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