Traditional notation option?

Question

I have a simple prime counting function using the Cyclotomic function.

myPi[n_] := Sum[KroneckerDelta[Cyclotomic[m, 1], m], {m, 1, n}]  
myPi[1001] == PrimePi[1001]  

When I copy as latex I get, $$\text{myPi} n\text{:=}\sum _{m=1}^n \delta _{C_m(1),m}, $$ where I have to place $()$ around the $n$, which seems to be a bug.

However, my question: Is there an option to cause the $C$ to become the traditional $\Phi$, as below?

$$\text{myPi}(n)\text{:=}\sum _{m=1}^n \delta _{\Phi_m(1),m}.$$

Answer 1

A simple solution would be to define the function

\[CapitalPhi][m_, k_] := Cyclotomic[m, k]

Then write your comparision as

myPi[n_] := Sum[KroneckerDelta[\[CapitalPhi][m, 1], m], {m, 1, n}]
myPi[1001] == PrimePi[1001]

(* Out[505]= True *)

Copying the first line as Latex gives the string

\text{myPi}(\text{n$\_$})\text{:=}\sum _{m=1}^n \delta _{\Phi (m,1),m}

which shows up as

$$\text{myPi}(\text{n$\_$})\text{:=}\sum _{m=1}^n \delta _{\Phi (m,1),m}$$

Answer 2

Conversion to $\TeX$ internally uses TraditionalForm boxes. $C$ is already used there:

Cyclotomic[m, 1] // TraditionalForm

$ C_m(1) $

In definition of Cyclotomic:

?? Cyclotomic
(* ...
Cyclotomic/:MakeBoxes[Cyclotomic[BoxForm`a$_,BoxForm`b$_],TraditionalForm]/;BoxForm`sufficientVersionQ[6.1]:=
    TemplateBox[{MakeBoxes[BoxForm`a$,TraditionalForm],MakeBoxes[BoxForm`b$,TraditionalForm]},Cyclotomic]
... *)

we can see that conversion to TraditionalForm boxes use a TemplateBox with "Cyclotomic" style.

Inspection of "Cyclotomic" style:

CurrentValue[{StyleDefinitions, "Cyclotomic"}]
(* {TemplateBoxOptionsDisplayFunction ->
        (RowBox[{SubscriptBox["C", #1], "(", #2, ")"}] &),
    TemplateBoxOptionsTooltip -> Automatic} *)

reveals DisplayFunction, that is used by TemplateBox with this style, containing "C" that you'd like to change.

---

You can create your own StyleSheet with modified DisplayFunction:

Export[
    FileNameJoin@{$UserBaseDirectory, "SystemFiles", "FrontEnd", "StyleSheets", "MyCyclotomic.nb"},
    Notebook[{
        Cell[StyleData[StyleDefinitions -> "Default.nb"]],
        Cell[StyleData["Cyclotomic"], TemplateBoxOptions -> {
            DisplayFunction -> (RowBox[{SubscriptBox["Φ", #], "(", #2, ")"}] &),
            Tooltip -> Automatic
        }]
    }, StyleDefinitions -> "PrivateStylesheetFormatting.nb"]
]
(* ".../.Mathematica/SystemFiles/FrontEnd/StyleSheets/MyCyclotomic.nb" *)

and set it as StyleSheet of current notebook:

SetOptions[EvaluationNotebook[], StyleDefinitions -> "MyCyclotomic.nb"]

Now any conversion to $\TeX$ of Cyclotomic will give expected Φ:

Cyclotomic[m, 1] // TeXForm
(* \Phi _m(1) *)

Answer 3

Perhaps this slight workaround, or some elements of it, will be useful. First, save your expression in a variable myTradFcn

myTradFcn = TraditionalForm@Style[#, Black] &@ HoldForm[Sum[KroneckerDelta[Cyclotomic[m, 1], m], {m, 1, n}]]

Then ReplaceAll to swap the C for a φ

myNewFcn = myTradFcn /. {Cyclotomic[a_, b_] -> HoldForm[Subscript[Φ, a][b]]}

Once you've done this, you can Export it in png format (to produce the output as shown above)

tempimage = Rasterize[
  myNewFcn,
  RasterSize -> 1600, ImageSize -> {Automatic, 300}, ImageFormattingWidth -> 1600];
Export[
  "~/Desktop/image.png", 
  Framed[tempimage, FrameMargins -> 8, FrameStyle -> Directive[White]]]

or Export as "TeX"

Export[
  "~/Desktop/texformula",
    Framed[myNewFcn, FrameMargins -> 8, FrameStyle -> Directive[White]], "TeX"]

When I open the resulting texformula file in LaTeX and typeset, this last image displays with the summation indices in a compact form, but in LaTeX you can replace \sum_{m=1}^n with \sum\limits_{m=1}^n to force the indices to be above and below the summation sign.