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Re: Evaluate[] not needed in With[]
 To: mathgroup at smc.vnet.net
 Subject: [mg62974] Re: Evaluate[] not needed in With[]
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Fri, 9 Dec 2005 06:39:56 0500 (EST)
 Organization: Uni Leipzig
 References: <dnbnav$5ti$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
With[] does a (clever) ReplaceAll[] of the constants
you give, in its body before the body is evaluated.
This means that the argument of ParametricPlot[] in your
example is replaced by the value of hlines ..
and so you don't need a Evaluate[].
Regards
Jens
"Steven T. Hatton" <hattons at globalsymmetry.com>
schrieb im Newsbeitrag
news:dnbnav$5ti$1 at smc.vnet.net...
I started looking at Dr. Maeder's _Programming in
Mathematica_, and was
 doing quite well understanding everything until
I got to the first example
 in the first section of the first chapter. He
gives an example of using
 ParametricPlot and tells us "Because
ParametricPlot evaluates its arguments
 in a nonstandard way, we need to force
evaluation of the variable hline by
 wrapping in into Evaluate[]." He later tells me
I don't need to do that
 for a "constant" in a With[] expression. The
following is a cobbled
 together example showing both forms:

 Clear[z, x, y, cz, hlines, vlines];
 z = x + y I;
 cz = {Re[z], Im[z]};
 hg = With[{hlines = Table[N[cz], {y, 1, 1,
2/8}]},
 ParametricPlot[hlines, {x, Pi/2, Pi/2},
 DisplayFunction > Identity][[1]]
 ];
 vlines = Table[N[cz], {x, Pi/2, Pi/2, Pi/12}];
 vg = ParametricPlot[Evaluate[vlines], {y, 1,
1},
 DisplayFunction > Identity][[1]];
 Show[Graphics[Join[hg, vg], AspectRatio >
Automatic, Axes > True]]

 I can read the words, and follow the
instructions, but I still don't
 understand _why_ the version in the With[]
expression doesn't need the
 Evaluate[]. Is there a way to _explain_ this
behavior, or do I simply need
 to memorize the rule by rote?
 
 The Mathematica Wiki:
http://www.mathematicausers.org/
 Math for Comp Sci
http://www.ifi.unizh.ch/math/bmwcs/master.html
 Math for the WWW: http://www.w3.org/Math/

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