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

• To: mathgroup at smc.vnet.net
• Subject: [mg69189] RE: [mg69165] Unexpected "Invalid comparison" error when plotting function defined with a Condition pattern
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 1 Sep 2006 06:41:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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