Element–wise summation for custom function












8












$begingroup$


I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question.



Two Operator objects should sum in the following way:



Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d]


which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable?










share|improve this question









$endgroup$

















    8












    $begingroup$


    I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question.



    Two Operator objects should sum in the following way:



    Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d]


    which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable?










    share|improve this question









    $endgroup$















      8












      8








      8





      $begingroup$


      I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question.



      Two Operator objects should sum in the following way:



      Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d]


      which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable?










      share|improve this question









      $endgroup$




      I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question.



      Two Operator objects should sum in the following way:



      Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d]


      which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable?







      function-construction






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Dec 21 '18 at 15:12









      Dom MiketaDom Miketa

      704




      704






















          1 Answer
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          10












          $begingroup$

          One of the standard ways for such things is using TagSetDelayed



          Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]





          share|improve this answer











          $endgroup$













          • $begingroup$
            Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
            $endgroup$
            – Dom Miketa
            Dec 21 '18 at 15:44











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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









          10












          $begingroup$

          One of the standard ways for such things is using TagSetDelayed



          Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]





          share|improve this answer











          $endgroup$













          • $begingroup$
            Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
            $endgroup$
            – Dom Miketa
            Dec 21 '18 at 15:44
















          10












          $begingroup$

          One of the standard ways for such things is using TagSetDelayed



          Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]





          share|improve this answer











          $endgroup$













          • $begingroup$
            Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
            $endgroup$
            – Dom Miketa
            Dec 21 '18 at 15:44














          10












          10








          10





          $begingroup$

          One of the standard ways for such things is using TagSetDelayed



          Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]





          share|improve this answer











          $endgroup$



          One of the standard ways for such things is using TagSetDelayed



          Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]






          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Dec 21 '18 at 15:36









          Bob Hanlon

          59.2k33595




          59.2k33595










          answered Dec 21 '18 at 15:27









          AndrewAndrew

          1,9511115




          1,9511115












          • $begingroup$
            Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
            $endgroup$
            – Dom Miketa
            Dec 21 '18 at 15:44


















          • $begingroup$
            Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
            $endgroup$
            – Dom Miketa
            Dec 21 '18 at 15:44
















          $begingroup$
          Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
          $endgroup$
          – Dom Miketa
          Dec 21 '18 at 15:44




          $begingroup$
          Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up.
          $endgroup$
          – Dom Miketa
          Dec 21 '18 at 15:44


















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