
Re: Mystifying Scoping of Piecewise Variable?
Posted:
Feb 3, 2011 5:29 AM


(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

