Re: Unexpected "Invalid comparison" error when plotting function defined with a Condition pattern

• To: mathgroup at smc.vnet.net
• Subject: [mg69266] Re: Unexpected "Invalid comparison" error when plotting function defined with a Condition pattern
• From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
• Date: Mon, 4 Sep 2006 04:47:06 -0400 (EDT)
• References: <ed93pr\$t4f\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi David, thanks for your reply. For now I'm using a workaround like
one of yours below.

David Park wrote:
> Andrew,
>
> I do not know precisely why you obtain those error messages. It seems to be
> a combination of selecting values in Plot, the use of Abs and the form of
> the definition of g. But I think there are ways around it.
>
> The following give error messages.
>
> g[x_ /; 0 < x] = x;
> Plot[Abs[g[10^y]], {y, 1, 2}];
>
> Clear[g]
> g[x_ ] = If[x > 0, x, 0];
> Plot[Abs[g[10^y]], {y, 1, 2}];
>
> Clear[g]
> g[x_] := Piecewise[{{0, x <= 0}, {x, x > 0} }]
> Plot[Abs[g[10^y]], {y, 1, 2}];
>
> The following do not give error messages.
>
> Clear[g]
> g[x_ /; 0 < x] = x;
> Plot[Sqrt[g[10^y]^2], {y, 1, 2}];
>
> Clear[g]
> g[x_ /; 0 < x] = x;
> Plot[Abs[g[10^y]] // ComplexExpand // Evaluate, {y, 1, 2}];
>
> Clear[g]
> g[x_ /; 0 < x] = x;
> data = Table[{y, Abs[g[10^y]]}, {y, 1, 2, 0.025}];
> ListPlot[data, PlotJoined -> True];
>
> Clear[g]
> g[x_?Positive] = x;
> Plot[Abs[g[10^y]], {y, 1, 2}];
>
> Clear[g]
> g[x_] := Piecewise[{{0, x <= 0}, {x, x > 0} }]
> Plot[Abs[g[10^y]] // ComplexExpand // Evaluate, {y, 1, 2}];
>
> So try using ComplexExpand on your more complicated expression.
>
> David Park
>
>
>
> From: Andrew Moylan [mailto:andrew.j.moylan at gmail.com]
To: mathgroup at smc.vnet.net
>
> Hi,
>
> Please consider the following simple function, defined for positive x
> using a Condition pattern:
>
>   g[x_ /; 0 < x] = x;
>
> When I try to plot this function in the following way:
>
>   Plot[Abs[g[10^y]], {y, 1, 2}];
>
> I unexpectedly receive some "Less::nord : Invalid comparison with 10. +
> 0. I attempted" errors. Can anyone explain why this is, and how I
> should best prevent it?
>
> Relevant note:
> Both of the following different plots of g succeed with no errors:
>   Plot[Abs[g[y]], {y, 1, 2}];
>   Plot[g[10^y], {y, 1, 2}];
>
> Irrelevant note:
> In my actual application, the function g is more complicated and is
> complex-valued (hence my use of Abs); but the error is reproducable
> with the very simple real-valued function g as defined above.
>
> Thanks for any insight you might be able to give me on this.
>
> Cheers,
>
> Andrew

```

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