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






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      edited 1 hour ago









      kglr

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      161k8185384










      asked 2 hours ago









      Thela Hun Ginjeet

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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






















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            up vote
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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


























              up vote
              2
              down vote













              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
























                up vote
                2
                down vote










                up vote
                2
                down vote









                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 31 mins ago

























                answered 2 hours ago









                kglr

                161k8185384




                161k8185384



























                     

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