       What we get from (0.0*x), (0.0^x) and similar stuff

• To: mathgroup at smc.vnet.net
• Subject: [mg58798] What we get from (0.0*x), (0.0^x) and similar stuff
• From: ted.ersek at tqci.net
• Date: Tue, 19 Jul 2005 04:10:06 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I think some of the code I sent in my last message on this subject was a
bad idea. My current thoughts on this subject are summarized below.
------------------------------

I like what I get from the next line. If a user wants to ignore the fact
that certain values will give (0^0) or (0*Infinity) they can add
definitions to do what they want. If a user wants (0^x) to return
If[x==0,Indeterminate,1] they can add a definition to do that.

In:=
Clear[x,y];
{0^x,0.0^x,0.0*x*y}

Out=
{0^x, 0.x, 0. x y}

------------------------------
The next line should return the approximate number 0.

In:=
FullSimplify[ 0.0*x, -Infinity < x < Infinity ]

Out=
0. x

-------------------------------
(0^-2) and (0.0^-2) return ComplexInfinity.  Shouldn't the next line
return {ComplexInfinity, ComplexInfinity}.

In:=
FullSimplify[ {0^x,0.0^x}, -Infinity < x < 0 ]

Out=
{Infinity, Indeterminate}

-------------------------------
Sqrt[0.0] and  (0.0^2.3) return the approximate number 0.  Shouldn't the
next line also return approximate zero.

In:=
FullSimplify[ 0.0^x, 0 < x < Infinity]

Out=
Indeterminate

--------------------------------
The following are automatically simplified and it seems there is nothing
you can do to prevent this simplification.  This is bad since certain
values for (x,y) give (0*Infinity) or (0^0) which are Indeterminate.  If
in a future version these simplifications are not automatic, then Simplify
and/or FullSimplify should make the simplifications below when given the
right assumptions.

In:=
{x^0.0,x^0,0*x*y}

Out=
{1.,1,0}

-----
Ted Ersek

```

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