Evaluate current cell without leaving or losing the position in it in Mathematica

Question

I am experimenting with logo designs in Mathematica (8 or above) using the notebook interface and I want to change the generating formula A LOT. The problem is I only know SHIFT + ENTER which makes me jump outside my current cell and lose my position.

Is there a way to evaluate the current cell without leaving it and losing your position within it? So: Evaluate a cell and land back inside the same cell at the exact position I pressed SHIFT + ENTER at.

What I once came to use was along the lines:

a = Exp[1.994 \[Pi]/(3 I)];

b = Nest[{#, a #, a\[Conjugate] #, #} &, 1, 5];

{Re[#], Im[#]} & /@ 
   Accumulate[
    Flatten[{0, a b, a\[Conjugate] b, -b}]] // {\[Rho]\[Chi], # // 
     Line} & // Graphics

NotebookFind[EvaluationNotebook[], "E" <> "xp", Previous];

but I hope there is just another key combination or sth. that I am not aware of.

Edit:

a = Exp[(*1*)1.994 \[Pi]/(3 I)];

b = Nest[{#, a #, a\[Conjugate] #, #} &, (*2*)1, (*3*)5];

{Re[#], Im[#]} & /@ 
   Accumulate[
    Flatten[{0, a b, a\[Conjugate] b, -b}]] // {\[Rho]\[Chi], # // 
     Line} & // Graphics

Do[NotebookFind[EvaluationNotebook[], "(*1*)", Previous], {2}];

is a nice little improvement to my solution as partly suggested by Chris Dengen.

Edit 2:

NotebookFind[EvaluationNotebook[], "(*1*)", EvaluationCell]

This solves:

• these only work with cells that produce one or a known number of output cells

EvaluationCell is sparsely documented so hard to find in fact I just stumbled upon it. Using the EvaluationCell the search starts from above (eliminating the Do twice construct) as we do not come from an output cell further down the screen.

What remains to be solved:

• one needs to do manual cell-keeping (bookkeeping at cell level) to land at places of interest
• using comment-based landing markers clutters the input cells

Note This question is about not losing current position when one presses SHIFT + ENTER inside a Mathematica notebook cell. It is not about content or Manipulate. Sorry for not making that clear at the beginning.

Temporary Note

Now trying the following:

1. use event handlers to define an alternative evaluation key combination
2. when triggered, find a way to store the exact keyboard position in the current input cell
3. evaluate the current input cell
4. restore the position in the current input cell

I internally hope some function might just take care of the store/restore by chance being optimistic. Being realistic though, I first hope I can even find a way to get at the current keyboard position. Will follow up here if anything materializes out of my attempt.

Answer 1

You can run this cell over and over:

If[NumberQ[x], x++, x = 1];
Print[x]
Do[SelectionMove[EvaluationNotebook[], Previous, Cell], {2}]

This version places the cursor after the Exp in line 1:

a = Exp[1.994 \[Pi]/(3 I)];
b = Nest[{#, a #, a\[Conjugate] #, #} &, 1, 5];
{Re[#], Im[#]} & /@ 
   Accumulate[
    Flatten[{0, a b, a\[Conjugate] b, -b}]] // {# // 
     Line} & // Graphics
Do[NotebookFind[EvaluationNotebook[], "Exp", Previous], {3}];
SelectionMove[EvaluationNotebook[], "Exp", After];

You could also put Evaluate & move on a key combination, e.g. ctrl+r in the example below. This assignment only lasts for the current session but it can be loaded with pre-initialisation so that it is always present. (The key combo item is added to the Insert menu.)

FrontEndExecute[
 FrontEnd`AddMenuCommands[
  "DuplicatePreviousOutput", {Delimiter, 
   MenuItem["Evaluate and return", 
    FrontEnd`KernelExecute[Module[{nb}, nb = SelectedNotebook[];
      SelectionMove[nb, Previous, Cell];
      SelectionMove[nb, Next, Cell];
      SelectionEvaluate[nb];
      Do[SelectionMove[EvaluationNotebook[], Previous, Cell], {2}]]], 
    MenuKey["r", Modifiers -> {"Control"}], 
    System`MenuEvaluator -> Automatic]}]]

To set pre-initialisation save the above code to a package .m file as EvaluteReturn.m in your Documents directory and evaluate the following.

InitializationValue[$PreInitialization] = Hold[Get[
   FileNameJoin[{$HomeDirectory, "Documents", "EvaluateReturn.m"}]]]

To inspect the value

InitializationValue[$PreInitialization]

To clear the value

obj = InitializationObjects[$PreInitialization, {"Local"}]

DeleteObject[obj]

Answer 2

How about using Manipulate? Something like

Manipulate[
 c = a;
 b = Nest[First@f, 1, 
   5]; {Re[#], Im[#]} & /@ 
    Accumulate[
     Flatten[{0, c b, c\[Conjugate] b, -b}]] // {Red, # // Line} & // 
  Graphics, {a, Exp[1.994 \[Pi]/(3 I)], 
  ControlType -> InputField}, {f, 
  HoldForm[{#, c #, c\[Conjugate] #, #} &], ImageSize -> Full, 
  ControlType -> InputField}]

You can just edit the values, and upon hitting enter get a new version of the plot. You can save examples you like by using the '+' button in the top-right corner of the Manipulate to either set bookmarks or paste a snapshot.

Answer 3

You can use dynamic to make things really nice.

The cell to display results in:

Dynamic[b = Nest[{#, a #, a\[Conjugate] #, #} &, 1, 5];]
Dynamic[{Re[#], Im[#]} & /@ 
    Accumulate[
     Flatten[{0, a b, a\[Conjugate] b, -b}]] // {\[Rho]\[Chi], # // 
      Line} & // Graphics]

The cell to edit in:

k = 1.994;
a = Exp[k \[Pi]/(2 I)];
NotebookFind[EvaluationNotebook[], ToString[k], Previous];

You can then just edit the cell below the display one. It automatically puts you right where you entered your value. If you'd like to make things even easier on yourself you can use Manipulate:

Manipulate[a = Exp[k \[Pi] / (f I)];
 b = Nest[{#, a #, a\[Conjugate] #, #} &, 1, 5];
 {Re[#], Im[#]} & /@ 
    Accumulate[
     Flatten[{0, a b, a\[Conjugate] b, -b}]] // {\[Rho]\[Chi], # // 
      Line} & // Graphics,
 {{k, 1.994}, -3, 3},
 {{f, 3}, -3, 3}]