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Re: Re: Re: Bug Report - Two numerical values for a same variable
*To*: mathgroup at smc.vnet.net
*Subject*: [mg54355] Re: [mg54300] Re: [mg54271] Re: Bug Report - Two numerical values for a same variable
*From*: DrBob <drbob at bigfoot.com>
*Date*: Sat, 19 Feb 2005 02:31:56 -0500 (EST)
*References*: <00ed01c512b0$2f242850$6400a8c0@Main> <curpbn$r28$1@smc.vnet.net> <200502150438.XAA29728@smc.vnet.net> <200502161936.OAA19223@smc.vnet.net> <d3d3aacf7f18939828890ce85676bd26@mimuw.edu.pl> <opsmcn3rqciz9bcq@monster> <276a5ca71b030c5949d6abad4b33c5d7@mimuw.edu.pl>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
Right. The arguments of Complex have to be explicitly real constants, and the arguments of Rational must be explicitly Integer constants. By "explicitly" I mean the same as Help for NumberQ means by "manifestly".
But none of that is documented, so let's all try to be patient, please, when anyone seeks clarification.
Bobby
On Thu, 17 Feb 2005 23:01:23 +0100, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> *This message was transferred with a trial version of CommuniGate(tm) Pro*
> It has occured to me that it may be a good idea to summarize what (in
> my opinion) is the situation concering this issue of Complex, Rational,
> Atoms etc.
>
> The following are the two basic Matheamtica principles.
>
> 1. All numbers, that is all expressions for which NumberQ returns True
> are atoms:
>
> In[1]:=
> NumberQ[2/3]
> AtomQ[2/3]
> AtomQ[2/3]
> NumberQ[I]
> NumberQ[2+I]
> AtomQ[2+I]
>
>
> Out[1]=
> True
>
> Out[2]=
> True
>
> Out[3]=
> True
>
> Out[4]=
> True
>
> Out[5]=
> True
>
> Out[6]=
> True
>
>
>
> 2. Numeric quantities that are not numbers (NumberQ returns False) are
> Atoms only if they have Head Symbol:
>
> In[7]:=
> NumberQ[Pi+I]
> AtomQ[Pi+I]
>
> Out[7]=
> False
>
> Out[8]=
> False
>
>
> However
>
> In[9]:=
> NumberQ[Pi]
>
> Out[9]=
> False
>
> In[10]:=
> AtomQ[Pi]
>
> Out[10]=
> True
>
> In[11]:=
> Head[Pi]
>
> Out[11]=
> Symbol
>
>
> Expressions of the form Complex[a,b], Rational[a,b] are only defined
> where a and b are (certain) numbers. In particular they are not defined
> for numeric quantities whcih are not numbers, e.g. Complex[Pi,E] and
> Rational[Pi,Pi] are just undefined expressions.
>
> Andrzej Kozlowski
>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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