Handling expression differently for display vs. calculation?

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I have a function I wrap a lot of my numbers with to factor them and display them out a certain way. Usually I do this at the last step of a calculation, but sometimes it would be nice if I could designate that a number should be displayed one way, but handled another way for computation.



For example, suppose I wanted prime numbers in some list to be printed out bold. I might do that with:



nums = If[PrimeQ@#, Style[#,Bold], #]& /@ nums


The problem is that if I then want to, say, take all the elements in that list that are under 100, any code that hits Style instead of a number will freak out.



Is there something like a wrapper that designates an expression to be handled as some value for subsequent evaluation, but print out a certain way when it comes to display preparation? I know you could achieve this by messing with $PrePrint, but it seems like there might be a better way.










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  • Have a look at Interpretation
    – Jason B.
    9 hours ago










  • @JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
    – Sjoerd C. de Vries
    9 hours ago














up vote
3
down vote

favorite












I have a function I wrap a lot of my numbers with to factor them and display them out a certain way. Usually I do this at the last step of a calculation, but sometimes it would be nice if I could designate that a number should be displayed one way, but handled another way for computation.



For example, suppose I wanted prime numbers in some list to be printed out bold. I might do that with:



nums = If[PrimeQ@#, Style[#,Bold], #]& /@ nums


The problem is that if I then want to, say, take all the elements in that list that are under 100, any code that hits Style instead of a number will freak out.



Is there something like a wrapper that designates an expression to be handled as some value for subsequent evaluation, but print out a certain way when it comes to display preparation? I know you could achieve this by messing with $PrePrint, but it seems like there might be a better way.










share|improve this question







New contributor




Trev is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.



















  • Have a look at Interpretation
    – Jason B.
    9 hours ago










  • @JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
    – Sjoerd C. de Vries
    9 hours ago












up vote
3
down vote

favorite









up vote
3
down vote

favorite











I have a function I wrap a lot of my numbers with to factor them and display them out a certain way. Usually I do this at the last step of a calculation, but sometimes it would be nice if I could designate that a number should be displayed one way, but handled another way for computation.



For example, suppose I wanted prime numbers in some list to be printed out bold. I might do that with:



nums = If[PrimeQ@#, Style[#,Bold], #]& /@ nums


The problem is that if I then want to, say, take all the elements in that list that are under 100, any code that hits Style instead of a number will freak out.



Is there something like a wrapper that designates an expression to be handled as some value for subsequent evaluation, but print out a certain way when it comes to display preparation? I know you could achieve this by messing with $PrePrint, but it seems like there might be a better way.










share|improve this question







New contributor




Trev is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I have a function I wrap a lot of my numbers with to factor them and display them out a certain way. Usually I do this at the last step of a calculation, but sometimes it would be nice if I could designate that a number should be displayed one way, but handled another way for computation.



For example, suppose I wanted prime numbers in some list to be printed out bold. I might do that with:



nums = If[PrimeQ@#, Style[#,Bold], #]& /@ nums


The problem is that if I then want to, say, take all the elements in that list that are under 100, any code that hits Style instead of a number will freak out.



Is there something like a wrapper that designates an expression to be handled as some value for subsequent evaluation, but print out a certain way when it comes to display preparation? I know you could achieve this by messing with $PrePrint, but it seems like there might be a better way.







evaluation output-formatting






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asked 9 hours ago









Trev

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Trev is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Check out our Code of Conduct.











  • Have a look at Interpretation
    – Jason B.
    9 hours ago










  • @JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
    – Sjoerd C. de Vries
    9 hours ago
















  • Have a look at Interpretation
    – Jason B.
    9 hours ago










  • @JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
    – Sjoerd C. de Vries
    9 hours ago















Have a look at Interpretation
– Jason B.
9 hours ago




Have a look at Interpretation
– Jason B.
9 hours ago












@JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
– Sjoerd C. de Vries
9 hours ago




@JasonB. That doesn't work if you put the Interpretation wrapped numbers in a variable. Try nums = Interpretation[If[PrimeQ@#, Style[#, Red], #], #] & /@ Range[15] and then 2*nums.
– Sjoerd C. de Vries
9 hours ago










3 Answers
3






active

oldest

votes

















up vote
3
down vote













Using $PrePrint is fairly easy.



