How to declare derivatives of a multivariable function as real in order to get Re and Im part of the expression?

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Re and Im work properly, with appropriate assumptions, in the example like this



Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]


On the other hand, if the derivative of the function is also present, similar approach does not work



Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


i.e. does not give back 3*D[g[r, r2], r]



More dramatically,



Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].



In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.






calculus-and-analysis functions function-construction symbolic complex







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    up vote
    2
    down vote

    favorite












    Re and Im work properly, with appropriate assumptions, in the example like this



    Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]


    On the other hand, if the derivative of the function is also present, similar approach does not work



    Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


    i.e. does not give back 3*D[g[r, r2], r]



    More dramatically,



    Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


    gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].



    In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.






    calculus-and-analysis functions function-construction symbolic complex







    share|improve this question

























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Re and Im work properly, with appropriate assumptions, in the example like this



      Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]


      On the other hand, if the derivative of the function is also present, similar approach does not work



      Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


      i.e. does not give back 3*D[g[r, r2], r]



      More dramatically,



      Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


      gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].



      In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.






      calculus-and-analysis functions function-construction symbolic complex







      share|improve this question















      Re and Im work properly, with appropriate assumptions, in the example like this



      Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]


      On the other hand, if the derivative of the function is also present, similar approach does not work



      Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


      i.e. does not give back 3*D[g[r, r2], r]



      More dramatically,



      Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


      gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].



      In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.






      calculus-and-analysis functions function-construction symbolic complex




      calculus-and-analysis functions function-construction symbolic complex






      share|improve this question















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      edited Sep 22 at 19:14









      kglr

      163k8188387




      163k8188387










      asked Sep 22 at 18:02









      Thela Hun Ginjeet

      445




      445




















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          Use the FullForm of the derivatives:



          Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals, 
           Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


          enter image description here



          Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals, 
           Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


          enter image description here






          share|improve this answer


















          • 1




            Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
            – Thela Hun Ginjeet
            Sep 23 at 10:50










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          1 Answer
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          active

          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          3
          down vote



          accepted










          Use the FullForm of the derivatives:



          Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals, 
           Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


          enter image description here



          Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals, 
           Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


          enter image description here






          share|improve this answer


















          • 1




            Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
            – Thela Hun Ginjeet
            Sep 23 at 10:50














          up vote
          3
          down vote



          accepted










          Use the FullForm of the derivatives:



          Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals, 
           Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


          enter image description here



          Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals, 
           Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


          enter image description here






          share|improve this answer


















          • 1




            Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
            – Thela Hun Ginjeet
            Sep 23 at 10:50












          up vote
          3
          down vote



          accepted







          up vote
          3
          down vote



          accepted






          Use the FullForm of the derivatives:



          Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals, 
           Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


          enter image description here



          Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals, 
           Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


          enter image description here






          share|improve this answer














          Use the FullForm of the derivatives:



          Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals, 
           Simplify[Im[3*I*D[g[r, r2], r] + 45]]]


          enter image description here



          Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals, 
           Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Sep 22 at 20:17

























          answered Sep 22 at 18:48









          kglr

          163k8188387




          163k8188387







          • 1




            Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
            – Thela Hun Ginjeet
            Sep 23 at 10:50












          • 1




            Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
            – Thela Hun Ginjeet
            Sep 23 at 10:50







          1




          1




          Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
          – Thela Hun Ginjeet
          Sep 23 at 10:50




          Great, it works! Form Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.
          – Thela Hun Ginjeet
          Sep 23 at 10:50

















           

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