Converting linear combinations of symbols (with numbers) to linear combinations of list elements
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
asked Nov 10 at 12:31
wilsnunn
465210
add a comment |
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
asked Nov 10 at 12:31
wilsnunn
465210
This looks like a clear example of an XY problem.
– AccidentalFourierTransform
Nov 10 at 19:51
add a comment |
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
asked Nov 10 at 12:31
wilsnunn
465210
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
asked Nov 10 at 12:31
wilsnunn
465210
asked Nov 10 at 12:31
wilsnunn
465210
asked Nov 10 at 12:31
wilsnunn
465210
asked Nov 10 at 12:31
wilsnunn
465210
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
add a comment |
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
add a comment |
1 Answer
1
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votes
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]]
answered Nov 10 at 13:06
xzczd
25.8k469246
Thanks for this, I am not entirely sure that I follow exactly how it works though!
– wilsnunn
Nov 10 at 13:28
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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]]
answered Nov 10 at 13:06
xzczd
25.8k469246
Thanks for this, I am not entirely sure that I follow exactly how it works though!
– wilsnunn
Nov 10 at 13:28
add a comment |
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]]
answered Nov 10 at 13:06
xzczd
25.8k469246
Thanks for this, I am not entirely sure that I follow exactly how it works though!
– wilsnunn
Nov 10 at 13:28
add a comment |
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]]
answered Nov 10 at 13:06
xzczd
25.8k469246
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]]
answered Nov 10 at 13:06
xzczd
25.8k469246
answered Nov 10 at 13:06
xzczd
25.8k469246
answered Nov 10 at 13:06
xzczd
25.8k469246
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
add a comment |
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
add a comment |
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This looks like a clear example of an XY problem.
– AccidentalFourierTransform
Nov 10 at 19:51