Manipulate controls don't work

Question

I find one solution to make +/- buttons near Slider Control of Manipulate. But I don't understand why it works so bad.

Manipulate[Null, 
 Grid[{{Control[{{l, 0.007, "l"}, {0.001, 0.0025, 0.005, 0.006, 0.007,
        0.008, 0.009, 0.01}, 
      Grid[{{Slider[##, ImageSize -> 100], 
          InputField[#, ImageSize -> 40], 
          Animator[##, AnimationRunning -> False, 
           AppearanceElements -> {"StepLeftButton", 
             "StepRightButton"}]}}, 
        Alignment -> {Center, Center}] &}]}, {Control[{{n, 0.005, 
       "n"}, {0.001, 0.0025, 0.005, 0.01}, 
      Grid[{{Slider[##, ImageSize -> 100], 
          InputField[#, ImageSize -> 40], 
          Animator[##, AnimationRunning -> False, 
           AppearanceElements -> {"StepLeftButton", 
             "StepRightButton"}]}}, 
        Alignment -> {Center, Center}] &}]}, {Control[{{m, 500, "m"}, 
      10, 1000, 10, 
      Grid[{{Slider[##, ImageSize -> 100], 
          InputField[#, ImageSize -> 40], 
          Animator[##, AnimationRunning -> False, 
           AppearanceElements -> {"StepLeftButton", 
             "StepRightButton"}]}}, 
        Alignment -> {Center, Center}] &}]}}]]

Manipulating m works fine. n +/- buttons don't work at all. l button "-" does not work, but the "+" button does.

How can I fix this?

Answer 1

Example

DynamicModule[
 {value = 10},
 Panel @ Row @ {
    Slider[Dynamic @ value, {1, 100, 1}, ImageSize -> Small],
    InputField[Dynamic @ value, Enabled -> False, ImageSize -> {36, 18}],
    Button["-", value--],
    Button["+", value++]
    }
 ]

Output

EDIT

In order to restrict Slider to a set of pre-defined values, please see implementation below.

Example

DynamicModule[
 {
  index = 1,
  options = {1, 10, 20}
  },
 Panel @ Row @ {
    Slider[Dynamic @ options[[index]], {options}, ImageSize -> Tiny],
    InputField[Dynamic @ options[[index]], Enabled -> False, 
     ImageSize -> 40],
    Button["+", If[index <  Length @ options, index++]],
    Button["-", If[index !=  1, index--]]
    }
 ]

Output

However, I would recommend to use a different control all together. I suggest SetterBar. Please see example below.

Example

DynamicModule[
 {f, arg},
 Panel @ Column[{
    SetterBar[Dynamic @ f, {Sin, Cos, Tan}],
    Dynamic @ Plot[f[arg], {arg, 0, 2 Pi}]
    },
   Alignment -> Center]
 ]

Output

Answer 2

Based on the documentation, Slider is the only control object used in your code that supports a list of expression as its settings. Here is a custom alternative.

DynamicModule[{list = {0.001, 0.0025, 0.005, 0.006, 0.007, 0.008, 0.009, 0.01}, l},
 Row[{
   Slider[Dynamic@l, {list}],
   Spacer[5],
   InputField[Dynamic[l, If[MemberQ[list, #], l = #] &], FieldSize -> 3.5],
   Spacer[5],
   Toggler[Dynamic@l, 
    Thread[Reverse@list -> Framed[Text[Style["-", FontSize -> 14]], 
       FrameMargins -> {{3, 3}, {1, 0}}]], 
    Enabled -> Dynamic[l > Min[list]]],
   Toggler[Dynamic@l, 
    Thread[list -> Framed[Text[Style["+", FontSize -> 14]], 
       FrameMargins -> {{3, 3}, {1, 0}}]], 
    Enabled -> Dynamic[l < Max[list]]]
   }]
 ]

Answer 3

The problem is with Animator. When it is passed a list, the +/- buttons increment the index of the setting by about 5-10%. It seems to pick a "nice" increment that is 1, 2 or 5 times a power of 10. When the length of the list is less than 10, it does not behave well. It seems that an increment of 0 is what is sometimes calculated. (Personally, I would call this a bug. A minimum increment of 1 seems entirely reasonable to me.) Further, when the length of the list is 6 to 9, a forward increment of 1 is used, but the backward increment is 0.

You can play with the following to explore:

DynamicModule[{x = 3, n = 5},
 {Manipulator[Dynamic@n, {1, 10000, 1}, Appearance -> "Labeled"], 
  Dynamic@{Dynamic@x, 
    Animator[Dynamic@x, {Range@n}, AnimationRunning -> False]}}]

This does not happen for the discrete-increment form

Animator[Dynamic[x], a, b, 1]

It seems to me the only workaround for short lists is to explicitly increase the index. Here is my take on the OP's control. (Update: Thanks to Karsten 7 for a workaround to a bug.)

ClearAll[myControl];
myControl[Dynamic[x_], arg : {list_List}, opts___] := (* special case for list of values *)
  Grid[{{Slider[Dynamic[x], arg, ImageSize -> 100], 
     InputField[Dynamic[x], ImageSize -> 40],
     DynamicModule[{i},
      Dynamic[
       i = First@Nearest[list -> Automatic, x];
       Animator[
        Dynamic[i, (i = #; x = list[[i]]) &],
        {1, Length@list, 1},
        AnimationRunning -> False, 
        AppearanceElements -> {"StepLeftButton", "StepRightButton"}]
       ]]}},
   Alignment -> {Center, Center}];
myControl[Dynamic[x_], arg : {list__?NumberQ}, opts___] :=  (* the standard iterator *)
  Grid[{{Slider[Dynamic[x], arg, ImageSize -> 100], 
     InputField[Dynamic[x], ImageSize -> 40],
     Animator[Dynamic[x], arg, AnimationRunning -> False, 
      AppearanceElements -> {"StepLeftButton", "StepRightButton"}]}},
   Alignment -> {Center, Center}];

Manipulate[Null, 
 Grid[{{Control[{{l, 0.007, "l"},
     {0.001, 0.0025, 0.005, 0.006, 0.007, 0.008, 0.009, 0.01}, myControl[##] &}]},
   {Control[{{n, 0.005, "n"}, {0.001, 0.0025, 0.005, 0.01}, myControl[##] &}]},
   {Control[{{m, 500, "m"}, 10, 1000, 10, myControl[##] &}]}}]]