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Re: D under Sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128391] [mg128391] Re: D under Sum
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Fri, 12 Oct 2012 00:00:27 -0400 (EDT)
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  • References: <20121011060947.F240268D8@smc.vnet.net>

It is recommended that user-defined functions always start with a
lower case letter to avoid any potential naming conflicts with current
or future built-in functions.

Use UpValues

holdSum /: D[
   holdSum[expr_, iter_?VectorQ],
   x_Symbol] :=
  holdSum[D[expr, x], iter];

holdSum /: ReleaseHold[holdSum[arg__]] :=
  Sum[arg];

D[holdSum[p*i, {i, 1, n}], p]

holdSum[i, {i, 1, n}]

% // ReleaseHold

(1/2)*n*(1 + n)


Bob Hanlon


On Thu, Oct 11, 2012 at 2:09 AM, Nicolas Venuti
<nicolas at virtualdynamics.fr> wrote:
> Hello
>
> I want the derivation D to be applied under the Sum sign,
> I have a function HoldSum that do not evaluate but is similar to Sum in form
>
> In[3]:= D[HoldSum[p*i, {i, 1, n}], p]
>
> I get the output :
>
> Out[3]=i*HoldSum^(1, {0, 0, 0})[i p, {i, 1, n}]
>
> but I would want that D be applied under the Sum sign like done by hand here :
>
> In[5]:= HoldSum[D[p i, i], {i, 1, n}]
>
> Out[5]= HoldSum[p, {i, 1, n}]
>
> Obviously I want D to work for any expression containing HoldSum (even on nested HoldSum expression)
>
> Does anybody knows how to do that ?
>
> Best regards
>
> Nicolas
>



  • References:
    • D under Sum
      • From: Nicolas Venuti <nicolas@virtualdynamics.fr>
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