Skip to main content

programming - Prevent iterator name from being confused with symbol passed into function body


I have a massive amount of code with lots of Table and Sum inside a Module. Each with their own iterators, and I have completely lost track of all of them. But if the user calls the function with an argument matching the name of the iterator, the code no long works as intended.


An example is this function that is supposed to return a list of three repeated symbols:



function[x_] := 
Module[{},
answer = Table[x, {i, 1, 3}];
Return[answer];
]

For example:


function[a]
(*{a,a,a}*)


But this can be broken by


function[i]
(*{1,2,3}*)

Obviously, Table is confusing the input x=i with its own iterator i. What is the fool-proof fix for this? Is there a solution without:




  1. Finding the names of all the iterators and listing them all as private variables inside Module?





  2. Finding all the iterators and renaming them longAndComplicated1, longAndComplicated2, etc.?





Answer



Make use of Module's capability to localize variables.


f[x_] := Module[{i}, Table[x, {i, 1, 3}]]
f[i]


{i, i, i}


Also, with i localized, you don't need to use distinct iterator names in different iteration constructs.


g[x_] :=
Module[{i, a, b},
a = Table[x, {i, 3}];
b = Table[x^3, {i, 2}];
{a, b}]
{g[i], g[a], g[b]}



{{{i, i, i}, {i^3, i^3}}, 
{{a, a, a}, {a^3, a^3}},
{{b, b, b}, {b^3, b^3}}

Further, note that you don't need to use Return if you use the semicolon ( ; ) operator properly. (Yes, semicolon is an operator in Mathematica, not a terminator.) See this answer for more information on the semicolon operator. Actually, it likely you will benefit from all answers given on the page I have linked to.


Comments

Popular posts from this blog

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-...

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...

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...