Define a helper function to use with $PrePrint to deconflict multiple uses of Slot (#)



boldPrime = If[PrimeQ[#], Style[#, Bold], #] &;

$PrePrint = If[Head[#] === List, boldPrime /@ #, #] &;


boldPrime is mapped onto lists



nums = Range[25]


enter image description here



nums can be used subsequently



nums^(1/2)


enter image description here



RandomInteger[0, 100, 20]


enter image description here



It is not mapped onto other forms of expressions



3 x^5


enter image description here






share|improve this answer



























    up vote
    3
    down vote













    I have tried to do this before and found it ultimately to be a complex problem. Certainly there are easier ways to accomplish specific tasks, such as what Bob Hanlon showed, but that doesn't actually provide the functionality requested.



    I believe you will need to choose either a "whitelist" or "blacklist" approach to how functions handle your wrapper. For example we could use UpValues (created with TagSetDelayed) to tell all functions besides If, List, and MakeBoxes to strip the wrapper. (These specific functions only because I need them for the example to function.)



    Foundation:



    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]

    p1 = Except[If | List | MakeBoxes];

    hiddenStyle /: (h : p1)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]


    Usage:



    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
    2*nums


    enter image description here



    Here you see that your style is applied (by way of the MakeBoxes definition), but arbitrary functions outside of our p1 pattern see the wrapper hiddenStyle as transparent. This is only a minimal working example and is not intended to be robust.



    The other approach is to overload each function that you want to use to see the wrapper as transparent. For example we could write:



    ClearAll[hiddenStyle]
    p2 = Plus | Times | Power;
    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]
    hiddenStyle /: (h : p2)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]

    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
    2*nums
    foo /@ nums


    enter image description here



    With more work it is possible to create more complex behaviors such as passing on styling to output, but they often come at a significant cost of performance, e.g. interfering with Listable behavior.



    If you describe your application in more detail I can try to provide additional examples.






    share|improve this answer



























      up vote
      0
      down vote













      Why not create a form wrapper to output primes in bold? For example:



      MakeBoxes[myForm[expr_],StandardForm] ^:= Internal`InheritedBlock[MakeBoxes,
      MakeBoxes[i_Integer,StandardForm] := If[PrimeQ[i], StyleBox[ToString[i],Red], ToString[i]];
      MakeBoxes[expr]
      ]

      Unprotect[$OutputForms];
      $
      OutputForms = DeleteDuplicates[Append[$OutputForms, myForm]];
      Protect[$
      OutputForms];


      (I used red instead of bold so that the difference is a bit more noticeable). Then:



      foo /@ Range[10] //myForm


      enter image description here



      Because myForm is a member of $OutputForms, the myForm wrapper gets stripped before getting stored in Out:



      %//InputForm



      foo[1], foo[2], foo[3], foo[4], foo[5], foo[6], foo[7], foo[8], foo[9], foo[10]




      Copy/paste of will also strip the myForm wrapper.






      share|improve this answer




















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        3 Answers
        3






        active

        oldest

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        3 Answers
        3






        active

        oldest

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        active

        oldest

        votes






        active

        oldest

        votes








        up vote
        3
        down vote













        Using $PrePrint is fairly easy.



        Define a helper function to use with $PrePrint to deconflict multiple uses of Slot (#)



        boldPrime = If[PrimeQ[#], Style[#, Bold], #] &;

        $PrePrint = If[Head[#] === List, boldPrime /@ #, #] &;


        boldPrime is mapped onto lists



        nums = Range[25]


        enter image description here



        nums can be used subsequently



        nums^(1/2)


        enter image description here



        RandomInteger[0, 100, 20]


        enter image description here



        It is not mapped onto other forms of expressions



        3 x^5


        enter image description here






        share|improve this answer
























          up vote
          3
          down vote













          Using $PrePrint is fairly easy.



