2, e[1, 2] + e[2, 1], 2 e[2, 2]};


Then the solution can be simplified to:



symbol2 /. e[num__] :> list[[Length@{num}, num]]





share|improve this answer












Try the following:



symbol = {e1, e2, 2 e11, (e12 - e21)/2, e12 + e21, 2 e22};

list = {{1, 2}, {{3, 2}, {4, 5}}};



makeitconvenient = 

  a_Symbol /; StringTake[ToString@a, 1] === "e" :> 

   With[{str = Characters@ToString@a}, str[[1]]@ToExpression@Rest@str];



extract = "e"[{num__}] :> list[[Length@{num}, num]];



symbol /. makeitconvenient /. extract

(* {1, 2, 6, -1, 6, 10} *)


Notice if you can make the input be something like



symbol2 = {e[1], e[2], 2 e[1, 1], (e[1, 2] - e[2, 1])/2, e[1, 2] + e[2, 1], 2 e[2, 2]};


Then the solution can be simplified to:



symbol2 /. e[num__] :> list[[Length@{num}, num]]






share|improve this answer












share|improve this answer



share|improve this answer










answered Nov 10 at 13:06









xzczd

25.8k469246




25.8k469246












  • Thanks for this, I am not entirely sure that I follow exactly how it works though!
    – wilsnunn
    Nov 10 at 13:28


















  • Thanks for this, I am not entirely sure that I follow exactly how it works though!
    – wilsnunn
    Nov 10 at 13:28
















Thanks for this, I am not entirely sure that I follow exactly how it works though!
– wilsnunn
Nov 10 at 13:28




Thanks for this, I am not entirely sure that I follow exactly how it works though!
– wilsnunn
Nov 10 at 13:28


















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