Skip to main content

How can I return a Sequence?


Recently I had the need to redefine a certain symbol in my init.m so it would be automatically omitted from any lists it appears in. I decided to redefine it to an empty sequence, e.g. Locked = Sequence[], but that got me thinking. What if I wanted to return a sequence (not necessarily an empty one) in a := definition? Return doesn't have the SequenceHold attribute, and adding it in a package might cause problems, so what would I do?


EDIT: I think I've figured out what exactly causes me to have the problem. I've defined it to display a Message first to let me know whenever a package I'm importing attempts to "attack my computer". (It is trying to cause my computer to behave in a manner not consistent with my wishes, after all.) So I defined it as Locked := (Message[Locked::nope]; Sequence[]), but strangely it just returns Null. (It doesn't show a return value, but if I do {Locked}, it returns {Null}, and if I try to set it as an attribute it says that Null is not a valid attribute and doesn't set any of them.)



Answer




Calculate the List of results you wish to return and use Apply to replace the head:


listFn[a_, b___] := If[a > 0, {b}, {0}];
seqFn[args___] := Sequence @@ listFn[args];
f[1, seqFn[2, 3, 4, 5], 6]
f[1, seqFn[-2, 3, 4, 5], 6]

(*--> f[1, 3, 4, 5, 6] *)
(*--> f[1, 0, 6] *)

Here listFn represents the calculation of the results and does not need to be a separate function. The particular example above can be written more simply as



seqFn[a_, b___] := Sequence @@ If[a > 0, {b}, {0}]

Edit


It should be stressed that the method assumes listFn actually evaluates to the List of desired inputs; if not, the Head of the expression returned will be replaced with Sequence, perhaps with undesired results. In such a case, a method such as @Jens's may be used.


For instance if a is non-numeric, say a Symbol, in the example above, then you get


f[1, seqFn[x, 3, 4, 5], 6]
(*-> f[1, x > 0, {3, 4, 5}, {0}, 6] *)

Often one can construct a List of the actual results, though. (With thanks to @Mr.Wizard.)


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