          Define a helper function to use with $PrePrint to deconflict multiple uses of Slot (#)



          boldPrime = If[PrimeQ[#], Style[#, Bold], #] &;

          $PrePrint = If[Head[#] === List, boldPrime /@ #, #] &;


          boldPrime is mapped onto lists



          nums = Range[25]


          enter image description here



          nums can be used subsequently



          nums^(1/2)


          enter image description here



          RandomInteger[0, 100, 20]


          enter image description here



          It is not mapped onto other forms of expressions



          3 x^5


          enter image description here






          share|improve this answer






















            up vote
            3
            down vote










            up vote
            3
            down vote









            Using $PrePrint is fairly easy.



            Define a helper function to use with $PrePrint to deconflict multiple uses of Slot (#)



            boldPrime = If[PrimeQ[#], Style[#, Bold], #] &;

            $PrePrint = If[Head[#] === List, boldPrime /@ #, #] &;


            boldPrime is mapped onto lists



            nums = Range[25]


            enter image description here



            nums can be used subsequently



            nums^(1/2)


            enter image description here



            RandomInteger[0, 100, 20]


            enter image description here



            It is not mapped onto other forms of expressions



            3 x^5


            enter image description here






            share|improve this answer












            Using $PrePrint is fairly easy.



            Define a helper function to use with $PrePrint to deconflict multiple uses of Slot (#)



            boldPrime = If[PrimeQ[#], Style[#, Bold], #] &;

            $PrePrint = If[Head[#] === List, boldPrime /@ #, #] &;


            boldPrime is mapped onto lists



            nums = Range[25]


            enter image description here



            nums can be used subsequently



            nums^(1/2)


            enter image description here



            RandomInteger[0, 100, 20]


            enter image description here



            It is not mapped onto other forms of expressions



            3 x^5


            enter image description here







            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 9 hours ago









            Bob Hanlon

            56k23589




            56k23589




















                up vote
                3
                down vote













                I have tried to do this before and found it ultimately to be a complex problem. Certainly there are easier ways to accomplish specific tasks, such as what Bob Hanlon showed, but that doesn't actually provide the functionality requested.



                I believe you will need to choose either a "whitelist" or "blacklist" approach to how functions handle your wrapper. For example we could use UpValues (created with TagSetDelayed) to tell all functions besides If, List, and MakeBoxes to strip the wrapper. (These specific functions only because I need them for the example to function.)



                Foundation:



                MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]

                p1 = Except[If | List | MakeBoxes];

                hiddenStyle /: (h : p1)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]


                Usage:



                nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                2*nums


                enter image description here



                Here you see that your style is applied (by way of the MakeBoxes definition), but arbitrary functions outside of our p1 pattern see the wrapper hiddenStyle as transparent. This is only a minimal working example and is not intended to be robust.



                The other approach is to overload each function that you want to use to see the wrapper as transparent. For example we could write:



                ClearAll[hiddenStyle]
                p2 = Plus | Times | Power;
                MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]
                hiddenStyle /: (h : p2)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]

                nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                2*nums
                foo /@ nums


                enter image description here



                With more work it is possible to create more complex behaviors such as passing on styling to output, but they often come at a significant cost of performance, e.g. interfering with Listable behavior.



                If you describe your application in more detail I can try to provide additional examples.






                share|improve this answer
























                  up vote
                  3
                  down vote













                  I have tried to do this before and found it ultimately to be a complex problem. Certainly there are easier ways to accomplish specific tasks, such as what Bob Hanlon showed, but that doesn't actually provide the functionality requested.



                  I believe you will need to choose either a "whitelist" or "blacklist" approach to how functions handle your wrapper. For example we could use UpValues (created with TagSetDelayed) to tell all functions besides If, List, and MakeBoxes to strip the wrapper. (These specific functions only because I need them for the example to function.)



                  Foundation:



                  MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]

                  p1 = Except[If | List | MakeBoxes];

                  hiddenStyle /: (h : p1)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]


                  Usage:



                  nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                  2*nums


                  enter image description here



                  Here you see that your style is applied (by way of the MakeBoxes definition), but arbitrary functions outside of our p1 pattern see the wrapper hiddenStyle as transparent. This is only a minimal working example and is not intended to be robust.



