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MathGroup Archive 1999

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Re: Question about evaluation with Sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19607] Re: [mg19587] Question about evaluation with Sum
  • From: "Tomas Garza" <tgarza at mail.internet.com.mx>
  • Date: Sat, 4 Sep 1999 21:09:14 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

CORNIL Jack Michel [jmcornil at club-internet.fr] wrote:I have a big problem of
evaluation with the function Sum.

> I have a big problem of evaluation with the function Sum.
> With the very simple following example,
>
>    p=k
>
>    Sum[p,{k, 1, n}]
>
>      p k
>
>    Sum[Evaluate[p], {k, 1, n}]
>
>      1
>      - n (1+n)
>      2
>
>    Sum[p,{k, 1, 5}]
>
>      15
>
> how can I explain my students that
>
>    in the first case p is left unevaluate and it needs Evaluate,
>
>    in the last case p is evaluate correctly  ?
>
> I do not understand how the "Attributes" of Sum can explain this.

Use Trace[expr] to generate a list of all expressions used in the evaluation
of expr.

In[1]:=
Sum[p, {k, 1, n}] // Trace

will show that p is taken as a constant, so that the sum equals p n. Only
after the sum is evaluated it will be replaced by p = k. Hence k n. However,

In[2]:=
Sum[Evaluate[p], {k, 1, n}] // Trace

will show that p is first replaced by its preassigned value k, and only then
the sum is evaluated.

Tomas Garza
Mexico City



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