About the possibility that the expressions being close to zero but not exactly the same, that does not matter much. For example
expr1*pwdelta(x-a)
if at(abs(expr1), x=a) < 10^-10 then changing expr1*pwdelta(x-a) -> 0 will not have much effect on the answer most of the time.
if at(abs(expr1), x=a) = 0 then changing expr1*pwdelta(x-a) -> 0 will have no effect on the answer when using exact arithmetic.
(x-0.24) ^-100 * pwdelta(x-0.2400000000000001)
In inexact cases I suppose it is safer to keep it as it is. I don't know how to detect the exact cases so there I also leave it
alone.
Rich
----- Original Message -----
From: "Richard Hennessy" <rvh2007 at comcast.net>
To: "Richard Fateman" <fateman at cs.berkeley.edu>
Cc: "Richard Fateman" <fateman at EECS.Berkeley.EDU>; <maxima at math.utexas.edu>; "Barton Willis" <willisb at unk.edu>
Sent: Sunday, December 21, 2008 11:00 AM
Subject: Re: [Maxima] pw.mac version 2.3.1
I changed my mind which is why I retracted this comment, it's not needed to know the numerical value here. So I do not simplify
this to 0.
Rich
----- Original Message -----
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Richard Fateman" <fateman at EECS.Berkeley.EDU>; "Barton Willis" <willisb at unk.edu>; <maxima at math.utexas.edu>
Sent: Sunday, December 21, 2008 9:57 AM
Subject: Re: [Maxima] pw.mac version 2.3.1
Richard Hennessy wrote:
> "Numerical indecision". I want x*pwdelta(x) to return 0, that would be my decision.
>
> Rich
>
>
That is, x*pwdelta(y) --> when x=y. The decision, is x=y may not be
obvious in some instances. For example, x and y may be complicated
expressions or may be numerical values that are very slightly
different. (In Mathematica, there is a notion of accuracy associated
with software floats -- two numbers may be deemed equal if their
uncertainty is sufficiently large, even if they are not identical).
Rjf
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