                  The other approach is to overload each function that you want to use to see the wrapper as transparent. For example we could write:



                  ClearAll[hiddenStyle]
                  p2 = Plus | Times | Power;
                  MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]
                  hiddenStyle /: (h : p2)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]

                  nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                  2*nums
                  foo /@ nums


                  enter image description here



                  With more work it is possible to create more complex behaviors such as passing on styling to output, but they often come at a significant cost of performance, e.g. interfering with Listable behavior.



                  If you describe your application in more detail I can try to provide additional examples.






                  share|improve this answer






















                    up vote
                    3
                    down vote










                    up vote
                    3
                    down vote









                    I have tried to do this before and found it ultimately to be a complex problem. Certainly there are easier ways to accomplish specific tasks, such as what Bob Hanlon showed, but that doesn't actually provide the functionality requested.



                    I believe you will need to choose either a "whitelist" or "blacklist" approach to how functions handle your wrapper. For example we could use UpValues (created with TagSetDelayed) to tell all functions besides If, List, and MakeBoxes to strip the wrapper. (These specific functions only because I need them for the example to function.)



                    Foundation:



                    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]

                    p1 = Except[If | List | MakeBoxes];

                    hiddenStyle /: (h : p1)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]


                    Usage:



                    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                    2*nums


                    enter image description here



                    Here you see that your style is applied (by way of the MakeBoxes definition), but arbitrary functions outside of our p1 pattern see the wrapper hiddenStyle as transparent. This is only a minimal working example and is not intended to be robust.



                    The other approach is to overload each function that you want to use to see the wrapper as transparent. For example we could write:



                    ClearAll[hiddenStyle]
                    p2 = Plus | Times | Power;
                    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]
                    hiddenStyle /: (h : p2)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]

                    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                    2*nums
                    foo /@ nums


                    enter image description here



                    With more work it is possible to create more complex behaviors such as passing on styling to output, but they often come at a significant cost of performance, e.g. interfering with Listable behavior.



                    If you describe your application in more detail I can try to provide additional examples.






                    share|improve this answer












                    I have tried to do this before and found it ultimately to be a complex problem. Certainly there are easier ways to accomplish specific tasks, such as what Bob Hanlon showed, but that doesn't actually provide the functionality requested.



                    I believe you will need to choose either a "whitelist" or "blacklist" approach to how functions handle your wrapper. For example we could use UpValues (created with TagSetDelayed) to tell all functions besides If, List, and MakeBoxes to strip the wrapper. (These specific functions only because I need them for the example to function.)



                    Foundation:



                    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]

                    p1 = Except[If | List | MakeBoxes];

                    hiddenStyle /: (h : p1)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]


                    Usage:



                    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                    2*nums


                    enter image description here



                    Here you see that your style is applied (by way of the MakeBoxes definition), but arbitrary functions outside of our p1 pattern see the wrapper hiddenStyle as transparent. This is only a minimal working example and is not intended to be robust.



                    The other approach is to overload each function that you want to use to see the wrapper as transparent. For example we could write:



                    ClearAll[hiddenStyle]
                    p2 = Plus | Times | Power;
                    MakeBoxes[hiddenStyle[x_, sty__], _] := ToBoxes @ Style[x, sty]
                    hiddenStyle /: (h : p2)[a___, hiddenStyle[x_, __], b___] := h[a, x, b]

                    nums = If[PrimeQ@#, hiddenStyle[#, Red], #] & /@ Range[15]
                    2*nums
                    foo /@ nums


                    enter image description here



                    With more work it is possible to create more complex behaviors such as passing on styling to output, but they often come at a significant cost of performance, e.g. interfering with Listable behavior.



                    If you describe your application in more detail I can try to provide additional examples.







