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Re: Fine control of evaluation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126452] Re: Fine control of evaluation
  • From: A Retey <awnl at gmx-topmail.de>
  • Date: Sat, 12 May 2012 04:51:03 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <joi3pj$n55$1@smc.vnet.net>

Hi,

> Hello, I am struggling with evaluation control and was hoping someone might
> point me in the right direction. I vaguely remember seeing something in the
> manual or the tutorials addressing this issue, but I can't find the section
> I saw it in.

the general documentation is this (which I consider a must-read):

tutorial/Evaluation

your particular problem is documented here:

ref/Evaluate (possible issues section)

> How does one get fine control over things wrapped in Hold and HoldForm. Say
> I have some functions
>
> func1[x_]:= f[x];
> func2[x_] := g[x];
> step1 = HoldForm[ func1[x]+ func2[x] ];
>
> Now say I want the statements wrapped in HoldForm,  func1[x]+ func2[x]  to
> evaluate to f[x]+ func2[x]
>
> I thought naturally it would be something like
>
> step2 = HoldForm[ Evaluate[func1[x]]+ func2[x] ] ;
>
>   But then HoldForm seems a bit overzealous about it's task, and outputs
> Evaluate[func1[x]]+ func2[x]---it leaves Evaluate unevaluated.  (I tried
> wrapping it func1[x] in ReleaseHold to no avail.)

from the documentation of Evaluate: "Evaluate works only on the first 
level, directly inside a held function:"

> The above is just pseudocode, Maybe there is some specifics about what I
> was actually doing that was causing the unintuitive behavior (i.e. HoldForm
> holding Evaluate, instead of, well, evaluating.) What I was doing was more
> along these lines:
> ----------------
> ubounds= {u,0, pi};
> vbounds={v,0,2pi};
> t[dir_]:= D[s[u,v],dir_];    (*where dir_ is going to be either u or v*)
>
> (*here is the difficult part:*)
> formattedOutput= Integrate[HoldForm[t[u]] , ubounds, vbounds ]
> //TraditionalForm;
> ----------------
> The issue is that I want the t[u] wrapped in the HoldForm to evaluate to
> D[s[u,v],dir_], and hold that. If I wrap it in Evaluate, HoldForm holds
> Evaluate (puzzling), and tries to integrate Evaluate as if it is the
> integrand. I've tried all kinds of permutations of HoldForm, Defer,
> ReleaseHold, Evaluate, and I haven't had anything to work.

What you want to do is to insert evaluated subexpression into a held 
expressions. There are many ways to achieve this, but the most common is 
to use With:

With[{ubounds = ubounds, vbounds = vbounds, expr = t[u]},
  HoldForm[Integrate[expr, ubounds, vbounds]]
  ]

(note that I've wrapped everythin with HoldForm and also inserted 
ubounds and vbounds. Without that Integrate would try to integrate 
HoldForm, which it can't do and I assume you don't even actually want it 
to try...)

hth,

albert




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