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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
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