Re: How to evaluate parts of an expression, but not other parts?

• To: mathgroup at smc.vnet.net
• Subject: [mg122701] Re: How to evaluate parts of an expression, but not other parts?
• From: "andre.robin3" <andre.robin3 at wanadoo.fr>
• Date: Mon, 7 Nov 2011 05:50:46 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <32289202.13251.1320484280567.JavaMail.root@m06> <j95pg2\$m87\$1@smc.vnet.net>

```EvaluateAt[] is not part of Mathematica.

So far I kown it was a idea from Villegas (from Wolfram, see his
presentation
"workingwith unevaluated expression". It is not for beginners).
Ted Ersek also has developped a EvaluateAt[].

For such a problem I suggest rather to try to use Mathematica
existing functions. (there are so many !)

"David Park" <djmpark at comcast.net> a écrit dans le message de news:
j95pg2\$m87\$1 at smc.vnet.net...
> I'm sure that you will obtain some answers to do this with plain
> Mathematica, but the Presentations package does have routines that allow
> selective manipulation of expressions.
>
> Along with HoldForm your can use EvaluateAt or EvaluateAtPattern to do
> selective evaluations of held expressions. You can also use
> CreateSubexpression, OperateSubexlression and ReleaseSubexpressions to tag
> and group things together to prevent Mathematica from mixing there
> elements
> with other elements outside the subexpressions. Tagged Subexpressions also
> show the tag in a tooltip when the mouse hovers over the Subexpression. We
> also have MapLevelParts that allows an operation to be performed on
> selected
> level parts in an expression (usually a sum, product or list).
>
> So, as a simple example we could do:
>
> <<Presentations`
>
> a = 1; b = 2; c = 3; d = 4;
> HoldForm[a + b] + HoldForm[c + d]
> % // EvaluateAt[{1, 1}]
> % // EvaluateAt[{2, 1}]
> % // ReleaseHold
>
> (a+b)+(c+d)
>
> 3+(c+d)
>
> 3+7
>
> 10
>
> Using tagged Subexpressions we could do the following. We can also specify
> that a subexpression should always show parentheses.
>
> a = 1; b = 2; c = 3; d = 4;
> CreateSubexpression[HoldForm[a + b], True, tag1] +
> CreateSubexpression[HoldForm[c + d], True, tag2]
> % // OperateSubexpression[ReleaseHold, tag1]
> % // OperateSubexpression[ReleaseHold, tag2]
> % // ReleaseSubexpressions[All]
>
> (a+b)+(c+d)
>
> (3)+(c+d)
>
> (3)+(7)
>
> 10
>
> If we want to show the individual values before they are combined in a
> Subexpression we could use nested Subexpressions and the following more
> complicated construction.
>
> Clear[a, b, c, d]
> step1 = Plus @@
>   CreateSubexpression[#1, #2] &, {HoldForm /@ {a, b, c, d}, {taga,
>     tagb, tagc, tagd}}]
> a = 1; b = 2; c = 3; d = 4;
> step2 = step1 //
>   MapLevelParts[CreateSubexpression[#, tagcd] &, {{3, 4}}];
> step3 = step2 //
>  MapLevelParts[CreateSubexpression[#, tagab] &, {{1, 2}}]
> step4 = Fold[OperateSubexpression[ReleaseHold, #2][#1] &,
>  step3, {taga, tagb, tagc, tagd}]
> step5 = Fold[ReleaseSubexpressions[#2][#1] &,
>  step4, {taga, tagb, tagc, tagd}]
> FixedPoint[ReleaseSubexpressions[All], step5]
>
> (a)+(b)+(c)+(d)
>
> ((a)+(b))+((c)+(d))
>
> ((1)+(2))+((3)+(4))
>
> (3)+(7)
>
> 10
>
>
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/
>
>
> From: Julian Francis [mailto:julian.w.francis at gmail.com]
>
> Dear all,
>
> I'd like to use the TreePlot function to visualise the expression of a
> dynamic programming problem I am working on.
>
> If I have something like: ( (a+b) + (c+d )
>
> Mathematica helpfully simplifies this to: a + b + c + d
>
> But I'd prefer it to be in the original form.
>
> I can't write Hold[ ( (a+b) + (c+d) )] because I do want a,b,c & d to
> be evaluated.
>
> I want to write something like:
> Hold[ ( (Evaluate[a]+Evaluate[b]) + (Evaluate[c]+Evaluate[d]) ) ]
>
> But this just leaves the Evaluate expressions unevaluated.
>
> Any help greatly appreciated.
>
> Thanks,
> Julian.
>
>

```

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