RE: With[{software=Mathematica}, Frustration]

*To*: mathgroup at smc.vnet.net*Subject*: [mg24317] RE: [mg24308] With[{software=Mathematica}, Frustration]*From*: Wolf Hartmut <hwolf at debis.com>*Date*: Sun, 9 Jul 2000 04:52:29 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

> -----Original Message----- > From: AES [SMTP:siegman at stanford.edu] To: mathgroup at smc.vnet.net > Sent: Friday, July 07, 2000 6:12 AM > To: mathgroup at smc.vnet.net > Subject: [mg24308] With[{software=Mathematica}, Frustration] > > [Hartmut Wolf] The Mathematica Book of course is the central reference. For programming (and deaper understanding) I recommend Roman Maeder's "Programming in Mathematica" > Pages 359-360 of The Mathematica Book says (admittedly, taken a little > out of context), > > "You can think of With as a generalization of the /. operator. . ." > [Hartmut Wolf] This is exactly that kind of diction in the book I dislike. However "you can think of..." should have warned you to *respect* the context! > and > > " With[{x=x0}, body] works essentially like body /. x->x0 . . . " [Hartmut Wolf] Same here with "essentially" > > Great, looks neat, let's try it for evaluating expressions without > permanently setting the variables in them: > > In[1]:= c = a b > > Out[1]= a b > > In[2]:= c > > Out[2]= a b > > In[10]:= c /. {a -> 2, b -> 3} > > Out[10]= 6 > > In[3]:= With[{a = 2, b = 3}, c] > > Out[3]= a b > > *Not* what I was hoping for . . . > [Hartmut Wolf] In[2]:= With[{a = 2, b = 3}, Evaluate[c]] Out[2]= 6 will do what you want! Why? What was meant saying by the quotations is that With gives a *textual* substitution for the given variables occuring in the *unevaluated* body. Here within the unevaluated body (= literal c) a and b are not visible; you make them so, if you force the evaluation of c before the substitution is tried. A warning added: the substitution by With works not the same way as by ReplaceAll, With respects the scoping of Module, Function, and With (but not of Block), ReplaceAll doesn't. And for ReplaceAll body is evaluated before substitution. Admittedly you have to try to understand these points when proceeding along your learning curve, but it's worth it! After some time you'll agree to With[{software=Mathematica}, Exp[much joy!]]