                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 8 hours ago









                    Mr.Wizard♦

                    228k294651019




                    228k294651019




















                        up vote
                        0
                        down vote













                        Why not create a form wrapper to output primes in bold? For example:



                        MakeBoxes[myForm[expr_],StandardForm] ^:= Internal`InheritedBlock[MakeBoxes,
                        MakeBoxes[i_Integer,StandardForm] := If[PrimeQ[i], StyleBox[ToString[i],Red], ToString[i]];
                        MakeBoxes[expr]
                        ]

                        Unprotect[$OutputForms];
                        $
                        OutputForms = DeleteDuplicates[Append[$OutputForms, myForm]];
                        Protect[$
                        OutputForms];


                        (I used red instead of bold so that the difference is a bit more noticeable). Then:



                        foo /@ Range[10] //myForm


                        enter image description here



                        Because myForm is a member of $OutputForms, the myForm wrapper gets stripped before getting stored in Out:



                        %//InputForm



                        foo[1], foo[2], foo[3], foo[4], foo[5], foo[6], foo[7], foo[8], foo[9], foo[10]




                        Copy/paste of will also strip the myForm wrapper.






                        share|improve this answer
























                          up vote
                          0
                          down vote













                          Why not create a form wrapper to output primes in bold? For example:



                          MakeBoxes[myForm[expr_],StandardForm] ^:= Internal`InheritedBlock[MakeBoxes,
                          MakeBoxes[i_Integer,StandardForm] := If[PrimeQ[i], StyleBox[ToString[i],Red], ToString[i]];
                          MakeBoxes[expr]
                          ]

                          Unprotect[$OutputForms];
                          $
                          OutputForms = DeleteDuplicates[Append[$OutputForms, myForm]];
                          Protect[$
                          OutputForms];


                          (I used red instead of bold so that the difference is a bit more noticeable). Then:



                          foo /@ Range[10] //myForm


                          enter image description here



                          Because myForm is a member of $OutputForms, the myForm wrapper gets stripped before getting stored in Out:



                          %//InputForm



                          foo[1], foo[2], foo[3], foo[4], foo[5], foo[6], foo[7], foo[8], foo[9], foo[10]




                          Copy/paste of will also strip the myForm wrapper.






                          share|improve this answer






















                            up vote
                            0
                            down vote










                            up vote
                            0
                            down vote









                            Why not create a form wrapper to output primes in bold? For example:



                            MakeBoxes[myForm[expr_],StandardForm] ^:= Internal`InheritedBlock[MakeBoxes,
                            MakeBoxes[i_Integer,StandardForm] := If[PrimeQ[i], StyleBox[ToString[i],Red], ToString[i]];
                            MakeBoxes[expr]
                            ]

                            Unprotect[$OutputForms];
                            $
                            OutputForms = DeleteDuplicates[Append[$OutputForms, myForm]];
                            Protect[$
                            OutputForms];


                            (I used red instead of bold so that the difference is a bit more noticeable). Then:



                            foo /@ Range[10] //myForm


                            enter image description here



                            Because myForm is a member of $OutputForms, the myForm wrapper gets stripped before getting stored in Out:



                            %//InputForm



                            foo[1], foo[2], foo[3], foo[4], foo[5], foo[6], foo[7], foo[8], foo[9], foo[10]




                            Copy/paste of will also strip the myForm wrapper.






                            share|improve this answer












                            Why not create a form wrapper to output primes in bold? For example:



                            MakeBoxes[myForm[expr_],StandardForm] ^:= Internal`InheritedBlock[MakeBoxes,
                            MakeBoxes[i_Integer,StandardForm] := If[PrimeQ[i], StyleBox[ToString[i],Red], ToString[i]];
                            MakeBoxes[expr]
                            ]

                            Unprotect[$OutputForms];
                            $
                            OutputForms = DeleteDuplicates[Append[$OutputForms, myForm]];
                            Protect[$
                            OutputForms];


                            (I used red instead of bold so that the difference is a bit more noticeable). Then:



                            foo /@ Range[10] //myForm


                            enter image description here



                            Because myForm is a member of $OutputForms, the myForm wrapper gets stripped before getting stored in Out:



                            %//InputForm



                            foo[1], foo[2], foo[3], foo[4], foo[5], foo[6], foo[7], foo[8], foo[9], foo[10]




                            Copy/paste of will also strip the myForm wrapper.







                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 2 hours ago









                            Carl Woll

                            60.3k279155




                            60.3k279155




















                                Trev is a new contributor. Be nice, and check out our Code of Conduct.









                                 

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