Date: Feb 3, 2011 5:29 AM
Author: DrMajorBob
Subject: Re: Mystifying Scoping of Piecewise Variable?
(BUG ALERT. See the last line of code.)

The function

myFunc[y_] = Piecewise[{{x^2, x < 0}, {x, x >= 0}}]

depends only on y on the left, but it depends only on x on the right.

That obviously cannot work, but how, exactly, should we expect it to fail?

If x has no value, Piecewise has no numeric value:

x=.

Piecewise[{{x^2,x<0},{x,x>=0}}]

\[Piecewise] x^2 x<0

x x>=0

0 True

so the first plot is empty.

In the second plot, x is given values across the range from -10 to +10, so

Piecewise also gets numeric values:

Table[myFunc[x], {x, -10, 10, 1}]

{100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, \

10}

hence the second plot is not empty.

That doesn't mean your definition of myFunc is suddenly a good one. It's

still completely wrong.

But it works when you're passing x to the function AND varying x at the

same time.

So this plot is empty (because x still has no value):

Plot[myFunc[x], {y, -10, 10}]

But this plot is a constant:

x = -7;

Plot[myFunc[x], {y, -10, 10}]

When passing z and varying z, we see what I'd call a bug:

z =.

Plot[myFunc[z], {z, -10, 10}]

It plots the value of myFunc[-7] from the previous plot, even though x is

not involved, and z doesn't have a value.

Bobby

On Wed, 02 Feb 2011 05:08:08 -0600, Frank Iannarilli <frankeye@cox.net>

wrote:

> Perhaps I'm tired, but this is weird:

>

> Clear[myFunc]

>

> myFunc[y_] = Piecewise[{{x^2, x < 0}, {x, x >= 0}}]

> (Same behavior below for either Set(=) or SetDelayed(:=) )

>

> Plot[myFunc[y], {y, -10, 10}]

> (returns empty plot)

>

> Plot[myFunc[x], {x, -10, 10}]

> (returns "expected" piecewise function plot)

>

> What is the scoping of the Piecewise variable, in this case "x"?

>

> How can one write a Module that creates and returns a Piecewise

> function? The scope of its argument is unclear to me.

>

> Thanks

>

--

DrMajorBob@yahoo.com