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Re: Re: Re: More /.{I->-1} craziness

• To: mathgroup at smc.vnet.net
• Subject: [mg106273] Re: [mg106247] Re: [mg106203] Re: More /.{I->-1} craziness
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 7 Jan 2010 02:29:00 -0500 (EST)
• References: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

Some good points, David. When help says "You can enter a complex number in  
the form x + I y", it is seriously misleading, without the qualification  
you added below.

x + I y is NOT a number (of any kind) when a and b are undefined, and  
neither is Complex[x, y]:

NumericQ@Complex[x, y]

False

If they ARE defined, the result isn't necessarily complex (or even  
sensible):

Complex[0, I]
N@%

Complex[0, I]

Complex[0., 0. + 1. I]

What the heck is that?

Complex[0.`, 0.` + 1.` I] // Simplify

Complex[0., 0. + 1. I]

Bobby

On Wed, 06 Jan 2010 04:59:15 -0600, David Park <djmpark at comcast.net> wrote:

> I don't think that it is correct to expect that a mathematical object  
> has a
> Head. Mathematica only gives us various representations of objects and
> different representations have different Heads. Thus
>
> 3 + 4 I, ComplexPolar[5, ArcTan[4/3]] (in Presentations), 5 E^(I
> ArcTan[4/3]), Complex[3,4]
>
> all represent the same mathematical object but all have different Heads.
> (Plus, ComplexPolar, Times, Complex).
>
> What might be confusing is that Complex is a NUMBER and not a symbolic
> expression. WRI could improve the Help for Complex by changing the first
> note to:
>
> "You can enter a complex number in the form x + I y, where x and y are
> Integer, Real, Rational or Complex numbers."
>
> "Expressions such as Complex[a,b] with Symbols are not meaningful and are
> left unevaluated. Symbolic complex expressions contain Complex numbers  
> only
> as subparts."
>
> And then, among the first examples, they might show:
>
> "Complex expressions may contain Complex numbers as subparts and can be
> manipulated with routines such as Conjugate and ComplexExpand."
>
> x + I y
> % // FullForm
> ComplexExpand[Conjugate[%]]
> % // FullForm
>
> x + I y
> Plus[x,Times[Complex[0,1],y]]
> x - I y
> Plus[x,Times[Complex[0,-1],y]]
>
> Very few users would use Complex numbers in isolation without combining  
> them
> in symbolic expressions. So why not stand users up and point them in the
> right direction instead of just saying that the Help is 'formally  
> correct'?
>
> For those who use Help, of course.
>
>
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/
>
>
> From: Richard Fateman [mailto:fateman at cs.berkeley.edu]
>
> [SNIP]
>
> Are you describing Mathematica here?   It seems to me that it is an
> exception that Head[a+b*I] is Plus, but Head[3+4I] is Complex.
>
> [SNIP]
>
> You assume that people read the documentation. This is provably false.
>
> RJF
>
>
>


-- 
DrMajorBob at yahoo.com