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[1]:=
Clear[x,y];
{0^x,0.0^x,0.0*x*y}

Out[2]=
{0^x, 0.x, 0. x y}

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

In[3]:=
FullSimplify[ 0.0*x, -Infinity < x < Infinity ]

Out[3]=
0. x

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

In[4]:=
FullSimplify[ {0^x,0.0^x}, -Infinity < x < 0 ]

Out[4]=
{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[5]:=
FullSimplify[ 0.0^x, 0 < x < Infinity]

Out[5]=
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[6]:=
{x^0.0,x^0,0*x*y}

Out[6]=
{1.,1,0}

-----
Ted Ersek

```

• Prev by Date: Re: Eliminating Annoying Minus Signs
• Next by Date: Mathematica 5.2: The 64-bit and multicore release Dear Mathematica User, Mathematica 5.2--the 64-bit computing and multicore release--is now available! Mathematica 5.2 brings 64-bit technology to all supported platforms--an industry first. In addition, 5.2 enables threading of numerical linear algebra over multiple CPUs or multicore computers, making Mathematica an ideal environment for large computations and simulations. We know you will also appreciate this version's many other improvements. Upgrading will get you: * 64-bit-enhanced arbitrary-precision numerics * Vector-based performance enhancements * Automatic binary installation selection * Bundled notebook indexing for desktop search * SSH support for secure remote kernels * vCard and RSS import/export * New algorithms for symbolic differential equations * Enhanced performance for linear Diophantine systems * Enhanced quadratic quantifier elimination * Singular-case support for high-level special functions * Enhanced statistics charts * MathematicaMark 5.2 benchmark now covering grids and clusters See examples, explanations, and details at: http://www.wolfram.com/mathematica/newin52 As a special offer, you can save 50% on your upgrade by ordering Premier Service (http://www.wolfram.com/products/service) at the same time. Upgrade now at http://store.wolfram.com/upgrade or contact Customer Service using the information that follows this message. Use our download option and you could be up and running within an hour. Enjoy Mathematica 5.2! Sincerely, The Mathematica Product Team Wolfram Research +++++++++++++++++++++++++++++++++++++++++++++ Wolfram Research Customer Service In the U.S. and Canada: Call us at +1-800-WOLFRAM (965-3726) or send email to orders@wolfram.com In the UK and Ireland: Call us at +44-(0)1993-883400 or send email to orders@wolfram.co.uk Elsewhere, please contact your local reseller listed at: http://www.wolfram.com/international +++++++++++++++++++++++++++++++++++++++++++++
• Previous by thread: Re: What we get from (0.0*x), (0.0^x) and similar stuff
• Next by thread: Re: What we get from (0.0*x), (0.0^x) and similar stuff