       Re: Controlling the order of evaluations

• To: mathgroup at smc.vnet.net
• Subject: [mg93031] Re: Controlling the order of evaluations
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Fri, 24 Oct 2008 02:30:28 -0400 (EDT)
• References: <gdms84\$en\$1@smc.vnet.net>

```anguzman at ing.uchile.cl wrote:
> Hello:
> Several times I have faced similar problems to this one:
>
> Suppose I have a function f[x,y] well defined only in numbers, I mean,
> it drops errors if I try to evaluate symbols. You could suppose that
> is a function that include numerical integration in its definition...
>
> What I want to do is plotting several curves f[x,y1], f[x,y2],...f[x,yn]
> with x as abscissa for specific (and fixed) values of y in the same plot.
>
> So, what I always end up trying is something like:
>
>
> Plot[f[x,#]&/@{y1,y2,....,yn},{x,a,b}]
>
>
> Mathematica (5.2 Version for Windows) complains but finally interprets
> correctly what I meant and does the plot correctly (sometimes)with all
> the curves , but this errors are annoying. They are always of the form:
>
> \" bla bla.. f[x,y1] is not numerical at ....\"
>
>
>
> I would be very gratefull if somebody could explain me (or just give
> the solution to this thing) the correct order of Holds, HoldFirsts,
> HoldPatterns , Evaluate , Unevaluated etc... that make Mathematica
> happy.
> By the way, I already tried:
> Plot[Evaluate[f[x,#]&/@{y1,y2,....,yn}],{x,a,b}]
> but didn=B4t work.
>
> I=B4ll give an specific example:
>
> f[x_, y_] := NIntegrate[2^(s*x), {s, 0, y}]
>
> Plot[Evaluate[f[x, #] & /@ {2, 3, 4, 5}], {x, 0.5, 1.5}]
>
> Generates the 4 curves after giving errors like:
>
> \"NIntegrate::\"inum\" \"Integrand 2^(s*x) is not numerical at s = 1. \"
>
> So what I want to do is that the x of the Plotting evaluation enters
> f[x,y] before f even sees the x and start freaking out.
>
>
> Atte. Andres Guzman
>
> ----------------------------------------------------------------
> This message was sent using IMP, the Internet Messaging Program.
>
>
You should define your function with pattern conditions that prevent
evaluation when the argument(s) is not a number:

f[x_?NumericQ,y_?NumericQ]:= NIntegrate[2^(s*x), {s, 0, y}]

David Bailey
http://www.dbaileyconsultancy.co.uk

```

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