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Re: Re: Cross results?

• To: mathgroup at smc.vnet.net
• Subject: [mg63230] Re: [mg63205] Re: [mg63201] Cross results?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 20 Dec 2005 04:19:27 -0500 (EST)
• References: <200512181234.HAA24522@smc.vnet.net> <200512191200.HAA10926@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

I now think that a more convincing explanation why 0.* x does not  
return 0. than the one I gave below (about the unknown size of x and  
the possibility that it could be infinity)  is that in an expression  
like 0.*x, where x is a symbol,  Mathematica can't even be sure the  
symbol stands for a simple number!  For example, x could stand for an  
interval and then we get things like:


0.*x /. x -> Interval[{-1, 1}]


Interval[{-2.2250738585072014*^-308,
    2.2250738585072014*^-308}]

Andrzej Kozlowski





On 19 Dec 2005, at 21:00, Andrzej Kozlowski wrote:

>
> On 18 Dec 2005, at 21:34, Virgil Stokes wrote:
>
>> I have the following
>>
>>   x=.
>>   Cross[{10 Sin[x],-10 Cos[x],2.5},{0.12 Sin[x],-0.12 Cos[x], 0.0}]
>>
>> which gives,
>>
>>   {0.3 Cos[x], 0.3 Sin[x], 0.Cos[x]Sin[x]}
>>
>> why does it not set the last term to 0.0?
>
>   It would never make sense to set 0.0 * u to 0.0, where u is a
> symbol since there is nothing known about the size of u. In general,
> u could be arbitrarily large and in fact it can even be Infinity. Of
> course for real x the value of 0. Cos[x]*Sin[x] will be approximately
> 0, but by taking x to be a purely imaginary number of huge modulus we
> can make Cos[x]*Sin[x] also have arbitrarily large modulus. In fact,
> taking x= I Infinity we get:
>
>
> 0. Sin[x]*Cos[x]/.x->I*Infinity
>
> Indeterminate expression DirectedInfinity,  encountered.
>
>
> Indeterminate
>
>
> In any case, as a rule Mathematica never replaces 0.* non numeric
> symbolic expression by 0. With numeric symbols the situation is of
> course quite different (for the obvious reasons):
>
>
> 0.*Pi
>
>
> 0.
>
> Andrzej Kozlowski
>

• References:
  • Re: Cross results?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>